AN ANALYTICAL EXPRESSION FOR THE DISPERSION COEFFICIENT IN POROUS MEDIA USING CHANG'S UNIT CELL

作者：Lugo Mendez Helen D; Valdes Parada Francisco J; Alberto Ochoa Tapia J

来源：Journal of Porous Media, 2013, 16(1): 29-40.

• dispersion
• porous media
• creeping flow
• upscaling
• Chang's unit cell
• analytical solution

Mathematical modeling of transport phenomena in hierarchical systems is often carried out by means of effective medium equations resulting from upscaling techniques. For the case of convection and diffusion taking place at the pore scale, the upscaled model is expressed in terms of a total dispersion tensor, which encompasses the essential features from the microscale. Several theoretical and experimental works have evidenced that the dispersion coefficient follows a power-law dependence with the particle Peclet number. In this work, we show that such functionality can be derived analytically using the method of volume averaging with Chang's unit cell. Our derivations lead to an expression for the dispersion coefficient that reduces to the classical result by Maxwell under purely diffusive conditions. Interestingly, the dispersivity is found to follow a nontrivial functionality with the particle Peclet number. The predictions from our analytical expression are compared with those obtained by solving the same closure problem in periodic unit cells showing, in general, good agreement, especially for homothetic unit cells.

• 出版日期2013