Moscow State University of Printing. Viscosity of liquid aggregation-stable disperse systems

Classification of raw materials	Product Name	Typical rheological properties
Hard Brittle	Chocolate, cookies, crackers, waffles, extruded products, caramel, crackers, dryers, pasta, bread	Tensile strength, elastic modulus
Elastic-plastic	Bread, wheat dough, pasta dough, marmalade, marshmallows, marshmallows, candies, hard fat, gingerbread, gluten, gelatin	Tensile strength, modulus of elasticity, ultimate shear stress, adhesion
Viscous-plastic	Rye dough, shortbread dough, sour cream, mayonnaise, gelling products, semi-finished confectionery products	Viscosity, adhesion, ultimate shear stress (plastic strength)
Liquid-like	Yeast suspension, salt solution, sugar solution, melted margarine, whole milk, whey	Viscosity, surface tension coefficient
Powdery	Flour, granulated sugar, starch, table salt	Angle of repose, mechanical characteristics during pressing

The main rheological properties include elasticity, plasticity, viscosity and strength.

This means that the same material, depending on its state and loading conditions, may exhibit more or less different rheological properties. For example, a viscous-plastic material such as pasta dough, when subjected to instantaneous load, generally behaves like an elastic body, and plastic deformation and viscous flow are almost absent. Under other loading conditions, plastic and viscous properties are more important. Therefore, first of all, it is necessary to find out which properties of the material under study under given conditions are the main, determining ones.

Let us consider the basic physical, mechanical and mathematical concepts used in rheology.

Types of deformations. When an external load is applied to a material, it is subjected to an impact that results in a change in its size and shape. These changes in the material are called deformation. Depending on the application of load, deformations are fundamentally divided into two types: the first - volumetric (linear) tension-compression deformations and the second - shear deformations. With the first, only the volume (linear size) of the material changes, and its shape does not undergo noticeable changes. During shear deformation, the shape of the material changes, but its volume remains the same. There is a close relationship between these types of deformations, determined by the Punch ratio. The ability to deform under the influence of external forces is the main property of the materials of all real bodies.

Deformation- this is a change in the shape or linear dimensions of a body under the influence of external forces, with changes in humidity, temperature, etc., in which particles or molecules are displaced relative to each other without violating the continuity of the body.

Depending on the type of body deformation, they are divided into volumetric, linear (normal) and shear. Changes in the linear dimensions of a body are usually expressed in relative units of deformation.

The relative deformation of a body under normal tension-compression, denoted by , represents the ratio of the absolute deformation to the initial dimensions of the body, determined by the formula: . (2.1)

Volumetric relative deformation of the body is determined by the formula

where , , are the relative deformations of the body along the axes x, y, z.

Relative shear strain represents the ratio of the absolute value of the shear displacement of a layer under the influence of tangential forces to its thickness h, determined by the formula

Deformations are divided into elastic, i.e. disappearing after removing the load, and residual, irreversible, not disappearing after removing the load. Residual deformations that are not accompanied by destruction of the material are called plastic, and the materials themselves are called plastic.

Strain rate, , s -1 , this is the change in deformation over time, determined by the formula

in tension-compression: ;

when shifting: . (2.4)

Voltage, , Pa, is a measure of internal forces, N, arising in the body under the influence of external influences per unit area, m, normal to the vector of force application, determined by the formula

normal voltage;

shear stress (shear). (2.5)

Elasticity- the ability of a body after deformation to completely restore its original shape, i.e. the work of deformation is equal to the work of restoration. The elasticity of bodies is characterized by elastic moduli:

in tension-compression - modulus of elasticity of the first kind, Pa;

in shear - modulus of elasticity of the second kind, Pa.

The magnitudes of stresses and strains are related by Hooke’s law and have the form of equations:

Adhesion, Pa, is the adhesion of dissimilar solid or liquid bodies touching their surfaces. The adhesion strength of bodies is determined by tearing off, introducing the indicator as stickiness , N/m, which is calculated by the formula: , (2.7)

where is the pull-out force, N; - geometric area of ​​the plate, m.

The separation of materials from one another can be of three types (Fig. 2.1):

Rice. 2.1. Types of separation

External friction- interaction between bodies at the boundary of their contact, preventing their relative movement along the contact surface. It depends on the normal force and stickiness, and is calculated by the formula: , (2.8),

Where R tr- external friction, N; - true coefficient of external friction;

Normal force of the shear surface (contact force), N.

External friction coefficient f. For food materials, depending on the rheological properties, the state of the friction surfaces and the sliding speed, the coefficient of external friction f determined in various ways. The classic type of device for measuring the force of external friction is a pair of bodies in contact with flat surfaces, the area of ​​which can be from fractions of square millimeters to tens of square centimeters. In this case, one of the bodies is displaced relative to the other. The force applied to displace (friction) one body relative to another is measured by strain gauges, dynamometers or some other sensors.

Viscosity, Pa·s, is the ability of a body to resist the relative displacement of its layers. Viscous flow is realized in truly viscous, Newtian fluids at any, no matter how small, shear stresses, and is described by Newton’s equation: . (2.9)

During the flow of non-Newtian (anomalously viscous) fluids, viscosity does not remain a constant value; it depends on the shear stress and velocity gradient. In this case, the concept of “effective viscosity” is used, Pa s, which is calculated using the formula: (2.10)

Plastic, Pa, is the ability of a body to be irreversibly deformed under the influence of external forces without breaking its continuity. Plastic flow begins at a stress value equal to the yield stress.

5.Technological processes related to the rheology of food masses. Many technological processes in the food industry are associated with mechanical impact on the product, which is in a viscoplastic state. In the baking industry, this means kneading dough, dividing dough, and molding dough pieces. In the production of confectionery products, such processes include mixing, plasticizing the mass and molding by casting, pressing, cutting, etc. Interoperational transportation of semi-finished products through pipes and on various conveyors is also of great importance. In all of these cases, the choice of technological equipment and the determination of its operating mode are determined by the physical-mechanical and, first of all, rheological properties of processed or transported food masses, semi-finished products and finished products. When creating perfect technological processes that make it possible to obtain a high-quality finished product, it is necessary to study a whole range of physical and mechanical properties in almost every specific case. These properties characterize the behavior of food masses under the influence of mechanical loads from the working parts of machines. Objective assessment of the quality of food products and semi-finished products is of great importance in the food industry. In this regard, the creation and application of methods and instruments for objective quality control not only provides a replacement for organoleptic control, but also creates the prerequisites for the development of automatic control systems for technological processes in food production. Currently, the food industry has a fairly large and diverse arsenal of technical means for determining and studying the physical and mechanical properties of food materials at various stages of preparation: from raw materials to the finished product. To study these properties, methods of physical and chemical mechanics of food products are used.

6. Classification of real bodies. The belonging of a real body to one or another type of “ideal” rheological body, identified on the basis of preliminary experiments, allows one to correctly select a device for research and determine the properties to be studied.

Shear properties represent the main group of properties that are widely used both for calculating various motion processes in the working parts of machines, and for assessing the quality of food products. In this regard, methods for classifying food and other rheological bodies according to shear characteristics have become most widespread.

Classification of rheological bodies proposed by Gorbatov A.V. (Table 1.2), according to the ratio of the ultimate shear stress to their density and the acceleration of free fall [ θ 0 /(ρ ∙g)], which is a measure of a substance's ability to maintain its shape, is presented below.

Table 1.2 Classification of bodies by physical parameters:

B.A. Nikolaev proposed a generalized classification

(from solid to truly viscous state) according to the magnitude of mechanical properties: moduli of elasticity, viscosity, etc. The first group includes solid and solid-like bodies (solid fat, whole meat tissues, crackers, cookies, etc.), the second group includes solid - liquid (minced meat, cottage cheese, jellies, flour dough, etc.), to the third - liquid-like and liquid (melted fat, broths, milk, honey, water, etc.).

It is of interest to classify real bodies using the Herschel–Bulkley power equation: , (1.7) where: is a coefficient proportional to viscosity at a velocity gradient equal to unity, Pa s n; n– current index.

After some transformations we obtain the following expression:

, (1.8), where is the effective viscosity at a velocity gradient equal to unity, Pa s;

– dimensionless velocity gradient;

m– rate of structure destruction, flow index.

With this classification method, relationships are constructed between shear stress and velocity gradient (flow curves) and between effective viscosity and shear velocity gradient. Based on the nature of the resulting curves, six types of bodies are distinguished:

1. ideal rigid body Euclidean
2. Hooke's elastic body;
3. Saint-Venant's plastic body;
4. rheological body
5. true viscous Newtonian body;
6. ideal liquid (Pascal).

The systems listed above do not change their properties over time.

7. Dispersed systems. Classical objects of engineering physical and chemical mechanics are dispersed systems consisting of two or more phases. In them, the dispersion medium is a continuous phase, the dispersion phase is a crushed phase consisting of particles that are not in contact with each other. In this case, a phase is understood as a set of homogeneous parts of the system, limited from other parts by physical interfaces. A simplified classification of dispersed food products, which does not take into account the dispersion and type of contacts between phases, is given in Table 1 .

Table 1

Dispersed medium	Dispersed phase	Examples of systems
gas	+solid (aerosols) +liquid (aerosols mists) +gas (atmosphere)	Smoking smoke, dust Dispersion of blood, milk Atmosphere of the earth
liquid	+solid (suspension) +liquid (emulsion) +gas (foam)	Broth, minced sausage, pate Blood, fat in water, milk Cream, whipped egg white
Solid	+solid (solid suspension-alloy) +liquid (capillary systems, solid emulsion) +gas (porous bodies, solid foams)	Frozen muscle tissue Frozen butter, native muscle tissue, liquid in porous bodies Bone, cheese, isolated material, whipped and coagulated melange

When determining the rheological behavior of a product, the data given in the table allows us to classify it into one group or another: granular, liquid and solid (depending on the concentration of the dispersed phase) or solid. In rheology, liquid-like products are usually called sols, and solid-like products are called gels. The products in Table 1 are classified into one system or another according to the most important characteristics. For example, minced sausage after cutting is a suspension saturated with air bubbles, that is, a three-phase system. The same product (butter), depending on the temperature, can be classified into different systems. Mechanical action (cutting, beating, stirring) can also cause a transition from one type of dispersion to another.

Rice. 2.2. Dependence of viscosity on shear stress in laminar (a) and turbulent (b) flow regimes for Newtonian liquids and aggregation-stable dispersed systems

1. Rheological properties of disperse systems

1.1. Basic Concepts

Rheology is the science of deformation and flow of materials.

Rheological properties include viscosity and fluidity.

Viscosity () - internal friction between layers of a given substance (liquid or gas) moving relative to each other.

It is caused by the interaction between molecules. In gases, the internal thorn is of a kinetic nature, therefore, as T increases, the force of the thorn increases.

In liquids and solids, internal friction is of an energetic nature, therefore, as the temperature increases, the thorn force decreases.

Fluidity is the opposite property of viscosity - release">Structure- a spatial frame consisting of dispersed phase particles and filled with a dispersion medium.

In cohesively dispersed systems, particles of the dispersed phase are not able to move relative to each other. They have certain mechanical properties: elasticity, viscosity, plasticity. The set of mechanical properties determined by the structure is called structural-mechanical.

Structured systems are capable of deformation.

Deformation is a relative displacement of points of a system at which its continuity is not violated.

There are deformations elastic (reversible) and residuals.

With elastic deformation, the structure of the body is completely restored after the load is removed.

Permanent deformation is irreversible.

Residual deformation in which fracture does not occur is called plastic.

Among elastic deformations, volumetric deformations are distinguished: stretching, compression of the body, they are caused by normal shear stress.

Shear deformation- torsional deformation, occurs under the influence of tangential, tangential shear stress, is determined by the relative shear under the influence of shear stress (Fig. 1.1
).

Liquids and gases deform under minimal loads and flow under the influence of pressure differences. But liquids practically do not compress during flow, their densities are practically constant.

Properties such as elasticity, plasticity, viscosity and strength appear during shear deformation, which is considered the most important in real research.

The dependence of rheological properties on various factors is expressed graphically in the form of rheological curves (flow curves).

A liquid is characterized by two flows:

a) laminar in the form of parallel non-mixing layers

b) turbulent.

1.2. Rheological models

In rheology, the mechanical properties of materials are represented in the form of rheological models, which are based on three laws connecting shear stress and deformation. They correspond to 3 ideal models of idealized materials that meet properties such as elasticity, plasticity, viscosity:

1) Hooke's ideal elastic body

It can be represented as a spring (Fig. 1.2)

formula" src="http://hi-edu.ru/e-books/xbook839/files/f350.gif" border="0" align="absmiddle" alt=".

selection">Fig. 1.3 .

2) Newton's ideal viscous body is a piston with holes placed in a cylinder with liquid (Fig. 1.4 ).

An ideal viscous fluid flows in accordance with Newton's law.

Newtonian fluids are systems whose flow obeys Newton's law:

example ">P - shear stress causing fluid flow; dU/dx - velocity gradient, i.e. the difference in the speed of laminar flow of two layers of fluid spaced from each other at a distance x, related to this distance, determined"> viscosity coefficient, which for brevity is called viscosity (dynamic viscosity). The value is determined by kinematic viscosity, where defined by Shear stress during laminar flow of a liquid with a viscosity of the determined ">Physical meaning of the viscosity coefficient - viscosity is equal to the friction force between layers of liquid with an area of ​​contacting layers of liquid equal to 1 formula" src="http://hi-edu.ru/e-books /xbook839/files/f353.gif" border="0" align="absmiddle" alt=".gif" border="0" align="absmiddle" alt=".gif" border="0" align="absmiddle" alt="..gif" border="0" align="absmiddle" alt=".

Let's consider the concept velocity gradient. Let us imagine a liquid flowing laminarly under the influence of gravity in a plane-parallel flow through a cylindrical capillary with a speed U. However, not all liquid flows at the same speed, the flow speed is maximum in the center of the capillary, and liquid flows towards the capillary walls flow at a lower speed due to adhesion to the walls of the vessel.

The speed of movement of the layer directly adjacent to the wall (Prandtl layer) due to adhesion forces is zero, while the central layer of liquid moves at maximum speed..gif" border="0" align="absmiddle" alt="the gradient is equal to the selection">Fig. 1.5 ).

If the speed of movement is denoted by dy/dt, and y and t are independent variables, we change the order of differentiation: formula" src="http://hi-edu.ru/e-books/xbook839/files/f363.gif" border=" 0" align="absmiddle" alt="

According to the flow equation, for Newtonian fluids there is a linear dependence of dU/dx on P. Thus, the viscosity of Newtonian fluids does not depend on shear stress; it is equal to the cotangent of the angle of inclination of the straight lines in the indicated coordinates (the graphical meaning of the viscosity coefficient)..gif" border="0" align="absmiddle" alt="= f(p) or dU/dx = f(p) .

According to (1.2), for Newtonian liquids a linear dependence dU/dx is observed (Fig. 1.6
).

This means that the viscosity of Newtonian fluids does not depend on shear stress, and is equal to the cotangent of the angle of inclination (highlight">Fig. 1.6; for laminar flow, the formula" src="http://hi-edu.ru/e-books/xbook839 /files/f365.gif" border="0" align="absmiddle" alt="Newtonian fluids linearly depend on the development time at a constant load: release">Fig. 1.7 .

Measure the value of dynamic viscosity can be determined in various ways, for example, by the rate of liquid flow out of the capillaries.

Poiseuille obtained an empirical equation according to which the volume of liquid flowing from a capillary depends both on the parameters of the capillary - length l and diameter r, and the pressure P under which it is forced through the capillary, the viscosity of the liquid example ">t:

example">k. For a Newtonian fluid at constant volume, the viscosity

definition ">3) Model of an ideal plastic body of Saint-Venant-Coulomb

The model represents a solid body on a plane, during the movement of which constant friction arises, independent of normal shear stress - the law of “dry friction”: there is no deformation if the formula "src="http://hi-edu.ru/e-books /xbook839/files/f370.gif" border="0" align="absmiddle" alt="- yield strength) (Fig. 1.8 ).

Thus, with the formula" src="http://hi-edu.ru/e-books/xbook839/files/f371.gif" border="0" align="absmiddle" alt=".gif" border="0" align="absmiddle" alt=", the current moves at any speed.

Rice. 1.9 .

The “dry friction” element cannot be subjected to a voltage defined by ">4) Model of a real body. Bingham model - viscoplastic body

When connecting elements in series

formula" src="http://hi-edu.ru/e-books/xbook839/files/f376.gif" border="0" align="absmiddle" alt="

Rice. 1.10
.

Bingham's Law:

formula" src="http://hi-edu.ru/e-books/xbook839/files/f378.gif" border="0" align="absmiddle" alt=".gif" border="0" align="absmiddle" alt="

Newtonian viscosity takes into account all resistance to flow, and plastic viscosity does not take into account the strength of the structure, but reflects the rate of destruction, mainly by the viscosity of the dispersion medium, which can vary widely..gif" border="0" align="absmiddle" alt="(! LANG:and more.

The flow of such a system begins only when the shear stress exceeds a certain critical value determined by plastic, and the shear stress exceeds the yield stress. From the point of view of rheology, such systems are called plastic-viscous, and the patterns of their flow are described by the Bingham equation.

In the absence of a structural mesh, the value is selection">Fig. 1.11
.

According to Fig. 1.11, at loads exceeding the formula" src="http://hi-edu.ru/e-books/xbook839/files/f384.gif" border="0" align="absmiddle" alt="

Examples of systems that obey Bingham's equation well include clay pastes and greases. However, for most structured systems, the dependence of dU/dx on P is expressed not by a straight line, but by a curve (Fig. 1.11, b). The reason for this phenomenon is that when the yield point is reached, the structure does not collapse immediately, but gradually as P and dU/dx increase.

Three critical shear stresses can be distinguished on the curve: 1) formula" src="http://hi-edu.ru/e-books/xbook839/files/f386.gif" border="0" align="absmiddle" alt= "- Bingham yield strength, corresponding to the segment on the abscissa axis, cut off by the continuation of the straight section of the curve; 3) formula" src="http://hi-edu.ru/e-books/xbook839/files/f388.gif" border="0" align="absmiddle" alt=") viscosity is not a constant value and decreases as P increases. When P >subtitle">

2. Rheological properties of real bodies

2.1. Classification of bodies according to their rheological properties

All real bodies along the flow are divided into:

Liquid-like (formula" src="http://hi-edu.ru/e-books/xbook839/files/f389.gif" border="0" align="absmiddle" alt="> 0)

In turn, liquid-like bodies can be divided into:

Newtonian and non-Newtonian

stationary: non-stationary

pseudoplastic (thixotropy

dilatant rheopexy)

Experimental studies have shown that the flow of liquid-like systems can be represented in the form of a general dependence. This equation is known as the Ostwald-Weil mathematical model:

formula" src="http://hi-edu.ru/e-books/xbook839/files/f391.gif" border="0" align="absmiddle" alt="

Thus, the deviation of n from unity characterizes the degree of deviation of the properties of non-Newtonian liquids from the properties of Newtonian liquids (Fig. 2.1 ).

When n< 1 вязкость уменьшается с увеличением скорости сдвига и напряжения. Такие жидкости называются pseudoplastic.

For n > 1, the viscosity of liquids increases with increasing shear rate and stress. Such liquids are called dilatant.

Newtonian liquids include all pure liquids, as well as dilute colloidal systems with symmetrical particle shapes - suspensions, emulsions, sols.

Pseudoplastic liquid-like systems include dilute suspensions with asymmetric particle shapes and polymer solutions.

The fact is that long macromolecules and asymmetric particles exhibit different resistance to flow depending on their orientation in the flow. With increasing shear stress and fluid flow velocity, the particles gradually orient their major axes along the direction of flow. Their chaotic movement changes to ordered, which leads to a decrease in viscosity.

If the particles of the dispersed phase are anisometric (ellipsoids, rods, plates) or capable of deformation (droplets, macromolecules), then during the flow of the dispersion medium, different trends may appear depending on the nature and size of the particles.

formula" src="http://hi-edu.ru/e-books/xbook839/files/f393.gif" border="0" align="absmiddle" alt=".

Dilatant or spreading systems. In a spreading flow, the volume of the system decreases with increasing load, which leads to an increase in its viscosity.

In these cases, in particular, at large deformations, an increase in effective viscosity is observed with an increase in the velocity gradient (dilatancy - a decrease in the density of the structure when it is deformed under the influence of applied stresses - for example, during the initial stage of mixing starch in water, in ceramic masses, i.e. in powders and compacted dispersed materials).

In a dispersed system with a high content of solid phase at low loads, the dispersion medium plays the role of a lubricant, reducing the friction force and viscosity of the system, before the particles begin to move, their packing becomes looser, and the system increases in volume, viscosity decreases. As shear stress increases, the solid particles come into contact, which causes an increase in frictional force and the viscosity of the system increases.

Systems in which there is a dependence of viscosity on shear stress are called anomalous or non-Newtonian.

Non-stationary non-Newtonian fluids, characterized by the dependence of rheological properties on time, are characterized by the phenomena of thixotropy and rheopexy. Thixotropy is the ability of a structured system to restore its strength properties over time after its mechanical destruction. Restoration of the structure is usually detected by an increase in the viscosity of the system, so the phenomenon of thixotropy can be defined as a decrease in the viscosity of the system over time when a load is applied and a gradual increase in viscosity after the load is removed. Rheopexy is the opposite phenomenon of thixotropy - the emergence and strengthening of a structure over time as a result of mechanical action.

2.2. Viscosity of aggregation-stable disperse systems

In some cases, the viscosity of colloidal systems is practically no different from the viscosity of dispersed systems. Below a certain flow speed, laminar flow is observed and obeys the laws of Newton and Poiseuille.

For example, with laminar flow of sols Au, Ag, Pt, formula" src="http://hi-edu.ru/e-books/xbook839/files/f395.gif" border="0" align="absmiddle" alt ="

where is the formula" src="http://hi-edu.ru/e-books/xbook839/files/f397.gif" border="0" align="absmiddle" alt="= 2.5, for elongated particles

As the concentration of the dispersed phase increases, the interaction between particles increases, and strong deviations from the Einstein equation are detected. The viscosity of concentrated systems increases with increasing j almost exponentially (line 2 in Fig. 2.3 ), for them there is a dependence of viscosity on shear stress, i.e. Newton's law does not apply. These deviations from Newton's law and Einstein's equation are usually caused by the interaction of particles and the formation of a structure in which particles of the dispersed phase are oriented in a certain way relative to each other (structuring of systems).

Incompressible system

The fluid flow is laminar,

There is no sliding between particles.

Real disperse systems do not obey Einstein's equation the following reasons:

The presence of adsorption and solvate layers on particles, as well as DES

Interaction of dispersed phase particles,

Flow turbulence,

Particle anisometricity,

Temporal fluctuation.

Let's consider the simplest rheological properties - elasticity, plasticity and viscosity of three so-called ideal bodies. In rheology, ideal bodies are usually called after the scientists who first introduced them. For non-Newtonian fluids, the effective viscosity consists of two components:

1) Newtonian viscosity η , which is based on internal friction and represents a physical constant of the material;

2) structural resistance, which depends on the structural state of disperse systems and is a function of shear rate .

Effective viscosity  eff is the final variable characteristic that describes the equilibrium state between the processes of restoration and destruction of the structure in a steady flow and depends on changes in the velocity gradient and shear stress.

If, under conditions of steady shear flow, the shear stress τ not proportional to the rate of deformation , i.e. their attitude:
, varies depending on the value τ or , then such a liquid is called non-Newtonian. Several rheological equations have been proposed to describe the behavior of non-Newtonian fluids (see below).

The viscosity of liquids can depend on vibration (including ultrasonic), electrical, magnetic, and light influences; this applies to both polymer solutions and melts and dispersed systems.

In rheology, there are two types of flow: 1) viscous flow– realized in truly viscous, Newtonian fluids at any arbitrarily low shear stress τ . This flow is described by Newton's equation:

or
, (1.4)

Where η – coefficient of dynamic or absolute viscosity, which characterizes the magnitude of the forces arising between two elementary layers of liquid during their relative displacement, Pa∙s;

^F– resistance force between two elementary layers, N;

A– resistance surface area of ​​these layers, m2;
2) plastic flow– flow at voltage value τ , equal to the yield strength τ T.

Voltage– a measure of the intensity of internal forces F[H] arising in the body under the influence of external influences per unit area S[m 2 ], normal to the force application vector:

, Pa. (1.5)
Voltage at the point of the loaded body:

. (1.6)
Rheological properties qualitatively and quantitatively determine the behavior of a product under the influence of external factors and allow one to relate stresses, strains (or strain rates) during the application of force.

In rheology, two mutually exclusive concepts are distinguished: “solid ideally elastic body” and “non-viscous liquid”. The first is understood as a body whose equilibrium shape and tension are achieved instantly. The liquid is called residual, i.e. if the fluid is unable to create and maintain shear stresses. Between the limiting states of bodies (elastic solids and inviscid liquids) in nature there is a huge variety of intermediate bodies.

Let us consider the main models that may be encountered when studying the rheological properties of food masses. It is necessary to point out that exact mathematical laws were obtained only for Newtonian fluids; for all non-Newtonian flows, only approximate formulas were obtained.

Three intermediate models of idealized materials are known (Table 1.1): ideally elastic body (Hooke); ideally viscous liquid (Newtonian); ideally plastic body (Saint-Venant).

^ Hooke's ideally elastic body . In an ideally elastic body (model - spring), the energy expended on deformation accumulates and can be returned during unloading. Hooke's law describes the behavior of crystalline and amorphous solids under small deformations, as well as liquids under isotropic expansion and compression.

^ Newton's ideal viscous fluid . An ideally viscous liquid is characterized by the fact that the stresses in it are proportional to the strain rate. Viscous flow occurs under the influence of any forces, no matter how small they are; however, the strain rate decreases as the forces decrease, and when they disappear, it becomes zero. For such liquids, the viscosity, which is a constant, is proportional to the shear stress.
Table 1.1
Rheological models of idealized bodies

Model	Model type	Charts Currents	The equation
Hooke
Newton
Saint Venant			At τ < τ T no deformation; at τ = τ T current

Newton's law describes the behavior of many low molecular weight liquids under shear and longitudinal flow. The mechanical model of a Newtonian fluid is damper, consisting of a piston that moves in a cylinder of liquid. As the piston moves, fluid flows through the gaps between the piston and the cylinder from one part of the cylinder to the other. In this case, the resistance to movement of the piston is proportional to its speed (see table 1.1).

^ Saint-Venant's perfectly plastic body can be presented in the form of an element consisting of two plates pressed against each other. With the relative movement of the plates between them, a constant friction force arises, depending on the magnitude of the force compressing them. The Saint-Venant body will not begin to deform until the shear stress exceeds a certain critical value - the yield point τ T (ultimate shear stress), after which the element can move at any speed.

In order to describe the rheological behavior of a complex body depending on the properties of its components, it is possible to combine in various combinations the models of the simplest ideal bodies discussed above, each of which has only one physical and mechanical property. These elements can be combined in parallel or in series.

In rheology, the method of mechanical models is widely used. For example, to obtain a clear picture of the behavior of a material under stress, each of its properties (elasticity, plasticity, etc.) is replaced by a mechanical element (spring, sliding friction pair, etc.). Rheology also widely uses geometric, mathematical, physical and other modeling. Physical modeling is effective for obtaining qualitative and quantitative correspondence to natural objects.

The practical application of rheological research is associated, firstly, with the ability to compare different materials according to the form of rheological equations of state and the values ​​of the constants included in them; secondly, using rheological equations of state to solve technical problems in continuum mechanics. The first direction is used to standardize technological materials, control and regulate technological processes in almost all areas of modern technology. Within the second direction, applied hydrodynamic problems are considered - transportation of non-Newtonian fluids through pipelines, flow of polymers, food products in processing equipment, etc. For concentrated disperse systems, these tasks include the establishment of optimal technological regimes for mixing, molding products, etc. For solids, the stress-strain state of structural elements and products as a whole is calculated to determine their strength, elongation at break and durability.

^ Place of rheology as one of the sections of technical mechanics of a continuous medium (among other sections of technical mechanics) is clearly seen from the following classification:

A) ideal rigid body (Euclidean) - at any normal and tangential stresses, the deformation is zero (theoretical mechanics);

b) elasticbody(gukovo) - stress is proportional to deformation (resistance of materials);

V) plasticbody (Saint Venanovo) - when the maximum shear stress is reached, plastic deformation begins (resistance of materials);

G) rheologicalbody: linear - composed of bodies included in points A, b, d; nonlinear - empirical;

d) trueviscous liquid (Newtonian) - voltage is proportional to the velocity gradient to the first power;

e) perfectliquid(pascal) - viscosity and compressibility are zero.

The qualitative development of rheology, which plays an important role in engineering physical and chemical mechanics, is evident from the following stages of its change.

^ Classical rheology as the science of flow and deformation of real bodies (technical mechanics of real bodies or dispersed systems) sets the task of studying the properties of existing products and developing methods for calculating the processes of their flow in the working parts of machines, in order to obtain finished products of a given quality.

^ Physico-chemical mechanics how the science of methods and patterns of formation of structures of dispersed systems with predetermined properties solves the following problems:

1) establishing the essence of the formation and destruction of structures in dispersed and native systems, depending on a combination of physicochemical, biochemical, mechanical and other factors;

2) research, justification and optimization of ways to obtain structures with predetermined rheological (in the broadest sense of the word) properties.

3) development of methods for applying established laws for calculating machines and devices and operational monitoring of basic quality indicators based on the values ​​of structural and mechanical characteristics.

^ Control rheology includes the study and justification of such a combination of various types of influences on processed raw materials, which ensure a given level of rheological characteristics throughout the entire technological process and obtain a finished product with specified consumer properties.

The implementation of research using the methods of engineering rheology and physical and chemical mechanics makes it possible to stabilize the yield of products, obtain finished products of constant, predetermined quality, scientifically substantiate the concept of product quality, calculate, improve and intensify technological processes, “design” certain types of food products, etc. d.

Thus, rheology studies the SMS of various bodies, as well as methods and instruments for their determination and regulation, which food production engineers need to know.
^ 1.2 Classification of rheological bodies, flow curves
The object of research in food rheology is food materials. We will conduct a qualitative preliminary analysis and grouping of food materials. If we take gases, liquids and solids as the basic simplest (in terms of their state of aggregation) materials, then the vast majority of food materials are so-called dispersed systems. It is the latter that are especially characterized by significant deviations from the classical laws of deformation and flow.

Dispersed systems consist of two or more components or phases. Usually one of the phases is considered as continuous and is called a dispersion medium, the other, non-continuous, is called the dispersed phase. This division is conditional and more or less obvious in most cases. Formally, and to some extent conditionally, dispersed media can be divided into eight types:

1) two-phase systems of solid and gas phases;

2) two-phase systems of solid and liquid phases;

3) two-phase systems of liquid and gas phases;

4) two-phase systems of two solid phases;

5) two-phase systems of two liquid phases;

6) two-phase systems of two gas phases;

7) three-phase systems of solid, liquid and gas phases;

8) multiphase systems.

Food products, including raw materials and semi-finished products, depending on their composition, dispersed structure and structure, have different rheological properties. Highly concentrated disperse systems with spatial structures have the most complex rheological properties.

If we consider the classification of dispersed media in a broader sense, as part of the classification of the states of media encountered in the food industry, then it (in this classification) must include ideas about magnetic and electric fields, flows of electromagnetic radiation, radioactive radiation, ultrasound and etc.
^ 1.2.1 Classification of dispersed system structures
Structure, i.e. the internal structure of the product and the nature of the interaction between its individual elements (particles) determine the chemical composition, biochemical parameters, temperature, dispersion, state of aggregation and a number of technological factors.

According to the classification of academician P.A. Rebinder, the structures of food products can be divided into coagulation and condensation-crystallization.

^ Coagulation structures are formed in disperse systems by interaction between particles and molecules through layers of the dispersion medium as a result of van der Waals adhesion forces. The thickness of the interlayer corresponds to the minimum free energy of the system. Thermodynamically stable systems are those in which fragments of molecules are firmly bound to the surface of the particles and are capable of dissolving in a dispersion medium without losing this bond. In turn, the dispersion medium is in a bound state. Often these structures have the ability to spontaneously recover after destruction (thixotropy). The increase in strength after fracture occurs gradually, usually up to the initial strength as a result of the Brownian motion of highly dispersed particles when they hit coagulation contacts. The thickness of the layers depends to a certain extent on the content of the dispersion medium. As its content increases, the values ​​of shear properties usually decrease, and the system changes from solid to liquid. At the same time, dispersion, i.e. the prevailing particle size, even at a constant phase concentration, affects the state of the system, its strength or viscosity.

When coagulation structures are dehydrated (with an increase in the content of the dispersed phase), their strength increases, but after a certain limit they cease to be reversibly thixotropic. The recoverability of the structure is maintained in a viscous-plastic environment when the spatial frame is destroyed without breaking the continuity. With a further decrease in the content of the liquid phase, i.e. when switching to plastic pastes, restoration of strength after destruction of the structure is possible under the action of stress causing plastic deformations, which ensure true contact over the entire surface of the fracture. At the highest degree of compaction of the structure and the smallest thickness of the layers of the liquid medium, recoverability and plasticity disappear, and the strength curve depending on humidity shows a kink. In this case, the particle contacts still remain point-like. They can go into phase form by sintering or accretion with a significant increase in temperature and with a simultaneous change in the biochemical essence of the object.

During the formation of coagulation structures in many food products, a significant role is played by surfactants and proteins dissolved in water, which act as emulsifiers and stabilizers of the formed systems and can significantly change their structural and mechanical characteristics.

^ Condensation-crystallization structures inherent in natural products. However, they can be formed from coagulation structures when the dispersion medium is removed or when particles of the dispersed phase grow together during heat treatment (coagulation or denaturation of proteins), during cooling of melts and cooling or increasing the concentration of solutions. During the formation process, these structures can have a number of transition states - coagulation-crystallization, coagulation-condensation. Their formation is characterized by a continuous increase in strength. The main distinctive features of structures of this type are the following: greater strength, compared to coagulation ones, due to the high strength of the contacts themselves, the absence of thixotropy and the irreversible nature of destruction, high fragility and elasticity due to the rigidity of the skeleton of the structure, the presence of internal stresses arising during the formation of phase contacts and subsequently leading to recrystallization and a spontaneous decrease in strength up to a loss of continuity, for example, cracking during drying.

Thus, the type of product structure determines its quality and technological indicators and behavior in deformation processes.
^ 1.2.2 Classification of rheological bodies
The belonging of a real product to one or another type of “ideal” rheological body, identified on the basis of preliminary experiments, makes it possible to justify the choice of a device for research and correctly determine its properties.

Shear properties represent a main group of properties that are widely used both for calculating various motion processes in the working parts of machines and for assessing the quality of food products. In this regard, methods for classifying food and other rheological bodies according to shear characteristics have become most widespread.

If we take elastic and truly viscous bodies as boundary ones, then all other bodies will be located between them. The simplest classification (Table 1.2) is proposed based on the ratio of the ultimate shear stress to density and gravitational acceleration (
), characterizing the measure of a substance’s ability to maintain its shape.
Table 1.2
Classification of bodies by physical parameters

B.A. Nikolaev proposed a generalized classification (from solid to truly viscous state) based on the magnitude of mechanical properties. The first group includes solid and solid-like bodies, the second - solid-liquid, and the third - liquid-like and liquid. The minimum indicators that sufficiently characterize the rheological properties of products will be different for each group.

Solid and solid-like products of the first group (solid fat, whole meat tissues, crackers, cookies, etc.) are characterized mainly by elastic moduli, viscosity and the ratio of viscosity to elastic modulus, as well as the ultimate shear stress, which determines the onset of structure flow.

Solid-liquid products of the second group (minced meat, cottage cheese, jellies, flour dough, etc.), which have a variety of mechanical properties, are characterized by the largest number of indicators: elastic moduli, elasticity, ratio of viscosity to elastic modulus, ultimate shear stress, plasticity, and elasticity and liquefaction (hardening) coefficient.

Liquid and liquid products of the third group (melted fat, broths, milk, honey, water, etc.) are characterized by the values ​​of their ultimate shear stress, the dependence of structural viscosity on stress, pressure loss when flowing through pipes, maximum flow velocity and, mainly, viscosity .

Proposed by prof. V.D. Kosym and M.Yu. Merkulov’s classification of biotechnological media according to rheological shear characteristics divides materials into the following groups:

It is of interest to classify real bodies using the Herschel–Bulkley power equation:

, (1.7)

Where: – tension between product layers, Pa;

– ultimate shear stress, Pa;

– consistency coefficient proportional to viscosity, Pa s n;

n–current index.
With this classification method, relationships are constructed between shear stress and velocity gradient (flow curves, see below) and between effective viscosity and shear velocity gradient. Based on the nature of the resulting curves, the following types of bodies are distinguished, presented in Table 1.3.

The systems listed in Table 1.3 do not change their properties over time. There is also a group of systems with time-variable properties: thixotropic, which are characterized by isothermal restoration of the structure after destruction, as well as its continuous destruction (up to a certain limit) during deformation, and reopex, which are capable of being structured, i.e. form contacts between particles as a result of orientation or weak turbulence under mechanical action with small velocity gradients.

P.A. Rebinder and N.V. Mikhailov proposed dividing rheological bodies into liquid-like And solid-like depending on the nature of the curve η ef ( τ ) rice. 1.3 and from the relaxation period (the relaxation period is the time during which the stress in the loaded body decreases in e= 2.7 times).

Table 1.3
Values ​​of the constants in equation (1.7).

No.	Ultimate shear stress	Index Currents	Viscosity	Body name
1	0	∞	∞	Hooke's elastic body
2	> 0	0	> 0	Saint-Venant's plastic body
3	> 0	1	> 0	plastic-viscous body Shvedova-Binghama
4	0	< 1	> 0	pseudoplastic body
5	0	> 1	> 0	dilatant body
6	> 0	< 1	> 0	nonlinear plastic body
7	> 0	> 1	> 0	nonlinear dilatant body
8	0	1	> 0	true viscous Newtonian body
9	0	0	0	ideal liquid

Fluid-like bodies include Newtonian fluids and structured systems that do not have a static limiting shear stress ( τ 0 st = 0), i.e. Such systems flow when an arbitrarily small external influence is applied. Solid-like bodies include elastic-plastic and other bodies that have static and dynamic ultimate shear stress.

In order to systematically consider trends in the formation of a range of dairy products, it is necessary to use a scientifically based classification as an initial prerequisite, which will simplify the design of dairy products with a given consistency and chemical composition.

The basis for this classification is the consistency of products, which is a set of rheological properties of weakly structured liquids, a visco-plastic and elastic-elastic product.

P The first group includes weakly structured (conditionally Newtonian and Newtonian) liquids, which include: milk, cream, concentrated milk without sugar, etc. Weakly structured liquids practically do not exhibit viscosity anomalies and can be classified as Newtonian liquids, the flow of which is described by the equation:

. (1.8)
The second group includes dairy products that flow as viscous-plastic liquids (fermented baked milk, sour cream, yogurt, etc.). A visco-plastic body does not deform at stresses less than a critical value, and at greater stresses it flows as a viscous fluid (Bingham fluid):

. (1.9)
The third group includes elastic-elastic products (processed, rennet, sausage cheeses, butter).
^ 1.2.3 Flow curves
The deformation behavior of real disperse systems, which include food masses, can be characterized by the so-called flow curve. This curve is plotted according to experimental data in the coordinates: shear stress – shear rate. In general, this dependence can be written as:

, or
. (1.10)
This equation is applicable to real systems, which can be either liquids or solids. Liquids, in turn, are divided into Newtonian and non-Newtonian. Solid materials having extreme shear stress τ 0 are, as a rule, non-Newtonian media.

Fluid flow curves originate from the origin (Fig. 1.4). It follows from this that a liquid is a medium that can be deformed (flow) regardless of the viscosity value with an arbitrarily small applied external force. Solid systems can flow, exhibiting the properties of liquids only after the shear stress exceeds a certain critical value - the limiting shear stress τ 0, which determines the plastic properties of the material.

Figure 1.4. Current curves:

1 – Newtonian fluid; 2 – dilatant liquid;

3 – structurally viscous liquid; 4 – nonlinear plastic body;

5 – linear plastic body
Flow curves (rheograms) Newtonian liquids are a straight line 1 , passing through the origin of coordinates (Fig. 1.4). For such liquids, Newton's rheological equation is applicable:

. (1.11)
All flow curves ( 2 – 5 ), which deviate from a straight line, are called non-Newtonian (anomalously viscous) liquids. The non-Newtonian behavior of liquids can have various reasons: in liquid disperse systems, the determining role is played by the orientation of particles of the dispersed phase, changes in their shape and degree of aggregation; in colloidal liquids, the destruction (or change) of the internal structure gradually deepens with increasing stress; in polymers – the effects of mechanical relaxation, i.e. stress redistribution. In specific cases, there may be an overlap of different mechanisms; for example, the non-Newtonian behavior of filled polymers is associated with both structural rearrangements and relaxation phenomena. A special case of non-Newtonian behavior of a liquid is a change in viscosity over time due to chemical reactions occurring in the medium. If the reaction occurs in a homogeneous medium, the change in the viscosity of the medium reflects a change in its composition; in this case, deformation usually does not affect the kinetic laws of the reaction. However, for heterogeneous reactions, such as heterogeneous polymerization or solidification of oligomers, deformation affects the reaction kinetics (for example, shear flow in a reactor or exposure to ultrasonic vibrations).

Among food materials, there are those whose viscosity varies with the rate of deformation. Such liquids are described by the Ostwald-de-Ville rheological equation:

, (1.12)

Where TO– consistency coefficient, depending both on the nature of the material and on the type and geometry of the measuring elements of the device;

n– current index.

.
At the same time, the curve ^ 2 characterizes dilatant flow (at n> 1), characteristic mainly of concentrated disperse systems, in which, with an increase in the deformation rate, “shear difficulty” occurs, i.e. viscosity increases; curve 3 describes pseudoplastic flow (at 0< n < 1), что характерно для «сдвигового размягчения» вследствие разрушения структуры с увеличением скорости деформации;

Curve ^ 4 shows nonlinear plastic flow characteristic of most plastic bodies after reaching the limiting shear stress τ 0, the Herschel–Bulkley rheological equation describes their behavior:

. (1.13)
Linear dependence ^ 5 typical for Bingham's bodies and corresponds to ideal plastic flow, in which, after reaching the maximum shear stress τ 0 there is a proportionality between speed and shear stress. Such materials are described by the Bingham equation:

, (1.14)

Where η pl – plastic viscosity, Pa s.
Thus, the effective viscosity value can be taken as a controlled parameter for all dairy products η eff (at
). For dairy products that have a visco-plastic flow pattern, it is necessary to control the ultimate shear stress τ 0 and plastic viscosity η pl.

Many non-Newtonian liquids are characterized by such phenomena as thixotropy– reversible decrease in viscosity (“liquefaction”) of the liquid or structuring of the system over time (Fig. 1.5, A), And rheopexy– increase in the viscosity of extremely filled disperse systems with a viscous dispersion medium (Fig. 1.5, b).

Rice. 1.5. Flow curves characterizing:

A) thixotropic systems; b) rheopex systems
In many processes, the product is subjected to intense mechanical stress (pumps, mixers, etc.), i.e. its structure reaches partial or almost complete destruction. Therefore, when using the results of rheological studies for practical calculations, one should at least approximately select the flow curve that corresponds to a given degree of destruction. In accordance with this, when calculating various processes, it is necessary to use the characteristics determined in the corresponding range of stresses and strains. A qualitative assessment of the product must also be carried out according to the most significant characteristics for a given process.
^ 1.3 Shear, surface and compression

properties of materials
The rheological properties of materials manifest themselves when exposed to any external forces or factors. This exposure occurs during materials processing, transportation or storage. Based on the type of application of external forces to the product, these properties can be divided into three groups: shear, volumetric and surface (Figure 1.6).

Shear properties characterize the behavior of the product volume when exposed to shear and tangential stresses, Fig. 1.6, A.

Surface properties characterize the behavior of a product at the interface with another solid material when exposed to normal conditions (adhesion, Fig. 1.6, b) and tangential (external friction) stresses.

Compression (volumetric) properties determine the behavior of the product volume when exposed to normal stresses in a closed form or between two plates, Fig. 1.6, V.
^ 1.3.1 Shear properties
As noted above, shear properties represent the main group of properties. The characteristics that determine these properties can be used for a variety of purposes - from assessing the quality of a product to calculating pipelines, machines and apparatus. These properties manifest themselves when the product is exposed to tangential stresses (forces).

To the main shear properties weakly structured And visco-plastic systems, When τ > τ 0 , refer static And dynamic ultimate shear stress, effective And plastic viscosity, plasticity of the structure for visco-plastic systems and dynamic viscosity for semi-structured systems.

^ Static shear stress (τ 0 , Pa) is the force per unit surface of the product, above which the product begins to flow, i.e. stress, upon reaching which irreversible deformations begin to develop in the system.

^ Dynamic ultimate shear stress (τ 0d, Pa) – stress equal to the segment cut off on the abscissa axis of the direct zone of visco-plastic flow in the coordinates of the velocity gradient – ​​shear stress.

^ Effective viscosity – this is the so-called “apparent” viscosity, which is a variable value and depends on the product velocity gradient ( , s –1).

Effective viscosity is the final variable characteristic that describes the equilibrium state between the processes of restoration and destruction of the structure in a steady flow. It is characterized by the angle of inclination of a straight line connecting the origin of coordinates to the point for which its value is determined. With increasing shear stress, the effective viscosity decreases, i.e. the angle of inclination increases on the flow curve in the zone of avalanche-like destruction of the structure (zone 3 – 4, Fig. 1.7). Points A, V, With– corresponding to a certain value τ (τ A, τ V, τ c), connect to point 0, then the effective viscosity at each point is characterized by the angle of inclination of the straight line:
;
;
. The dependence of effective viscosity on shear rate on logarithmic scales (Fig. 1.8) obeys the following relationship:

(1.15)

Where: – effective viscosity at a unit value of the relative (dimensionless) velocity gradient:
(
s –1);

m– rate of structure destruction, i.e. tg of the slope of the logarithmic line.

^ Plastic viscosity – constant value, independent of shear stress and velocity gradient in the coordinate axes – shear stress is ctg α a straight line that does not extend from the origin of coordinates and cuts off on the axis τ segment equal to the static one (corresponding η 0) or dynamic (corresponding η m) ultimate shear stress:

Highest (Swedish) plastic viscosity:

, Pa ∙ s; (1.16)
lowest (Bingham) plastic viscosity:

, Pa ∙ s; (1.17)

Plasticity of structure is the ratio of the static ultimate shear stress to the plastic viscosity:

, s –1 (1.18)
Dynamic viscosity Newtonian or structured fluid is characterized by the angle of inclination of the straight line
, coming out from the origin, i.e. τ 0 = 0.

Structural and mechanical properties in the area of ​​practically intact structures, When τ < τ 0 can be characterized by Hooke's law. These include: conditionally instantaneous modulus of elasticity, elastic and equilibrium modulus, relaxation period. These properties are determined from the relative deformation kinetics diagram γ under constant shear stress τ when creep occurs (Fig. 1.9).

D The deformation kinetics diagram consists of two curves: OABC - load (action of constant shear stress τ ) and CDF – unloading (deformation after removal of the load). The moment of load removal is set after the appearance of an almost straight section on the ABC curve.

After removing the load, the conditionally instantaneous true elastic deformation disappears within 0.5–1.0 s γ 0 . The diagram shows the complete development of deformation γ m at the moment the load is removed expresses the equation:
γ m = γ 0 + γ e + γ η, (1.19)

Where: ( γ 0 + γ e = γ y) – elastic deformation that subsides spontaneously after removing the load;

γ η – residual deformation;

γ e – elastic aftereffect deformation (elastic).

Permanent deformation γ η, which is formed after unloading, does not disappear in time. After reaching the straight section of the unloading curve, it remains almost constant. This is expressed in the flow of the system, and the speed depends on its viscosity.

Elastic aftereffect or slowly developing (elastic) deformation is reversible. It is due to the structure of real bodies, in which, along with relaxation, the reversibility of stresses produces a redistribution of elastic deformations over time in different parts of the structure.

^ τ to the instantaneously elastic component of shear deformation γ 0 . The elasticity of bodies under shear is characterized by a modulus of elasticity of the second kind G mind:
G mind = τ / γ 0 . (1.20)
Elastic module G uh - this is an attitude τ to elastic γ y deformation, minus the instantaneously elastic component γ 0, i.e. to elastic deformation γ e:
G e = τ / (γ y – γ 0) = τ / γ e. (1.21)
Equilibrium module is the voltage ratio τ to general deformation γ m, where it is impossible to distinguish between elastic and elastic deformation:
G = τ / γ m. (1.22)
Relaxation period is the duration of stress relaxation (restoration) under constant deformation or deformation after stress removal ( t r, s).

To measure the characteristics that determine the shear properties of products, viscometers of various designs and operating principles are used. The choice of measuring unit for a specific product determines the obtaining of reliable results, which ensures the receipt of correct calculated data.

^ 1.3.2 Surface properties
A special place among structural and mechanical properties is occupied by surface properties(adhesion, cohesion, coefficient of friction). They characterize the interaction force between the working surfaces of the equipment and the processed product during tearing or shear.

During technological processing, food materials (adhesive) are in contact with the surfaces of various working parts of machines (substrate), transport devices, etc. The nature of the mass flow through the channels of forming machines of various types (screw, roll, gear, etc.), as well as through process pipelines, is determined both by its structural and mechanical properties and by the adhesion forces with the contact surfaces.

^ Adhesion is the adhesion of the surfaces of two dissimilar materials. This phenomenon often occurs in nature and is widely used in technology. Under cohesion understand the cohesion of particles inside the body in question. Food materials are characterized by different types of tearing (Fig. 1.10): A) adhesive; b) cohesive; V) mixed – adhesive-cohesive.

In some cases, it is difficult to establish the fracture boundary for two or more phase systems. After tearing off, the surface of the plate can be moistened with a dispersion medium or covered with a thin film of a finely dispersed fraction of the product under study.

a B C)

Rice. 1.10. Types of material separation:

A) adhesive; b) cohesive;

V) mixed – adhesive-cohesive
There is no general quantitative theory of adhesion yet, although attempts at a comprehensive explanation of adhesion based on various interaction mechanisms are very fruitful. In this sense, the fundamental works of academician P.A. are promising for the development of theoretical ideas about adhesion. Rebinder on adsorption and surface activity of thin films. As a result of witty and subtle experiments by V.A. Pchelin established surface tension, dielectric constant, surface potential, etc. for solutions of protein substances. In the phenomenon of adhesion of protein substances, as follows from the theoretical concepts of B.V. Deryagin, in addition to Van der Waals forces of attraction, electrostatic forces are involved, caused by the appearance of a double electric layer on the surface.

The amount of adhesion between two bodies is usually characterized by: the pull-off force; specific work of separation per unit area; the time required to break the bond between the substrate and the adhesive under the influence of a certain load. The most common test methods are:

1. 
   uneven detachment, which makes it possible to identify changes in the values ​​of adhesive strength in individual areas of the test sample;
2. 
   uniform separation, in which the force required to separate the adhesive from the substrate is measured simultaneously over the entire contact area;
3. 
   shift of one material relative to another.

Adhesion is often characterized by the minimum force required to pull off. This value is called adhesive strength, adhesive pressure (stress), adhesion pressure or specific adhesion.

The formation of an adhesive bond is greatly influenced by the rheological properties of the adhesive, the cleanliness of the substrate surface and its topography, the duration of contact between the adhesive and the substrate, the contact pressure, the temperature of the adhesive and the substrate, and the speed of separation from the substrate.

When operating equipment, as well as when designing and creating new machines, it is necessary to take into account adhesion phenomena in order to correctly select the material of parts or coatings and establish the optimal operating mode. For example, in the production of soft varieties of sweets from praline masses, creamy fudge and a number of others, depending on the purpose of certain organs of the machine, it is necessary either to increase their adhesive interaction, or to achieve minimal adhesion. So, if in the feed zone of the forming machine the adhesion of the mass to the walls should be the least, then in the screw chamber it should be the greatest. The surface of the screw, in contrast to what was said above, should be smooth, made of a material that is least sticky to the mass. The roller supercharger is characterized by a maximum increase in the forces of interaction between the mass and the surface of the rolls, which increases the efficiency of the machine.

Although the nature of adhesion has not been revealed to date, several theories are known that explain the physicochemical essence of adhesion phenomena:

1. 
   According to the adsorption theory of DeBroin and McLaren, adhesion is associated with the action of intermolecular forces: physical– van der Waals or chemical, for example covalent ionic;
2. 
   on electrical theory B.V. Deryagin and N.A. Krotova - with a potential difference at the boundary of dissimilar bodies, i.e. with the appearance in the contact zone of a kind of electric molecular capacitor caused by a double electric layer;
3. 
   according to electromagnetic – with electromagnetic interaction, i.e. emission and absorption of electromagnetic waves by atoms and molecules, which can occur in condensed bodies;
4. 
   according to the electrorelaxation theory of N.M. Moskvitin - with a double electric layer and a separation speed, the measurement of which causes the appearance of a deformation component of the force or work of destruction associated with the rate of relaxation processes in the destroyed joint;
5. 
   according to the diffusion theory of S.S. Voyutsky and B.V. Deryagin - with the diffusion of the ends of macromolecules across the boundary of the initial contact, as a result of which, in the limiting case, the phase boundary may disappear; similar to this is the mechanical theory, according to which adhesive contact is formed due to the mechanical engagement of molecular or supramolecular formations with microroughnesses of the surface;
6. 
   according to thermodynamic theory - with surface tension, which determines, according to Dupre's rule, the work of replacing the “solid-liquid” interface with the “solid-gas” surface, which is realized when the disk is separated from the product.

Formally, adhesion is defined as the specific force of normal separation of the plate from the product:
R 0 = F 0 / A 0 , (1.23)

Where: F 0 – pull-out force, N;

A 0 – geometric area of ​​the plate, m2.

^ External friction– interaction between bodies at the boundary of their contact, preventing their relative movement along the contact surface.

It is difficult to separate the forces of friction and adhesion that arise during the relative displacement of the contacting surfaces of two bodies. The relationship between the forces of friction and adhesion is determined by the Deryagin equation:

, (1.24)

Where: ^F tr – external friction force, N;

μ – true friction coefficient;

A 0 – true contact area, m2;

R 0 – specific adhesion, acting on areas of the area ^A 0 , Pa.
External friction force– a force acting tangentially to the product and causing a shift of solid material along the product. It can be static F tr st or dynamic F tr st.

Static– the maximum value that is achieved at the initial moment of shift of one surface relative to another, and is spent on overcoming the force of static friction (inertia) and the destruction of bonds between the material and the product (surfaces) formed during the period of preliminary contact. At the initial moment of shear, a transition occurs from a state of rest to uniform motion, accompanied by plastic deformations.

Dynamic– takes into account the force of sliding friction at a steady speed. At low speeds, and therefore accelerations, the dynamic friction force will be practically equal to the static one. The difference between dynamic and static force is inertial force R in.

True coefficient of external friction μ(static or dynamic) – the ratio of the corresponding external friction force ^F tr to the sum of normal contact forces N and separation (R 0 ∙ A 0) (1.26).

In some cases it is more convenient to operate effective coefficient of external friction μ ef:
μ ef = F tr/ N. (1.25)
This coefficient is related to the true coefficient of friction as follows:

. (1.26)
External friction depends on stickiness and a number of other factors (contact pressure, displacement speed, temperature, etc.), and the influence of these factors is ambiguous. To theoretically substantiate external friction, molecular kinetic, mechanical, physical and other theories similar to theories explaining adhesion have been proposed.
^ 1.3.3 Compression properties
Compression properties are used to calculate the working parts of machines and devices and to assess the quality of the product, for example, in tension and compression. These include volumetric and lateral pressure coefficients, Punch coefficient, elastic moduli and etc. In addition, a number of mechanical models (Maxwell, Kelvin, etc.) describe the behavior of the product under axial or volumetric deformation.

Density, as one of the compression properties, is an essential characteristic when calculating a number of machines and devices and when assessing the quality of the product. Average density ( ρ , kg/m3), for a relatively small volume is determined from the ratio:
ρ = M / V, (1.27)

Where: M– product mass, kg;

V– product volume, m3.
True Density equal to the limit of the mass-to-volume ratio when the latter tends to zero.

Between density ρ and specific gravity ( γ , N/m 3) there is a simple relationship:
γ = ρ ∙ g, (1.28)

Where: g– free fall acceleration, m/s 2 .
The density of a mixture of several components, when they do not interact, in which the composition or volume of the mixture changes, can be calculated from the dependence:

or
, (1.29)

Where: With i– concentration of one of the components in the mixture, kg per 1 kg of mixture;

ρ i– density of the component, kg/m3;

i– number of components.

Volumetric compression ratio (β, Pa –1) characterizes the change in volume (Δ ^V, m 3) of product when pressure changes (Δ R, Pa) per unit of its measurement.

For practically Newtonian structured liquids, it is almost independent of pressure and the duration of its action. For plastic-viscous systems, with increasing pressure the coefficient decreases and at sufficiently high pressures, for example at pressures (20 - 30)∙10 5 Pa, it reaches the value inherent in a dispersion medium, in particular water, since in many products of the dairy industry (curd mass etc.) it contains up to 70-75%.

The volumetric compression coefficient for Newtonian and practically Newtonian structured liquids is determined by the dependence:

. (1.30)
For plastic-viscous systems the coefficient β can be used as an integral characteristic depending on the duration of exposure and pressure on the product:

, (1.31)

Where: R– pressure acting on the product, Pa –1;

t– duration of pressure on the product, s;

ε V – relative volumetric deformation.
Lateral pressure coefficient ζ is the ratio of lateral pressure R b to the axial R o under the action of normal stresses in a closed volume:
ζ = R b/ R O. (1.32)
For Newtonian and structured fluids ζ = 1, and for plastic-viscous ζ < 1.

Under the condition of constant volume, for example, under uniaxial compression, the height of the body decreases and its transverse dimensions increase, which is characterized by relative deformations, which are interconnected through Poisson's ratio.

^ Poisson's ratio υ is the ratio of relative linear deformations, i.e. transverse to longitudinal in the range of Hooke's law, and characterizes the elastic properties of the product.

Elasticity– the ability of a body after deformation to completely restore its original shape, while the work of deformation is equal to the work of restoration.

Elasticity in tension and compression is characterized by the elastic modulus of the first kind ( E, Pa). To describe the elastic properties of products in various deformation zones (Fig. 1.11), classical concepts of elastic moduli are often not enough. Then you can apply modifications of elastic moduli: conditionally instantaneous, elastic, equilibrium.

^ Conditionally instantaneous modulus of elasticity represents the voltage ratio σ to the conditionally instantaneous truly elastic component of deformation ε 0 .

^ Elastic module is the voltage ratio σ to elastic deformation ε e.

R balanced (relaxation)ion) module is the voltage ratio σ to general elastic deformation ε unitary enterprise, when it is impossible to distinguish between conditionally instantaneous truly elastic and elastic deformations.

During technological processing, food materials are exposed to external loads that cause their deformation, as a result of which internal stresses arise in the material. Even at low stresses, the ratio between the elastic, viscous and plastic components of deformation does not remain constant, and a process that develops over time occurs in the material relaxation(resorption) of tension.

Maxwell first introduced the concept of stress relaxation in the late 70s of the last century. They gave an analytical expression for the process of relaxation of materials, based on the assumption of a directly proportional relationship between the rate of stress decrease over time and the magnitude of the acting stresses.

After Maxwell, F.N. studied the phenomena of plasticity. Shvedov, who developed the theory of elastic liquids, thereby laying the foundations of the rheology of dispersed systems. F.N. Shvedov gave the stress relaxation equation in the form of a function

, (1.33)

Where σ – voltage at time t, Pa;

σ 0 , σ k – initial and final stress, respectively, Pa;

T p – relaxation period, s.
Relaxation period (T p) – the period of time during which the material passes from a nonequilibrium stressed state to an almost equilibrium, steady state.

This equation puts into real form the idea expressed by Maxwell that plastic bodies flow within certain stress limits. Unlike Maxwell, who accepted that tension in the body relaxes to zero, Shvedov showed that any tension relaxes not to zero, but only to a certain limit σ k, which is the elastic limit or yield strength, below which relaxation should not occur.

The relaxation curves have two distinct sections, the first of which is characterized by a sharp drop in stress under conditions of a rapidly decaying relaxation rate, and the second is determined by a slow drop in stress with a very low relaxation rate. In the second section, the relaxation curve asymptotically approaches a certain straight line parallel to the abscissa axis and spaced from it by the amount of voltage at which practically no relaxation occurs.

The process of stress relaxation in food materials is accompanied by a process creep.

Creep–slow deformation of a body under the influence of a constant load.

The creep process is divided into two stages: the first is unsteady with a gradually decaying strain rate, the second is steady-state with a constant creep rate.

Stress relaxation and creep accompanying this process are types of plastic deformation. The occurrence of plastic deformation processes under stress relaxation conditions leads to a decrease in elastic properties and an increase in plastic properties. In turn, an increase in plasticity leads to a decrease in the energy spent on molding products, while the quality of the products improves.

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111. Rheological properties of freely dispersed systems

The main factors determining the structure and rheological properties of a disperse system are the concentration of particles φ (volume fraction) and potential of pair interaction of particles. Dilute aggregation-stable disperse systems, where the particles retain complete freedom of mutual movement or there is no specific structure, are Newtonian, their viscosity is calculated by Einstein's equation:

η = η 0 (1 + αφ ).

Where η 0 – medium viscosity; α – coefficient equal to 2.5 for spherical particles when they rotate freely in the flow.

Rheological properties freely dispersed systems: viscosity, elasticity, plasticity.

Shear stress created by external force F T goes entirely to overcome friction between layers of liquid and is proportional to the shear rate- This is Newton's law:

T = ηγ

Magnitude η = t/γ (viscosity) fully characterizes the rheological properties of a liquid in a laminar flow regime.

Viscous bodies differ from plastic ones in that they flow under any stress. The flow of ideally viscous bodies is described Newton's equation:

Where f– viscous resistance force; h– friction coefficient; u– linear flow velocity; X– coordinate normal to the flow.

A more general expression of this law is through shear deformation. In an elastic body, the work done by an external force T is stored in the form of potential energy of elastic deformation, and in a viscous medium it is entirely converted into heat. Part of the energy is dissipated, i.e. the material also creates viscous resistance to deformation. Such materials are called viscoelastic. An important rheological characteristic of a viscoelastic medium is the relaxation time of elastic deformations (time of shape restoration). In addition to the forces of viscous and elastic resistance to deformation, a number of materials have the ability to provide resistance similar to the force of external (static) friction. In dispersed and polymeric materials, a similar force arises simultaneously with viscous resistance; the total resistance is described by the equation:

T = T s + ηγ .

Magnitude η * = (t – t With) / γ is called plastic viscosity, and the material is called plastic. It is completely characterized by two rheological constants: T with and η *. Size T c is called the ultimate shear stress (yield stress). The behavior of a plastic material can be described by Newton's law, where η – a variable quantity, or the Shvedov-Bingham law with two constants ( T with and η *). Viscosity, according to Newton, takes into account all resistance depending on the rate of deformation. Plastic viscosity takes into account only part of the resistance.

Liquids and plastic-viscous bodies, the friction force of which does not obey Newton’s law, are called non-Newtonian(abnormal) liquids. Some of them are called Bingham liquids. Plasticity is the simplest (mathematically speaking) manifestation of non-Newtonian properties. The transition from creep to plastic and then Newtonian flow occurs gradually. Most often, the largest range of shear rates (from γ 1 to γ 2) falls on the area of ​​plastic flow. This determines the practical significance of the Shvedov-Bingham law and rheological constants η * And T With.

112. Rheological properties of coherently dispersed systems. Bingham's equation

The main method of rheology is the consideration of mechanical substances on certain models, the behavior of which can be described by a small number of parameters; in the simplest cases, rheology can be determined by only one parameter.

Elastic behavior- a process that can be characterized by the proportionality of stresses and strains, i.e., a sort of linear relationship between τ And γ . This dependence is expressed Hooke's law :

τ = Gγ,

Where G- elastic modulus cabin boy.

If depicted graphically, then according to Hooke's law the relationship between shear stress and displacement can be expressed by a linear dependence, the cotangent of the angle of inclination to this straight line will be Young's modulus of elasticity.

When the load is removed, the original parameters of the body are immediately restored; energy is not dissipated during the processes of loading and unloading the body. The process of elastic behavior can only be characteristic of solid bodies.

The nature of this phenomenon may lie in the reversibility of small deformations. The elastic modulus can depend on the nature of the interaction in a solid and is a very large value. The body may strive to recover with thermal movement that disrupts this orientation.

The elastic modulus also depends on temperature and can have a small value. Elastic deformation for solids can be determined and can occur up to a certain value, above which the destruction of the body occurs. This type of stress for fragile bodies characterizes strength.

Viscous behavior(or viscous flow), which can be characterized by the proportionality of stresses and the rate of deformation processes, is called Newton’s law:

T = ηγ 1 ,

Where t– shear stress; h– viscosity.

Once the influence of shear stress ceases, the previous shape of the body can no longer be restored. Such a viscous flow can be accompanied by energy dissipation, i.e., the energy that is dissipated in the volume of the body. Viscous flow is associated with the transfer of mass when exchanging places between atoms or molecules during their thermal motion.

An applied potential voltage can reduce the energy barrier for a particle to move in one direction and increase or decrease it in another. It can be assumed that the viscous flow process is a temperature-activated process and the viscosity will depend exponentially on temperature.

Plastic may present non-linear behavior. With this phenomenon, there is no dependence and proportionality between various influences and many types of deformation. Plasticity is a combination of both dislocation processes and the breaking and rearrangement of bonds between atoms. A plastic body, after stress is removed, retains any shape that was given to it during the process.

Bingham's equation:

The rate of deformation, which is described by the Bingham equation, must be proportional to the difference between both the effective stress and the ultimate shear stress. Moreover, the equation is based on a combination of the two simplest elements of rheology - the parallel connection of the viscous element and the Coulomb element of dry friction.

113. Rheological method for studying dispersed systems. Basic concepts and ideal laws of rheology

Rheology– a complex of knowledge and concepts that formulates laws and rules that allow us to determine the behavior of solid and liquid bodies. The main method that rheology uses is the consideration of the mechanical properties of materials on certain models, which are described by a small number of parameters.

Elastic deformation described by Hooke's law:

τ = Gγ,

Where t– shear stress; G– shear modulus (n/m 2); γ – relative shear strain.

The nature of the elasticity of each body lies in the reversibility of small deformations and bonds between atoms. The elastic modulus can be determined by the nature of interactions in a solid and is practically independent of temperature increases. The elastic modulus can be considered as a certain doubled amount of elastic energy, which is stored per unit volume with a unit deformation. Elastic deformation of a body can occur up to a certain limiting value, after which destruction of more fragile bodies occurs.

Strength– the property of a material to resist external influences under the influence of external stresses.

Viscosity described by Newton's law:

T = ηγ ,

Where h– viscosity (n/m2) – a parameter that is characterized by proportional stress and strain rate, and may also depend on the shear rate.

The viscosity of polymer materials can be accompanied by energy dissipation, i.e., a state when all the released energy can be converted into heat. Viscosity is a thermally activated process, and viscosity has an exponential dependence on temperature.

Plastic is a nonlinear element, there is an absence between impacts and various deformations. The plasticity of the material will be determined by the processes of rupture and rearrangement of interatomic bonds, for which dislocation is possible.

Internal tension– parallel combination of an elastic element and dry friction.

Deformation– relative displacement in time of some points of the system being determined, at which there is no change in the continuity of the material.

Plastic deformation– deformation in which destruction of the material does not occur.

Elastic deformation– deformation in which the body is completely restored after removing a certain load.

Simulation must be carried out using real different models of bodies. When using the model approach, the full load falls on each element, and accordingly, the total deformation of the system or the deformation rate will be the sum of all types of deformations acting on the body and the velocities of all elements causing the system to move. If we consider the parallel connection of strain and velocity elements, they will be the same for all elements, and the entire remaining load of the system will be the sum of the loads of all elements taken together. If you use the rules of serial and parallel deformation, you can simply use different rheological models. If we expand the possibilities of characterizing quantitative properties for real bodies, we can use several ideal models. It was accepted that there is no difference between the rheological properties of real liquids, as well as solids. This can be explained by the fact that these systems are condensed states of matter.

114. Rheological models

There are three main cases of mechanical behavior:

1) elasticity;

2) viscosity;

3) plasticity.

By combining these processes and rheological process models, it is possible to obtain more complex models that will describe the rheological properties of a wide variety of systems.

In all cases, each combination will be considered in a certain deformation mode characteristic of this phenomenon, in which the properties of the models will manifest themselves in comparison with the properties of its elements.

1. Maxwell's model– sequential connection of elasticity and viscosity. The sequential connection of such elements can mean, according to Newton’s third law, that equal forces (shear stress) will act on the two components of the model τ ), and elastic deformation ( γ G) and viscosity ( γ η ) can be folded:

γ = γ G + γ ?,

Where g– general deformation.

In this model, it is possible to quickly deform to a certain value and maintain it at a constant level. At large values ​​of time, this type of system can be close in properties to a liquid, but when a shear stress is applied, the system can behave like an elastic solid.

2. Kelvin model– parallel connection of elasticity and viscosity. In such a model, the deformations of both elements can be the same, and the shear stresses will be summed up. Under constant voltage, the Kelvin model behaves differently. A viscous element cannot allow immediate deformation of the elastic element to occur. Then the overall deformation can gradually develop over time:

This equation corresponds to a gradually slowing deformation. The general stress is relieved due to the energy accumulated by the elastic element; here the process of deformation of the elastic body occurs, and energy dissipation occurs on the viscous element. An example of such models: damping of vibrations, primarily mechanical ones in rubber.

3. Input of a nonlinear element into the system. A model is obtained that describes the occurrence of internal stresses with a parallel combination of an elastic element and dry friction. If the applied stress in the system exceeds the yield strength, then deformation occurs, which may be due to the accumulation of energy in the elastic element.

4. Bingham model– parallel connection of a viscous Newtonian element and a dry Coulomb friction element. Since the elements are the same, their deformations will also be the same, and the stresses will add up. Moreover, the stress on the Coulomb element cannot exceed the limiting value of the shear stress.

It follows from this that the rate of deformation, which is described by a viscous element, must be proportional to the difference between the effective stress and the ultimate shear stress.

As rheological models become more complex, the mathematical apparatus for describing deformations becomes more complicated, so they try to reduce all types of stresses to simpler models. One of the methods to facilitate such tasks is the use of the so-called. electromechanical analogies, i.e. obtaining rheological models using electrical circuits.

115. Classification of dispersed systems. Newtonian and non-Newtonian fluids. Pseudoplastic, dilatant liquids and solids

It is known that there are many types of structural and mechanical properties that can reflect the diversity of both natural and synthetic bodies. Many systems are dispersed phases, which, in turn, have many different combinations of phases, differing in nature, state of aggregation, and particle size. The structural and mechanical properties of many dispersed systems are continuous and infinite series, which include both old and new ones that arise when considering the system. Research in the field of structural and mechanical properties was carried out by P. A. Rebinder , who proposed dividing substances into condensation-crystallized and coagulation structures. Condensation-crystallized structure formation can occur through direct chemical interaction both between particles and during their accretion to the formation of a rigid structure with a large volume. If the particles participating in the process are amorphous, then the structures that form in dispersed systems are usually called condensation; if crystals are involved, then the resulting structures are crystallized. Structures of the condensation-crystallized type can be characteristic of dispersed systems of the associated type, i.e., systems with a solid dispersed medium. The use of such structures gives the products strength and fragility, but they are not restored after destruction. Coagulation structures can be those structures that can form only during coagulation. When such structures are formed, the interaction between the structures can occur through all layers of the dispersion phase, and are van der Waals forces; the use of such structures cannot lead to the stability of the structure. The mechanical properties of such structures are determined not only by the properties of the particles that make up the system, but also depend on the nature of the bonds and layers between the media. Coagulation-type structures have a liquid medium; for such systems, it is important to restore the system after its destruction. In practical use, both one and other materials are characteristic, which make it possible to regulate the composition and homogeneity of the material, and in the process of technology, the formation processes are regulated.

Liquid systems are divided into two types:

1) Newtonian;

2) non-Newtonian.

Newtonian systems are called in which the viscosity does not depend on the stress arising during shear and can be a constant value. These liquids are divided into two types: stationary(for such systems, rheological properties do not change over time), non-stationary, the rheological characteristics of which are determined by the time frame.

Non-Newtonian These are systems that are not subject to Newton's law, and the viscosity in such systems depends on the shear stress.

Dilatant liquids– systems in which there is a large amount of solid phase, in which the chaotic movement of molecules leads to a decrease in viscosity due to disorder. As the load on such systems increases, the dense packing of particles may be disrupted and the volume of the system may increase, which will lead to an increase in viscosity in the system.

Pseudoplastic liquids– systems that are characterized by a decrease in Newtonian viscosity with an increase in the strain rate of the entire shear.

116. Viscosity of liquid aggregation-stable disperse systems

The foundations of this theory were laid by A. Einstein, who studied dilute suspensions. A. Einstein studied hydrodynamic equations for all solid particles that have a spherical shape, which can acquire additional rotational motion. The dissipation that occurred in this case was the reason for the increase in viscosity. A. Einstein derived an equation that relates the viscosity of the system η and the volume fraction of the dispersed phase φ :

η = η 0 (1+ 2,5φ ).

When deriving the equation, the assumption was made that the system may not be compressed; there is no sliding between particles and liquid. The experiments that A. Einstein conducted many times confirmed his assumptions; he established that the coefficient that stands for the parameter of the fraction of the dispersed phase depends only on the shape of the particles.

From the theory of A. Einstein, we can conclude that dilute and stable systems are Newtonian liquids, their viscosity linearly depends on the volume fraction of the dispersed phase and does not depend on dispersity. The parameter 2.5 is generally larger for some particles. This is explained by the fact that the rotation of a non-spherical particle exceeds the volume of the particle itself. Such a particle has high resistance, which can increase the viscosity of the system. If significant deviations from the spherical shape occur, the system can turn into a non-Newtonian fluid, the viscosity of which depends on the shear stress.

Einstein's equation does not take into account the presence of surface layers (adsorption, solvate) on particles. An increase in viscosity may occur due to the presence of such layers. The surface layers do not change the shape of the particles; their influence is taken into account when the volume fraction of the phase increases. This theory was further supplemented by G. Staudinger, who used it to describe the viscosity of dilute polymer solutions. Staudinger equation:

η beat = KMc,

Where TO– constant characterizing the polymer; M– polymer mass; With– mass concentration of the polymer.

G. Staudinger suggested that as the polymer chain lengthens, its volume of rotation increases and the viscosity of the solution increases at the same concentration. The viscosity according to the equation does not depend on the concentration of the polymer solution and can be proportional to its molecular weight. An equation derived by G. Staudinger is used to determine the molecular weight of a polymer. This equation can only be valid for solutions of polymers with both short and rigid chains, while maintaining their shape. But the most commonly used equation to determine the mass of a polymer is Mark-Kuhn-Houwink equation:

{η } = K.M. α ,

Where α is a characteristic that can reflect the shape and density of a macromolecule; the values ​​of this quantity do not exceed one.

It follows from the equation that the higher the voltage in the system, the greater the unfolding of polymer molecules and the lower their viscosity becomes. This is due to an increase in the degree of dissociation of polymer materials upon dilution, which increases the growth of the charge of the molecule and increases its volume. In solutions of any polymers, intermolecular interaction can lead to a sharp increase in the viscosity of the system; at the same time, the viscosity can be determined by the effective volume of the particle per unit mass of the polymer. This is true for all polymeric materials for which the viscosity of the system can be determined.

117. Complete rheological curve of disperse systems with a coagulation structure

A sharp change in viscosity occurs for cohesively dispersed systems with a coagulation structure. In this consideration, a whole spectrum of values ​​is used between two extreme states of the system: with an indestructible or completely destroyed system. When considering the applied shear stress, the rheological properties of such systems vary over a very wide range, up to Newtonian fluids. This dependence of rheological properties on coagulation can be represented in the form of a rheological curve.

Rheological curve represents the dependence of the ultimate strain on the shear stress.

When studying the relaxation properties, it was discovered that at low shear stresses an elastic effect occurs, which is associated with the mutual orientation of the particles; they are characterized by thermal motion. High viscosity values ​​can be caused by the flow of a dispersion medium from cells that decrease in size into neighboring cells through narrow passages and when particles slide relative to each other.

When a certain value of the limiting shear stress is reached, a region of slow but viscoplastic flow or, as is commonly called, creep may appear.

1. In this area, a shift occurs, which occurs during fluctuations and is destroyed, but can be restored under the influence of externally applied stresses. In this case, all particles are combined into a single coagulation structure, which experiences fluctuations relative to their position in the contacts.

2. In this section, creep of the system occurs, which can be described by a rheological model of viscoplastic flow at low ultimate shear stress and sufficiently high viscosity.

3. In the third section of the curve, a flow region of an energetically destroyed structure is formed. This region can be described using the Bingham model.

4. At this stage, the properties of a Newtonian fluid appear, the viscosity of which is increased. With a further increase in voltage, a deviation from Newton's equation may occur, which is associated with the phenomenon of turbulence.

The rheological properties of the system can change when exposed to vibration. When analyzing the rheological curve, one can come to the conclusion that even very complex mechanical behavior of the system can be divided into several simple sections, which will be determined by a simple model.

To achieve equilibrium between the processes of destruction and restoration of contacts, a sufficiently long deformation of the system at a constant speed is necessary, which is not always possible in practical work.

But at the same time, phenomena with different molecular mechanisms, such as creep and viscoplastic flow, can be described by the same model, but with different parameters. The rheological characteristics of dispersed systems can change greatly when exposed to a vibration field.

Vibration can cause the contacts between particles to break down, resulting in liquefaction of the system at very low shear stresses. The rheological curve in modern technology using vibration allows you to see how you can control the different properties of dispersed systems, such as suspensions, various pastes or powders.