Multi-scale hybrid numerical model for the study of mass transfer through a microporous artificial membrane
Quantification of mass transfer processes across micro-porous membranes can give valuable insight in applications of industrial and medical relevance. In this paper, a hybrid lattice Boltzmann-Finite differences (LBM-FD) code with non-uniform grid that simulates the mass transfer on a chip-like micro-device with an embedded micro-porous membrane has been developed. The model is validated showing good agreement with results of the Graetz-Leveque problem, even for Péclet numbers above 106, where conventional numerical methods fail to predict the correct behavior. The errors obtained in our simulations are below 1%. Simulations of the micro-porous membrane model in two and three dimensions show a linear scaling of the average Sherwood number with the number of pores and a value 1/3 of the scaling exponent of the Péclet number.
Support from the Spanish Ministerio de Economía y Competitividad under grants CTQ2013-46799-C2-1-P and DPI2016-75791-C2-1-P is gratefully acknowledged.
- 13.Leveque A (1928) Les lois de la de la transmission de chaleur par convection. Ann des Mines 13:201–99Google Scholar
- 15.Holzbecher E (2008) Numerical solutions for the Leveque problem of Boundary Layer mass or heat flux. Excerpt from the Proceedings of the COMSOL Conference HannoverGoogle Scholar