The scientific hypothesis is the ability to solve the problem of high energy consumption for homogenization of milk by using a stream homogenizer with separate cream feeding. In such a homogenizer, when the fat fraction is fed into the stream of skim milk, a high difference of phase velocities is created between the dispersed and dispersive phases of the emulsion, which makes it possible to achieve higher values of the Weber criterion than in other types of homogenizers.

For the experimental research of the SHSCF, an installation was developed, the scheme of which is presented in Figure 2 (Samoichuk and Kovalyov, 2011; Samoichuk and Kovalyov, 2013).

Skim milk goes through the pipeline from the container 2 through the pump 1 into the homogenization chamber 4. From the tank for cream 12, with the pump 7 through the channel 11, the fat phase is supplied to the central zone of the homogenization chamber in the stream of skim milk, where the process of dispersion takes place.

To increase the flow of skim milk in the homogenization chamber, stream guides 5 made of stainless steel were installed, which are secured by hinges 10 and have adjustable rods to adjust the distance between the guides. The housing of the homogenization chamber is made of organic glass for process monitoring. A gauge 3 is required to control the fluid pressure values. In the container 2 there is an opening for draining the residues of the product. The finished product is poured into the container 8.

Prior to submission to the SHSCF, the milk is divided into skim milk and cream. Skimmed milk is fed under pressure at a certain rate, which increases in the central area of the device due to the narrowing of the flow, the value of which can be adjusted by rods. In the place of greatest narrowing, cream is supplied through a thin channel which diameter is 0.6 – 0.8 mm (Samoichuk and Kovalyov, 2013; Samoichuk, Kovalyov and Sultanova, 2015). The channel of such a small diameter creates minimal flow resistance and allows the flow of cream with a thin stream. By varying the flow velocity in the cream feed zone, the distance from the end of the cream feed channel to the edge of the narrowing channel and the cream supply it is possible to investigate their effect on the quality and energy consumption of the milk fat dispersion process.

Figure 3 presents a general view of the laboratory unit for studying SHSCF.

In the central part of the chamber 3 (Figure 3), at the place of maximum narrowing, radial channels for feeding the fat phase are made.

Thus, thin streams of cream are fed into the high-velocity stream of skim milk, which creates the conditions for high-efficiency dispersion of milk fat – a high difference in velocity of phases (velocity of sliding the fat globule relative to the dispersion medium), which by Weber's criterion is the main parameter of the disruption of fat globules of milk.

The main parameter that determines the dispersion of the milk emulsion after treatment in SHSCF (Figure 4) is the relative velocity of the dispersed and dispersive phases, which is most influenced by the velocity of skim milk stream ʋ_sm, the velocity of the flow of cream ʋ_c, the diameter of the feed channel of cream d_c and its fat content F_c.

For the experimental studies, whole milk was used (DSTU 8553:2015). Density 1027 – 1023 kg.m^-3, fat content 2.5 – 4.4%.

The average diameter of the fat globules of the emulsion (d), which should be provided as a result of homogenization, is 0.8 – 1.2 μm, which is sufficient for modern technological processes of milk processing.

The temperature of homogenization of milk was provided within the range of 60 – 65 °C. Numerous studies show that this temperature is optimal for the dispersion process. The minimum surface tension of the fat globule and the viscosity of the milk is ensured, the fat fractions go into the liquid state and no undesirable changes of properties occur under the action of high temperature (Ion-Titapiccolo, Alexander and Corredig, 2013).

The dispersive indices of the milk emulsion were determined by computer analysis of micrographs of milk samples obtained with an optical microscope and a digital camera Mustek Wcam 300 (resolution 640 x 480). Each experiment was repeated 3 times. From each experiment, 3 samples were selected and 2 dilutions were prepared from each sample. 6 characteristic microscope field of view photos were selected from each dilution. Thus, 36 microscope fields of view were analyzed to determine statistical characteristics of milk.

The method of analysis of geometric characteristics of fat globules based on digital image analysis technologies was used to analyze the obtained micrographs.

The number of fat globules in the microscope field of view and their diameter were determined in the process of calculations. The average diameter of the fat globule was determined by the statistical method of power average (arithmetic mean).

For this purpose, the software module has been developed that is implemented in Microsoft Visual Studio 2013 based on C # using the OpenCV Sharp library set 4.2.0. The exported numerical data and the calculation of the sample statistics were performed in Microsoft Office Excel 2013. McBrain VA 318 electric wattmeter (Volga region plant of power equipment, Russia) was used to record power.

The main influential factor in the dispersion of the fat phase in the SHSCF is the rate of flow of skim milk, the change of which was varied by the supply of skim milk Q_sm. The results of the experimental studies and their comparison with the theoretical ones by the formula (Samoichuk and Kovalyov, 2013; Samoichuk, 2018) are shown in Figure 5.

As shown by the obtained data, the change in the distance between the guides (the area of intersection of the working chamber) has virtually no effect on the dispersion of the milk emulsion, which is consistent with the results of theoretical studies (Samoichuk and Kovalyov, 2013; Samoichuk, 2018).

The slight increase in the size of the fat globules at а = 1 mm (by 2 – 5%) is explained by the increase in the Reynolds coefficient and the fluid turbulence. Increasing turbulence can be the cause of inefficient power dissipation, which is consistent with the results of the stream apparatus study (Abiev, 2000). For SHSCF, the main factor in the disruption of fat globules is the sliding velocity of the fat globules, which increases as the flow rate of skim milk increases. To obtain an average size of fat globules of 0.8 μm, it is necessary to provide a skim milk velocity of 60 – 65 m.s^-1.

The experimental data are in good agreement with the theoretical data at critical Weber number We_k = 130, coefficient of SHSCF (Samoichuk, 2018) kc = 0.7 in the range of 35 <υ_sm <70. However, the true critical Weber number can only be calculated after the experimental determination of the stream dispersion coefficient.

At a velocity of more than 70 m.s^-1, the dispersion is hardly increased. Similar is the graph of the dependence of the dispersion on the pressure for the valve (Rovinsky, 1994; Loncin and Merson, 1979), pulsation homogenization with a vibrating rotor (Samoichuk et al., 2016) and flow-stream (Samoichuk, 2018) homogenization, which testifies to the similarity of the mechanisms of dispersion of fat globules in them.

The use of higher fat cream increases the dispersion of the homogenized emulsion (Figure 6). This is due to the increase in the velocity of sliding fat globules of cream due to the decrease in the amount of plasma fed together with the cream. The dashed line shows the relationship between the size of the fat globules and the velocity of the cream in the disruption of the fat globules similar to the valve homogenization according to the formula by N. V. Baranovsky (Rovinsky, 1994). If υ_c >80 – 100 m.s^-1, the valve dispersion is the dominant principle of dispersion – the value of dispersion is close to that calculated by Baranovsky's formula.

In the range of 40 <υ_c <80, the sizes of fat globules are maximal, and at υ_c <30 m.s^-1 they are reduced by 6 – 10% (Samoichuk, 2018). The decrease in dispersion at the velocity of the stream of cream more than 30 m.s^-1 can be explained by the presence of a steady stream of cream, which is destroyed only at the chamber wall which is opposite to the location of the channel of the cream. In this zone, the velocity of the skim milk stream is minimal, which results in lower values of the flow rate of fat globules.

If you do not take into account the dispersion of the type of valve homogenization, which is energy inefficient (in the range of 20 <υ_c <80 m.s^-1), the highest degree of homogenization in SHSCF can be achieved at υ_c <20 m.s^-1. By predicting with Excel spreadsheet tools at υ_c <5 – 10 m.s^-1, the coefficient of influence of the flow velocity of the cream, SHSCF has a maximum value k_υ = 1.At 40 <υ_c <80 k_υ =0.75 – 0.80, and at 20 <υ_c <40 k_υ = 0.8 – 0.85.

Reducing the diameter of the cream channel leads to a decrease in the size of fat globules of milk (Figure 7).

This is due to the decrease in the central zone of the cream stream with a reduced flow rate of fat globules. Reducing the diameter of the channels from 0.8 to 0.6 mm leads to an increase in the dispersion by 8 – 10%. It is logical to assume that the maximum flow rate can be obtained by entering only one fat globule into the stream of skim milk. The maximum value of the coefficient of influence of the diameter of the channel of the fat phase will be at d_c = d. But testing this assumption in practice is difficult. The prediction made by Microsoft Excel (Figure 8) shows that at d_c = d the average size of fat globules is 0.26 microns, therefore the coefficient of cream feed channel diameter k_cd = 1 at d_c = 0.26 mm.

Then the formula for the definition of k_cd looks like

(1) k c d = 0.26 2.025 d c − 0.75 d c 2 + 0.2625

Example: at d_c = 0.6 mm k_cd = 0.46; at d_в = 0.7 mm k_cd = 0.44; at d_в = 0.8 mm k_cd = 0.43.

The graph of the dependence of the dispersion of the emulsion on the fat content of the cream (Figure 9) indicates a decrease in the rate of decrease in the size of fat globules with increasing fat content of cream (Samoichuk, 2018).

When the fat content of the cream is more than 40%, the dispersion of the emulsion is almost not reduced. The predicted minimum dispersion of milk is reached at F_c = 45 – 55%, where the coefficient k_cf = 1. For other values of the fat content of cream k_cf of the SHSCF are shown in the graph (Figure 10). In the range of F_c >30%, the values of the fat coefficient of stream dispersion do not differ for different d_c. At F_c <30% a significant effect is caused by the high turbulence of the flow and the mechanisms of disruption associated with the disruption of turbulent vortices, thus values of k_cf for d_c = 0.8 mm increase by 2 – 4% compared with d_c = 0.6 mm.

Therefore, to increase the degree of dispersion it is necessary to reduce the diameter of the feed channel of cream, use cream with a fat content of 30 – 50% and provide a feed rate of cream less than 30 – 40 m.s^-1 or more than 80 – 100 m.s^-1.

Thus, for the data shown in Figure 6, the coefficient of stream dispersion will be equal (at k_cd = 0.44; k_υ = 0.75; k_cf = 0.96) k_c = 0.44 × 0.75 × 0.96 = 0.32.

The critical Weber number corresponding to the experimental data is We_k = 28. Compared to opposite-flow stream homogenization (We_k^c = 500 (Samoichuk, 2008)), this value is much smaller. But a direct comparison of these values is incorrect due to the use of the modified Weber criterion for opposite-flow stream homogenization – that is such We_k, where instead of the velocity of the sliding of the fat globule, the flow rate of the milk emulsion is used.

According to the obtained data of the critical value of the Weber criterion and (Samoichuk, 2018; Samoichuk et al., 2019), the homogenization coefficient for SHSCF will be

K h = 28   x   0.024   x   0.1 8   x   980 6 3.14 3 = 3.300   x   10 − 6   m 3/2 . s -1 .

The importance of the obtained results is that this value is obtained for the disruption of the fat globule in "pure" conditions: subject to a single effect on the emulsion, without the influence of vibration and cavitation. Therefore, the value of К_h is the largest among other types of homogenizers. For example, for the valve homogenizer, high turbulence and cavitation have a significant effect on the dispersion of milk fat, leading to a reduction in K_h to 1100 × 10^-6 m^3/2.s^-1. For the pulsation homogenizer multiple treatments leads to a reduction in Kh to 225 × 10^-6 m^3/2.s^-1 (Deynichenko et al., 2018; Samoichuk, 2018; Samoichuk et al., 2019). For the pulsation homogenizer with a vibrating rotor, the influence of resonant phenomena, as well as the developed turbulence and cavitation in the gap between the rotor and the stator leads to a minimum K_h = 68 × 10^-6 m^3/2.s^-1 (Samoichuk et al., 2019).