Mathematical modeling of the diffusion process of liquid additives into extruded pellets of feed stuff for prime fish species
A mathematical model of the diffusion process of liquid components into extruded pellets of feed stuff for prime fish species under vacuum spraying is considered. This will increase the fat content up to 40% and improve the digestibility and nutritive properties of the feed stuff. It is suggested to use the differential equation of molecular diffusion with boundary conditions of the third kind to describe the process of diffusion of liquid in porous pellets. For a mathematical description, the solution of the equation of unsteady molecular diffusion for bodies with the geometric shape of an unbounded cylinder (extruded pellets can be considered such bodies) was used. The studies carried out with values of the Bio criterion over 100 showed that the concentration of liquid additives inside the extruded pellets becomes equal to the concentration of liquid additives on their surface. Given a constant concentration of liquid additives on the surface of extruded pellets, this solution takes place in the form of a rapidly converging series. Considering that for Fourier numbers greater than 0.3 the series converges quickly, then all the members of the series can be discarded except the first one. Thus, the obtained solution of the equation of unsteady molecular diffusion at a constant concentration of liquid additives on the surface of pellets had the form of a rapidly converging series. Taking the logarithm of the obtained equation and solving its Fourier criterion, we attained the expression for determining the duration of the diffusion process. Comparison of the calculated curves and experimental data showed that the root mean square deviation did not exceed 14.3%. The use of vacuum spraying of liquid additives on the surface of pellets made it possible to increase the diffusion coefficient from 4.78?10e-4 to 6.112?10e-4 м2/с in comparison with the traditional technology of pelleting in a drum apparatus.