In the study of the adsorption process in the stationary layer Shylov (Keltsev, 1984) introduced the concept of the dynamic activity of the sorbent. He, on the basis of a number of studies, proposed an equation that allows us to practically characterize the work of the sorbent layer under dynamic conditions. This equation links the length of the sorbent layer with the time of its protective action (the amount of bound substance) and has the form:

(1) τ = ΚL - t 0

Where:

τ ‒ time of protective layer property, min.;

It follows from the equation that the values of К and t₀ are empirical values for the practical characteristics of the interacting systems. The coefficient of protective action of K depends on the sorbent properties, interaction conditions, aerodynamic conditions and physico-chemical parameters of the flour-air mixture. The presence in the equation τ0 is due to the fact that, owing to the high and constant concentration in the flour, the adsorption property of the initial layer forming the velocity gradient region, is used in a short time and the time of the protective action per unit length of the layer influences less than for the subsequent layer.

In the work of other researchers (Braginsky, Begachev and Barabash, 1984) it is shown that the presence in equation (1) t₀ is regular and is a consequence of the short velocity of the adsorption process in dynamic conditions. This leads to the fact that the concentration conditions of any layer and the protective action time are different from the operating conditions of the subsequent layers.

Several of researchers indicate that the formation of the front of mixture does not end when dosed at a sufficiently large length of the layer and that the equation (1) only formally shows the adsorption process in dynamic conditions. However, this equation is the only one that allows us to characterize the system components interaction in dynamic conditions. The adsorption process is heterogeneous and consists of:

- diffusion of droplet molecules between sorbent particles to its outer surface;

The kinetics of the heterogeneous reaction is determined by the time course of its individual components, and the rate of the heterogeneous process coincides with the speed of the slowest process. Since the adsorption process itself is a purely superficial phenomenon, adsorption is practically instantaneous. Therefore, we can assume that the speed of the adsorption process is determined by the diffusion velocity, it means that it passes mainly in the diffusion region. In the diffusion region, all reactions have the first concentration of the reacting component at constant pressure. The constant of the reaction rate is the diffusion constant. So the expression of the external speed and internal diffusion can be represented by the equation:

d a 1 d τ = β 1 c 0 − c 1 and d a 11 d τ = β 11 c 1 − c 11

in general, the adsorption rate

d a d τ = β c 0 − c

Where:

β ‒ the mass transfer coefficient of;

The value is reversed β, the diffusion resistance is present.

1 β = R = R i n t e r n a l + R e x t e r n a l

To date, there is no complete theory describing the adsorption process in dynamic conditions. There are three points of view on the kinetics of the adsorption process. One author considers (Levich, 1952), that the velocity of the adsorption process is determined by the speed of external diffusion, others are derived from representations (Lykov, 1954), that the kinetics of adsorption is determined by the rate of internal diffusion. The third – to the corresponding period, the speed of the process is determined by external diffusion, and then – the speed of internal diffusion of the sorbent component. Consequently, the moment of these changes by different authors is determined differently.

Levich (1952) gave a general method for determining the diffusion flow from the surface. In his theory, the diffusion layer adopts an appropriate and quantitative definition: there is a convective and molecular transfer of matter on the outer boundary of the diffusion layer – one order of magnitude. The change in concentration c in the diffusion layer is determined by the differential equation:

(2) D ∂ 2 c ∂ y 2 = v x ∂ c ∂ x + v y ∂ c ∂ y

Where:

v_х і v_у projections of fluid velocities.

On the basis of literature data and research analysis, the third point of view most correctly display the essence of the adsorption process in dynamic conditions. Despite the large number of works that display the essence of the adsorption process, to date, in the literature on the adsorption of flour in the liquid phase, there is no rational calculation methodology. Using the methodology it would be possible to use the design of new constructive and technological parameters of the machine, to establish ways to intensify the mixing of components and to select the optimal conditions for conducting the technological process.

Modern food technologies are developing in the directions of technological processes intensification, therefore, it was necessary to obtain new experimental data for the qualitative design of modern types of mixing equipment, taking into account the filling of the working chamber, its length or contact area to ensure rapid concentration change.

In his writings (Lykov, 1954; Strenk, 1971)notes that the creation of a qualitative mixture is not equivalent to obtaining a uniform concentration of solids particles in the liquid throughout the volume of the apparatus. Often is hard to achieve this, but it is not necessary. The uniform concentration of the suspension in the entire volume of the mixer does not matter, but it is important that all solids are kept in a suspended liquid. Therefore, it is necessary to create a large turbulence of the liquid around the grains in order to reduce the thickness of the laminar layer on the boundary of the liquid ‒ solid.

A typical technological process associated with the formation of structural systems is the process of adsorption. Therefore, new advanced technological methods of interaction of the solid phase with gas, liquid phases in the heavy (boiling) layer and adsorption in the fluid layer (hypersorption) appeared in the food and pharmaceutical industries. The rapid growth of the technique of adsorption requires further researching of the statics and kinetics of the adsorption process for its use in various conditions, especially when mixing the components (Pawel et al., 2016).

The mixing process is considered as a purely mechanical process of mutual penetration (particles of a continuous medium with the same physical properties between particles of a continuous medium and other physical properties) in order to obtain a homogeneous continuous medium with new properties that differ from the properties of the mixed enviroments.

Mixing water and flour is a heterogeneous process. The speed of heterogeneous processes depends on the surface of the interphase contact and on diffusion. The increase in the reaction rate is mainly due to the renewal of matter on the contact surface of the phases, since the diffusion rate is negligible. The heterogeneous reaction consists of several successive stages. For example, the reaction between the liquid and the particles of flour passes through the following stages:

- supply of molecules of any reagent from the solution to the surface of the phase separation;

The resulting velocity of the entire process is determined by the speed of the last stage – the volume mixing in the working chamber of all components. If this stage is a chemical reaction, mixing is used to align the concentration field. In this case, a large circulation is required. Therefore, the main attention must be paid to the researching of the heterogeneous system structure formation in a mass condition under the influence of mechanical, vibrational, gravitational, hydrodynamic factors. It is necessary to use a combined method of research: theoretical and experimental. On the basis of research, to obtain mathematical models that allow to substantiate the structural, technological parameters and the mechanism of the adsorption process for the design of new mixing machines.

The mechanism of structuring is of fundamental importance for mixing components with given properties. There are several mixing mechanisms. The first one, when the diameter of the formed droplet of the emulsion is up to 20% of the diameter of the center of structure formation. Drops as a heat-carrier, due to adhesive-sorption forces, are fixed on flour particles, and due to their interaction, an intense penetration of the liquid occurs and the formation of a new layer of solid components on the surface of the mixture.

The second option when the diameter of the formed drop is more than 20% of the diameter of the center of structure formation. The solution forms a pellicle on the surface of the flour in the zone of intense heat-mass transfer and, a new layer of the mixture is formed (Figure 1). In case of exceeding the critical value of moisture content, the mixture is destroyed due to the reduction of strength and drains over the walls of the working chamber, or due to the creation of liquid bridges appear agglomerates.

Both methods of mixing are determined by the method of introducing the liquid phase into the apparatus and the hydrodynamic regime of the fluidized bed. To ensure the layered growth of the forming mixture structure forming, the required diameter of the liquid droplets should not exceed 300 μm. So, the presence of a dispersing device that can distribute a heterogeneous liquid phase inside a fluidized bed, and providing a predetermined droplet size, is a prerequisite for mixing the components in the design of a new machine.

The use of a fluidized-bed technique with mechanical stirring allows you to obtain a suspension with a uniform distribution of components throughout the volume of the working chamber of the machine. This multifactorial process with stochastic nature requires complex mathematical modeling (Neuvazhaev, 2000).

A significant number of transported substances in the environment, changes in their concentrations, the interaction between them and microorganisms, the presence of stimulants, etc., lead to relative instability of the system. Under these conditions, there is an understanding of which direction should assess the effects of individual factors. At first glance, it may seem that in best case should meet the maximum satisfaction or security at the upper levels of the factors of influence. However, the negative effects should also be programmed, for example, by the values of osmotic pressures, double and triple effects of factors, deterioration of quality indicators, etc. Evaluating the effects of changes in concentration (composition of factors), is more difficult. The results of transformations of physical factors determined from this point of view are not enough. If the influence of temperature is carefully observed, then there is no complete point of view relative to the change in the concentration in the layers of the movable components.

The change in the concentration of dissolved flour in the liquid phase of the environment means decreasing of the osmotic pressure and increasing the mass transfer mechanism at the interface between the surfaces of microbial cells and the liquid phase of the environment.Dynamics of changes in the direction of concentration in the three-phase system is possible due to forced mixing. Such effect on the formed environment is one of the most rational, since its manifestations relate to the total volume of the formed medium with the complete exclusion of local zones without their features. The implementation of transient processes based on concentration in three-phase systems is possible due to the successive synthesized gas and solid phases, which have signs of energy-saving technology.

The presence of complete flour interaction at the level of the state of saturation in the liquid phase establishes on their surfaces the separation of the phases of the gas-liquid-solid body and in the liquid film, which causes the main change in concentration, the resistance of the mass transfer, the acceleration of dissolution. Therefore, the speed of the mixing process is not only external, but also corresponds to the essence of the physical and chemical phenomena that occurs when mixing the components. Indeed, the mixing process should be considered as adsorption of flour to moisture with the help of mechanical influences.

Such a conclusion deserves an experimental review and development of proposals for use. A special need for effective flour disintegration technology refers to technologies in which partially exist an intensive aeration process that impedes their productivity and efficiency. However, the peculiarities of phase synthesis in blending machines practically remain aside from these studies. The latter relates to the change in the concentration in the layers of the high-altitude unevenness of the interacting components in the working chamber, the holding capacity and high-altitude gradient of solubility of the flour. It is important that in both these directions should expect to increase the efficiency of technological processes.

The generated impulse energy impacts on the basis of accumulated energy potentials when mixing components in the baking industry should lead to a limitation of material losses. The realization of phenomena of change in concentration in the formed media in the mixing technologies should be considered at the level of the simulation method.

The research process included the mixing of ingredients at different modes: the rotational speed of the shaft, the geometric dimensions of the working body, the distance between the working body and the bottom of the working chamber.

To determine the existence of a functional dependence describing the kinetics of some features of the adsorption process in a weighted state, a researhing was conducted on the physical model (Figure 2) in the TNTU laboratory.

According to the design features of a new mixing machine designed, the free-fall flour is doped into a cylindrical chamber 1 and is wetted downward by a sloping jet of liquid components 6. The jet of liquid components is formed by a pressure device with nine holes in the form of nozzles. The components are supplied from the dispenser of liquid components 4, which is experimentally installed at a certain height so that the prescribed dosage amount is dosed within 1 – 1.5 minutes.

For the control of leakage velocity, duration and quality of liquid components sputtering, the researching of dynamic activity in a curved state on the dispenser of liquid components was performed. The speed was changed from 2 to 3 L.min^-1, it corresponded to the speed at which the absorbent layer passed to the suspended state. The supply pressure of the components was controlled by the installation height of the dispenser.

In our experiments, the way of studying the heterogeneity of the distribution of solid particles of flour in the stream was chosen by analyzing the photos obtained on the microscope. Technologies of automated image analysis in the technological process allow to shorten the time and increase the accuracy of product quality control. The processing of digital images is a rather vivid and obvious example of conversion and analysis of measurement data, which are widely used in industrial systems of machine vision.

The light scattering phenomenon is at the basis of optical methods for estimating the size, concentration and structural and morphological features of agglomerates of the disperse phase. The main methods for the investigation of disperse systems using this phenomenon are electronic ultramicroscopy.

For data processing automation, a microscope, a digital camera, which provides image registration at predetermined intervals, image capture devices and digital camera control, is used. Also, software is used to interpret the information received in a convenient way.

Pre-ferment obtained for different mixing modes was examined. The main controlled parameter is the discretepulse input of components into the middle of the working chamber, which depends on the design parameters. The mixture was prepared by the developed method – mixing in a weighed condition with the influence of the container working bodies, which created the internal circulatory contour of the components in the chamber. After every 30 seconds of the process, by use the probe, five samples of a mixture of different parts of the volume of the working chamber were selected. Further samples were explored on a microscope.

Figure 3 shows an example of a 600x magnification shot using a biorex Konus-3 microscope and a Sigeta UCMOS 5100 digital camera with a resolution of 5 megapixels in the automatic shooting mode open in the ToupView program area.

The next step is to bring the digital image to the physical units of measurement using a scale based on the digital image of the measuring line with the same magnification factor.

Since the color of the sample is not interesting for further research, to facilitate further transformations, the photo was transformed into shades of gray.

Compared to the results of the visual analysis, while processing a part of the objects is lost. The main problem is the presence of unclosed areas that are not properly processed by the program. Therefore, various combinational lighting options were used to improve the "relief" of the image and the exclusion of "illumination", as well as the multiple use and combination of software filters. In Figure 4 are represented processed micrographs of samples.

The research results are mathematically processed using software packages: Excel, MathCAD.

Given the chaotic interaction of the components during their mixing, where the change in concentration occurs between the working plates, in the space of the working chamber and its surface, the task of planning the experiment with the use of a full factor experiment of the second order is drawn up. With two factors, the model of the experiment's function has the form: у = f (x₁ . x₂)

According to the results of the experiment, we obtain a regression equation of the second order.

y = b 0 + b 1 x 1 + b 2 x 2 + b 11 x 1 2 + b 22 x 2 2 + b 12 x 1 x 2

To conduct experiments a plan with corresponding matrices of experiment planning with the number of experiments and boundaries of factors change has been prepared. The matrix is a list of options taken in this series of experiments. Independent variables were chosen from the analysis of the nature of the effect on the change in concentration. As the optimization parameter, the frequency of rotation of the plate working body and their number on the shaft.Accordingly accepted: у₁ – number of turns of the working body; у₂ – n umber of working bodies. Experiments were conducted on the basis of mathematical planning (Table 3). Determining which factors influence on the change in concentration, determine their level variation and step of variation. The main factors and the equation of variation is given in the Table 2.

У₁ – change in the concentration of components in the height of their mixing in the gap between the plates. The height of mixing of the mass of components was recorded during the process by the method of visual control on a scale applied to the working camera.

У₂ – change in the concentration of components by mixing them in the working chamber. The mixed mass of components was selected by the sampler and recorded by the method (visual inspection according to the photographs).

У₃ – change in the concentration of components upon completion of their mixing in the working chamber.

On the basis of experimental data of mixing intensification, mathematical processing was performed using an application StatgraphicsPlus XV.1

According to the data of the dispersion analysis, the influence of the factors of the experiment is statistically significant at the value p = 5%( (for example: p <0.05).

Influence of independent variables on output parameter У₁. The greatest influence on the change in the concentration in the gap between the plates has the effect of their amount on the shaft (Х₂) (р-value for У₁ = 0.0017).

Table 4 shows the regression coefficients obtained during the mathematical processing of experimental data.

Using the obtained data of regression coefficients, we make a regression equation for У₁

y 1   =   0.125556   -   0 .0166667X 1   -   0 .0266667X 2   + 0 .0066666X 1 2   +   0 .0X 1 X 2   -   0 .00333333X 2 2

Experimentfailedfor У₁ = 0.0001111

Influence of independent variables on output parameter У₂. The greatest influence on the concentration change in volume has the influence of rotation frequency of plates on the shaft (Х₁) (р-value for У₂ = 0.0338).

Table 5 shows the regression coefficients obtained during the mathematical processing of experimental data.

Using the obtained data of regression coefficients, we make a regression equation for У₂

y 1   =   70.8889   -   0.283333 X 1   -   0.633333 X 2   − 0.183333 X 1 2 − 0 .2X 1 X 2 +0 .266667X 2 2

Experimentfailedfor У₂ = 0.104

Influence of independent variables on output parameterУ₃. The greatest influence on the change of concentration in volume has the influence of rotation frequency of plates on the shaft (Х₁) (р-value for У₂ = 0.0001). Table 6 shows the regression coefficients obtained during the mathematical processing of experimental data.

Using the obtained data of regression coefficients, we make a regression equation for У₃

y 3   =   83.5556   -   9 .0X 1   -   9 .83333X 2   +   1 .6666X 1 2 +   2 .25X 1 X 2   -   1 .83333X 2 2

Experimentfailedfor У₃ = 1.52

The results of the computational experiments allowed to study the kinetics of changes in the concentration of components in the volume of the working chamber. The rational constructive parameters, which contribute to the intensification of the process of mixing the components, are determined.

Today there is information about the mechanism of mixing in laminar mode, which proves in the complex movement of the exchange process. In the presence of circular motion of a fluid in a cylindrical working chamber, on the turns of the flow at its transition from the central zone to the reverse, this sharp change in the direction of flow leads to a restructuring of the profile of velocity and the appearance of landslide deformation, which facilitate the mixing of the components. Therefore, the difference between the existing mechanisms of mixing and mixing in a closed profile channel (Figure 5) is considered.

The influence of the physical nature, dispersion, the content of the mixture on the section forming the circulating circuit and the design parameters of the machine at the stage of the mixing process is relevant.

It is also necessary to justify the basic laws of improving the technological requirements and parameters of this process.

Accelerated in the air, a stream of liquid components is found with spray particles of flour during its free fall, partially takes it, hits the walls of the cylindrical chamber and the rotating plate of the working body (Figure 6).

Liquid components, getting on TRO, are sprayed and get an extra speed, which contributes to a greater number of wetted particles of flour. The particles are pressed against each other, mixed, and their speed is lowered at the bottom of the camera. Due to the cylindrical configuration of the working chamber, the jets (emulsions) are automatically lowered, where the surface of the working body acts on them. In this case, the time from the moment of entering the flour and liquid components into the chamber and until they reach the bottom of the chamber is τ1 = 5 – 10 s.

In the first period of time, the adsorption process is heterogeneous, which determines the first and second stages of mixing. We will assume that the process of adsorption is a purely superficial phenomenon that occurs instantaneously. This allows us to assume that the velocity of the adsorption process is determined by the diffusion velocity at constant pressure (atmospheric). Therefore, a number of questions regarding the pre-ferment blending process of free fall in the first stage have not yet been resolved and require further consideration.

When adsorbed in a working chamber, where the kinetics of a heterogeneous reaction is determined by the concentration of components and process conditions, the rate of the adsorption process is determined by the diffusion velocity, that is, the entire process occurs predominantly in the diffusion region, which is divided into two periods. The first period of adsorption – a period characterized by the amount of liquid components that the adsorbent – flour – perceives during time t1 to the contact surface of the working body and the mixing chamber. This plot is shown in Figure 5.

The first period – from the moment of the delivery of ingredients and until the completion of one of them – flour. The liquid components are dosed for 20 – 30 seconds longer. This period can be combined with the submission and termination of the ingestion of doses; then the second period in our case will be very short, but without the necessary effect of adsorption. Structure of flour streams from flour vibrator (VDB), flows of liquid components from the membrane dispenser of liquid components (MDRCs) when rotation of the container's working body, where the speed of the wheel is significantly greater thanthe speed of the mixture of components, in the working chamber of the mixing machinebetween the layers there is mixing not only in the places rotation of the flow, in the longitudinal displacement, in the boundary layer, but also in a significant part of the volume.

The working chamber has consistently connected zones with different mechanisms and level of mixing (Figure 5). The level of deviation of the heterogeneity of the solution of the local concentration C from the average (boundary) is considered that the smaller the value of the heterogeneity, the better the components are mixed. Since mixing occurs at its constant motion (weigth condition, mechanical action of the working body, vibration, gravitation), then it is expedient to apply the mathematical model (2) with the following boundary value problem at the first and second stages with the ideal mixing:

(3) ∂ 2 c ∂ x 2   ⋅   D L − ∂ c ∂ x ⋅ u = ∂ c ∂ t

With the initial conditions:

C x , 0 = 0 ,   ∂ c ∂ x x = L = 0 ,

Where:

с ‒ current concentration of the mixture components in the operating chamber;

The left side of the equation reflects the change in mass concentration in the pseudo-layer over the period of component dosing. The second part reflects a change in the concentration, fixed in time. Consider the scheme of the flow structure in weight mixing (Figure 5).

Based on the obtained data, mathematical calculations were performed to select the optimal function, which most likely reflects the dependence of the change in concentration on time from the mixing method at the first and second mixing stages.

Based on the concepts (Braginsky, Begachevand Barabash, 1984; Pirogov,Leonovand Shilov, 2008) of relative mass C and volumetric S concentrations of one of the two components in the solution and their interrelation, taking into account that the radial and longitudinal mixing is insignificant in straight lines of the initial and upstream streams, where the ideal mixing of the components takes place in a curved state and when they move into the working chamber and on the surface of the working body, and the ideal displacement in the process of centrifugal forces with longitudinal mixing, therefore, the process of perfect mixing of the first zone characterizes the dynamics of the concentration of concentrates which limited by time intervals up to 100 s.

The calculation of the change in the ideal mixing concentration in the working chamber volume is carried out by equation:

(4) d S d t = υ V S ′ − S

Where:

S and Sʹ ‒ current and equilibrium mixture concentration of components in working chamber,

The left side of the equation reflects the change in volumetric concentration in the pseudosilver for the period of component dosing. The second part reflects a change in the concentration fixed in space (volume) and speed when stirred in a stationary field. Then:

(5) d S ′ − S d t = υ V S ′ − S − d y d t = w ⋅ y ;   − ∫ d y y = ∫ w ⋅ d t ; − ln   y = w ⋅ t + C ; ln   y = C − w ⋅ t ; y = e C − w ⋅ t ,   S ′ − S = C 0 ⋅ e − υ V t ; at   t → ∞ ,   S → S ′ ; at   t = 0 ,   S = 0 ,   S ′ = C 0 ⋅ 1 ; S t = S ′ − S ′ ⋅ e − υ V t ,   S t = S ′ 1 − e − υ V t .

Initial conditions for the rate of flow of liquid components (ur) and flour (ut) to the mixing cylindrical chamber, kg.s^-1:

ur   =   2.05 90  ur   =   0.023 ut   =   3.55 60  ut   =   0.059  t=0,0.1   ..   240

Conduct the construction of graphical dependence of the volume velocity of flux changes in a chamber at given parameters:

u r c t = u r ⋅ t ⋅ i f   0 ≤ t ≤ 95 0 ⋅ i f   ⋅ ≤ t ≺ 5 205   o t h e r w i s e u t c t u t ⋅ t ⋅ i f   0 ≤ t ≺ 60 355   o t h e r w i s e u c t = u r c t + u t c t

Accordingly, the change in the maximum mass concentration in the volume of the mixture under given conditions:

v t   =   d dt uc t  vv   =   10 ss   =   ut ur   +   ut  ss=0.722

Algorithm for calculating the change of current and equilibrium concentration underthe conditions of the process in the working chamber of the machine (Figure 10, Figure 11, Figure13).

A general analysis of mathematical modeling and refined mathematical calculations of the rate of change in concentration shows (Figure 7, FIgure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13 and Figure 15) that at the beginning of the process flour and liquid components interact actively, with time the activity decreases and, starting from 20 s. dosing it turns out differently. The results of the researching (Figure 14) also indicate an intensive acceleration of the process at the initial stage, which confirms the assumption of the effect of mixing activity in the suppressed state with the help of the vibrational action of the VDB. This changes the physico-chemical properties of the components, which is essential for kineticallycontrolled processes.

The results of the researching and the analysis of the mathematical models of the process showed that the mass concentration is reached by 90 seconds of mixing. During this period, the first critical value is traced, where the curve has the first shift, which indicates that after 60 s the adsorption of the free surface of the flour ends and the absorption of free and bound flour begins.

Under different conditions of the process, it is observed that the volumetric consumption of raw materials (flour), which we can regulate with the help of a vibrating dispenser, significantly affect the change in concentration. It is also worth noting that the volume of the chamber is important, which can be changed during the research process. Such a change affects the creation of a larger contact, admired by the flow of liquid components.

From the scientific point of view, this is explained by the fact that at the beginning of the process, the adsorption bond is based on the molecular interaction of the flour with liquid components, which are the most strongly bound to the flour and are kept by the molecular force field on the external and internal active surfaces of the flour (Dolomakin, 2015; Scram, 2003). Adsorption moisture on the surface of the flour accelerates the concentration of the first period with the help of vibration action, which after 20 s of the process practically does not affect the intensification, since the formed liquid component layer, which continuously increases with time, these vibrations absorb.

It has been experimentally established that the impulses formed by the fluctuations of the dispenser lattice practically do not reach the free surfaces of the container's working body and the working chamber, but fade in the components layers. In this condition, the formation mass concentration increases the contact with the surfaces, reduces periodically the displacement with partial amplitude, but it accelerates the process.