A FRACTAL MODEL OF POWER-LAW FLUID THROUGH CHARGED FIBROUS POROUS MEDIA BY USING THE FRACTIONAL-DERIVATIVE THEORY

Abstract

The study characterizes power-law fluid through charged fibrous porous media with spatial fractional-derivative and fractal geometry. Seepage flow of power-law fluid across fractal fibrous porous media in the presence of electric double layers (EDLs) is investigated based on the capillary bundle model. The acquired velocity distribution equation in a narrow capillary is then transformed into the form of series with appropriate Taylor approximation. After that, an analytical formula for dimensionless permeability is derived based on the generalized Darcy’s law. The effects of diverse parameters, including the fractal dimension of pore area, porosity, fractional order and Zeta potential on dimensionless permeability, are discussed. It can be seen from the results that lower fractional order has an amplification effect on dimensionless permeability with the change in Zeta potential. The results provide some theoretical guidance for revealing the seepage mechanism of a power-law fluid in charged porous media.