A bi-dimensional diffusion mathematical model is proposed to study mass transfer in hollow fiber used for the concentration of juices by osmotic distillation (OD). The mathematical model was solved using the Finite Volume Method (FVM). The mass fraction at the boundaries was calculated by using the Functional-group Activity Coefficients (UNIFAC) method for the juice and by the Analytical Solutions Of Groups (ASOG) method for the brine. Calculated results were compared to an analytical solution for a case of mass diffusion in a cylinder with mass flow boundary condition. An algorithm to find the effective diffusion coefficient of gas through the membrane is proposed. To show its usefulness, different velocities were applied over the fiber surface to study the bi-dimensional effects that this velocity field has on the mass transfer inside the fiber. The results showed a maximum error of 5.6% when compared to experimental results.
Keywords: Chemical engineering; Food science; Theoretical chemistry.