Flow through charged membranes
Abstract
The Stokes equation is solved for flow through a basic cell with a relatively simple geometry. In an attempt to improve the pipe model, the membrane is modeled by a cubical array of charged spheres. Three sets of partial differential equations describe this system: flux equations (which we have developed from the generalized dusty gas model), NavierStokes equations and the PoissonBoltzmann equation. These equations are suitably averaged over a cell volume to yield a set of ordinary differential equations on the gross scale. It is shown that in hyperfiltration the cell model will reject salt more efficiently than the tube model and in the limit of Stokes flow this analysis reproduces the results obtained by the tube model. Results for the electrodialysis mode of membrane operation are presented both for linear and nonlinear cases.
 Publication:

Ph.D. Thesis
 Pub Date:
 August 1975
 Bibcode:
 1975PhDT........97M
 Keywords:

 Flow Distribution;
 Ion Exchange Membrane Electrolytes;
 Transport Theory;
 Ion Distribution;
 Linear Systems;
 NavierStokes Equation;
 Nonlinear Systems;
 Potential Flow;
 Stokes Flow;
 Fluid Mechanics and Heat Transfer