Analytical Solution For Mass Transfer Research Articles

Water diffusivity estimation in air-dried complex-shaped foods by the method of slopes: Application to oblate spheroid geometry

Water diffusivity is an important parameter for designing convective drying processes, as it is instrumental for determining the rate at which moisture is removed from solid foodstuffs. Most estimation methods for water diffusivity estimation rely in simple geometries and are based on analytical solutions for mass transfer under constant diffusivity in a rigid solid, assumptions that most often leads to unreliable estimations. In this study, the method of slopes is generalized to complex-shaped geometries lacking analytical solutions, allowing the estimation of variable diffusivities in shrinking solids. The method is validated with experimental drying data for fresh and osmodehydrated mushroom pilei and implemented by using the numerical solution to an unsteady state 2D drying model formulated in the oblate spheroidal coordinate system. Shrinkage descriptors of drying product were determined using the point set registration algorithm. Water diffusivities were further compared to those estimated by using a piecewise regression approach. Drying kinetics simulations using diffusivities obtained with the method of slopes showed an excellent agreement with experimental data, achieving moisture-averaged relative deviation values lower than 2.4%.

Mathematical Modeling of Heat, Mass and Moisture Transfer in Catalytic Porous Media

The discovery of ordered mesoporous materials has opened great opportunities for new applications in heterogeneous catalysis e.g. in soil purification processes. The focus of this study is the development of a mathematical model to simulate heat, mass and moisture transfer in soil arrays tacking into account catalytic micro- or nanoparticles. The nonlinear mathematical model of contaminant distribution in unsaturated catalytic porous media to the filter-trap in non-isothermal conditions is presented. The finite differences method was used to find the numerical solution of the corresponding boundary value problem and the analytical solution for mass transfer in catalytic micro- or nanoparticles was presented as well. Numerical experiments and their analysis were conducted using NanoSurface software complex.

Nonlinear Mathematical Model of Contaminant Distribution in Unsaturated Catalytic Porous Media

The nonlinear mathematical model of contaminant distribution in unsaturated catalytic porous media to the filter-trap in isothermal conditions is presented. The mathematical model takes into account the micro and the meso/macro scale factors of the heat and mass transfer processes. The numerical solution of the respective boundary value problem was obtained by the method of finite differences. The analytical solution for mass transfer in nanoparticles was presented as well.

Liquid—solid mass transfer in packed beds of variously shaped particles at low Reynolds numbers: experiments and model

The cathodic reduction of ferricyanide ions is used to characterize liquid—solid mass transfer in porous electrodes in the creeping flow regime. Our study deals with packed beds of spheres, long cylinders and plates of low height-to-side ratio. Correlations are proposed and compared with predictive equations based on the association of the capillary representation of the porous medium with the analytical solution for mass transfer at a pipe wall, for fully developed laminar flow in short tubes. The model leads to satisfying values of the mass transfer coefficient in the case of beds packed with spheres and parallelepipedal particles.

An analytical solution for mass transfer in turbulent falling films with or without chemical reaction

A simple analytical solution is presented for mass transfer in an isothermal turbulent falling liquid film with or without chemical reaction. The exact solutions are compared with previous work for the cases of physical absorption and first-order reaction. New solutions are presented for a zero-order reaction, and generalized results are presented for first and pseudo nth-order reactions. The method of superposition is used to generate the first ten eigenvalues and corresponding values of the Sherwood number for several limiting situations. The analytical solution offers substantial advantages over previous finite-difference numerical solutions both in computation time and in describing the effects of operating variables.