The effect of aspect ratio on longitudinal diffusivity in a porous medium of rectangular cross-section

Abstract

The Taylor dispersion model is extended to study the longitudinal diffusivity D^∗ for laminar flow in a porous medium of rectangular cross-section of breadth 'a' and height 'b' using the Brinkman model. It is shown that D^∗ is about 2Do for large values of the aspect ratio b/a, where D_o is the value of the longitudinal diffusivity obtained by ignoring all variations across the channel. In particular it is shown that D^∗ is uniform for higher values of the porous parameter ,σ ( =b/√ k ,where k is the permeability of porous media). The results are compared with the viscous flow results of Chatwin and Sullivan [11] and good agreement is found as σ tends to zero.