This study hypothesizes that it is possible to increase the dispersion efficiency of a counter-jet homogenizer by installing an annular reflector.

This article aims to evaluate the effectiveness of dispersing milk in a counter-jet homogenizer with a reflector.

To achieve this aim, it is necessary to:

For experimental research, the reflector device was designed, the scheme of which is presented in Figure 1 (Samoichuk, 2008).

The device consists of a chamber 15, in which the nozzles 16 are installed. The bottom of the chamber is conical with a slope to the centre, where the hole for removing milk after homogenization is placed. At the top, the chamber is closed with a transparent lid 10 to allow the process to be monitored. The sleeves 17 for adjusting the position of the nozzles with radially located screws allow the distance between nozzles to be changed and their alignment. Nozzles are collapsible and can be replaced.

The creation of the required milk pressure is achieved by the gas cylinder 1 and cylinder 11, which are connected by the air duct 3. The pressure is controlled by the pressure gauge 5. The discharge valve 2 is used to fill the cylinder with gas from the cylinder. The milk is poured into the cylinder using the funnel 7, the hose 8, and the filling valve 6. The outlet valve 4 is necessary for the release of gas from the cylinder when it is filled with milk. The piston 12 prevents the diffusion of gas into the milk and, thus, a change in its properties.

The cylinder and nozzles are connected by hydraulic hoses 14. The division of the main milk flow from the cylinder into two equal flows is carried out in the tee 9. The main valve 13 is used to supply milk under the required pressure to the nozzles.

When performing the tests, the required volume of milk was poured into the cylinder through the funnel, with filling and outlet valves open. The main valve was kept closed. To create the necessary pressure in the cylinder, a GOST 8050-85 carbon dioxide cylinder was used. After opening the discharge valve (outlet and filling valves closed), carbon dioxide was supplied to the cylinder and the pressure in it increased to the required value. The device uses a manometer with a measurement limit of 100 kg/cm², accuracy class 0.75 according to GOST 2405-85. When the main valve was opened, the milk under the required pressure was sent to the nozzles, in which jets were formed. After homogenization, the milk was gravitationally discharged through a hole in the lower part of the chamber.

The main factors of the experimental studies were the excess pressure of the milk supply to the nozzles Δp and the diameter of the nozzle cone d_n. The distance between the nozzles a was taken to be equal to half the diameter of the nozzle cone (Samoichuk, 2008). The temperature of milk during homogenization was assumed to be 60 – 70 °C (Walstra, Wouers and Geurts, 2006). For counter-jet homogenization, the excess pressure is related to the modified Weber criterion We^o-s by the ratio:

(1) We o-s = 6 ρ p ⋅ φ 2 ⋅ Δp 10 6 σ f-p ⋅ ρ m ,

Where: ρ_p, ρ_m – density of milk plasma and milk, kg.m^-3; φ – hydraulic coefficient of jet speed; σ_f-p – surface tension between milk fat and plasma, N.m^-1; Δp – excess milk supply pressure, Pa.

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

The degree of homogenization of milk was determined by the formula (Loncin and Merson, 1979; Nuzhin and Gladushnyak, 2007):

(2) Hm =  d 0 d k ,

Where:

d₀, d_k – average diameter of fat globules before and after homogenization, μm.

Average diameters of fat globules and other dispersive indices of the milk emulsion were determined by computer analysis of the micrographs of milk samples obtained with an optical microscope and a Mustek Wcam 300 digital camera (resolution 640×480) (Samoichuk et al., 2020). Each experiment was repeated three times. From each experiment, three samples were selected and two dilutions were prepared from each sample. Six characteristic microscope field of view photos were selected from each dilution. Thus, 36 microscope fields of view were analysed to determine the statistical characteristics of milk.

The geometric characteristics of fat globules were analysed based on digital image analysis of the micrographs obtained.

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 fat globules was determined by the statistical method of power average (arithmetic mean).

The qualitative uniformity of the measured data set was estimated by the coefficient of variation V. For dispersed indicators of milk fat globules, the coefficient of variation is sufficient for V >0.6 (Haponiuk, Zander and Probola, 2015; Di Marzo, Cree and Barbano, 2016). When this condition is satisfied, the values of V are not given separately.

For this purpose, a software module has been developed that is implemented in Microsoft Visual Studio 2010 based on C# using the OpenCV Sharp library set 4.2.0. The exported numerical data and calculation of the sample statistics were performed in Microsoft Office Excel 2010.

A McBrain VA 318 electric wattmeter (Volga Region Power Equipment Plant, Russia) was used to record power.

For efficient operation of the annular reflector, the liquid flows after their collision with the annular reflector mustn't intersect with the main jets of milk (coming out of the nozzles) (Fialkova, 2006; Innings and Trägårdh, 2005). Otherwise, there will be a violation of the continuity of the main jets and a decrease in the degree of dispersion of milk emulsions. To meet these requirements, the annular reflector in the radial cross-section must have the shape of an equilateral triangle, the vertex of which faces inwards of the annular reflector. With this design, the jets reflected from the surfaces of the reflector are removed outside the main jets of milk, which is necessary to prevent their crossing (Figure 2).

To prevent the intersection of the main jets of milk with those reflected from the reflector, it is necessary to calculate the angle β (Figure 3).

(3) β=180 0 − arctg a D .

The counter-jet homogenizer with a reflector works as follows. Whole milk is fed into the nozzles under the required pressure, which depends on the required degree of homogenization. After passing through the nozzle cones, the milk jets meet, while the fat fraction of milk is dispersed and mixed. The coaxial arrangement of the jets allows the fullest use of the kinetic energy of the fluxes for grinding the dispersed phase (Huppertz, 2011; Samoichuk, 2008). After collision and homogenization, the product flow diverges in a fan shape perpendicular to the direction of the jets and hits the annular reflector. This results in the final grinding and partial mixing of the dispersed phase of the mixture (Nuzhin and Gladushnyak, 2007). After contact with the annular reflector, the mixture is reflected from it and enters the housing of the homogenization device, where it is gravitationally removed from the machine. Moreover, due to the properly calculated angle of the annular reflector β, the product streams after contact with the annular reflector are reflected outside the jets coming out of the nozzles, so that there is no intersection of the flows of non-homogenized and homogenized products. Thus, in the counter-jet homogenizer with a reflector, dispersion of the fat phase of milk occurs in two stages: when the jets collide with each other and when the secondary jets collide with the reflector. This allows fuller use of the energy of the flow of milk.

To determine the effect of excess pressure and the angle of the reflector on the degree of homogenization, an experiment was performed, the results of which are shown in Figure 4.

With increasing excess pressure, the degree of homogenization increases with parabolic dependence. At higher values of excess pressure, the growth of the response function (Hm) slows down. The prediction performed by the computer program Microsoft Office Excel 2010 (Lawrence, Klimberg and Lawrence, 2009) shows a maximum achievable degree of homogenization of 5.6 at an overpressure value of 7.4 – 7.5 MPa.

The optimal value of the angle of the reflector, calculated by the formula (3), is 130°. This achieves the highest degree of dispersion of the fat phase of milk – milk flow after reflection from the surfaces of the reflector is directed to the nozzle body and does not interfere with the free exit of the main jet from the nozzles. At an angle of the reflector β = 150°, the flow of milk strikes further on the body of the nozzles. In this case, due to the greater distance, the jet speed becomes smaller, so the efficiency of additional homogenization decreases. At an angle of the reflector β = 110°, the milk flow after the reflector intersects with the jets coming out of the nozzles, so the continuity of the milk flow is disturbed and its normal velocity component falls, so the decrease in the degree of homogenization is more significant.

The deviation of the values of the experimental curve of the modernized homogenizer in comparison to the homogenizer without a reflector is 15 – 20%. Indeed, the increase in the degree of homogenization with the reflector installed is due to more complete use of the kinetic energy of the milk flow in additional contact with the reflector and the nozzle housing.

Approximating the data of Figures 5 with a straight line, we obtain an expression that is identical in content to the known dispersion formula (Loncin and Merson, 1979):

(4) Hm = 0.9 ⋅ 10 − 6 Δp ⋅ φ 2

The coefficient of determination (R²) in the range of 2.5 <Hm <6.0 is 95%, and at Δр = 5.0 – 6.0 MPa and a degree of homogenization of 4.5 – 5.2, the difference between theoretical and practical data is minimal. At Δр = 6.5 MPa, this difference reaches 6% and with a further increase in excess pressure, it is possible to predict its rapid increase. In the range Δр = 2 – 3 MPa, there is an intensive increase in the degree of grinding of the fat phase of milk. Here, the deviation of experimental data from the specified (approximated) dependence is maximal. At the value of Δр <2 MPa, homogenization practically does not occur.

The critical value of the Weber criterion (the beginning of the grinding of the fat phase) corresponds to the range of excess pressure of 1.8 – 2.2 MPa, at which We = 500 – 600.

Therefore, the optimal parameters of counter-jet homogenization for d_c = 1 mm are: a = 0.5 mm and T = 60 – 65 °C. The value of excess pressure depends on the required degree of homogenization and is Δp = 6.5 MPa at Hm = 5.0.

The results of experimental determination of the degree of homogenization and Weber criterion, with nozzle cone diameters of 1.0, 1.5, and 2.0 mm, depending on the distance between the nozzles cones, are shown in Figure 6. The diameter of the cone does not affect the maximum degree of homogenization.

It should be noted that at a < d_c/2 the degree of homogenization is higher by 15 – 40% than that theoretically calculated (Samoichuk, 2008), and the velocity of the jets at a < d_c/2 corresponds to the calculated data. This can be explained by a more sudden change in the velocity of the fat globules after the collision of jets (which leads to an increase in the velocity difference between the fat globules and the surrounding plasma), due to the strict limitation of boundaries of the jet flow that is diverted by the edges of the nozzles (Samoichuk and Kovalyov, 2013). Therefore, the optimal location of the nozzles is at a distance equal to half the diameter of the nozzle cone (Samoichuk, 2008).

To determine the diameter of the annular reflector of the counter-jet homogenizer, the experimental study was conducted with reflector diameters D = 40, 50, and 60 mm. The results are shown in Figure 7.

It is optimal to use a reflector with a diameter of 50 mm as we obtain the maximum degree of fat dispersion. At D = 40 mm, the degree of homogenization decreases by 0.2 – 0.3, that is by 5%. This can be explained as follows. When using a reflector with a smaller diameter to comply with the formula (3), the angle β decreases and the impact on the reflector becomes more sliding, which reduces the degree of homogenization. At D = 40 mm, the degree of homogenization decreases by 0.5 – 0.6, i.e. by 10%. This is due to the increase in loss of flow velocity before the collision with the reflector.

Changes in the fractional composition of fat globules after counter-jet homogenization (Samoichuk, 2008) (at T = 65 °C, Δp = 3.5 MPa) and comparing them with homogenization with a reflector (at a pressure of 4 MPa and T = 65 °C) and whole milk (Dhankhar, 2014; Nuzhin and Gladushnyak, 2007; Oreshina, 2010; Haponiuk, Zander and Probola, 2015) are graphically represented in Figure 8, and micrographs of fat globules are shown in Figure 9.

Milk before homogenization is characterized by the following parameters: average diameter of fat globules d_k = 2.49 mm, dispersion σ = 1.66, coefficient of variation (the share of scattering of the trait relative to the average) V = 67% (Di Marzo, Cree and Barbano, 2016; Floury, Desrumaux and Lardieres, 2000; Hussain et al., 2017). Respectively for milk after counter-jet and countercurrent-jet homogenization with a reflector: d_k = 0.99 mm and 0.83 mm, σ = 0.51 and 0.47, V = 51% and 56%.

The value of the coefficients of variation indicates the reliability of the data sample.

The average diameter of the fat globules for the counter-jet homogenization treatment with the reflector decreased by 19% (from 0.99 to 0.83 μm) compared to that with the non-upgraded homogenizer. The dispersion value also decreased, which indicates the advantage of counter-jet homogenization with a reflector.