Dispersion in non-Newtonian fluid flows in a conduit with porous walls

Abstract

Solute transport in a conduit (channel or tube) adjacent to a porous medium is drastically influenced by the porous walls. However, an appropriate relationship between the porous walls and the transport coefficients due to non-Newtonian fluid flows still needs further investigation. In this study, a reduced-order model for advective–dispersive transport due to flow of a non-Newtonian power-law (or Ostwald-de Waele) fluid in a conduit with porous walls is derived through which the dispersion coefficient can be obtained. It is revealed that the dispersion coefficient is controlled by the Peclet number and the flow behavior index. The dispersion coefficients for shear-thinning fluids are smaller than the case of Newtonian fluid while the dispersion coefficients for shear-thickening fluids are larger than that for Newtonian fluid. The ratio of dispersion coefficient in a conduit with porous walls to that in a conduit with non-porous walls recognizes three distinct transport regimes of diffusion-dominated, transition, and advection-dominated. The results exhibit that the exchange of solute between the conduit and the neighboring porous medium should be taken into consideration in determination of the dispersion coefficient for the last two transport regimes. It is also found that the larger the flow behavior index the earlier the breakthrough of a solute in a conduit with porous walls. In addition, the breakthrough time in a conduit with porous walls is larger than that in a conduit with non-porous walls. The presented results in this study are of great importance in many science and engineering applications, including drug delivery to blood vessels, separation of emulsions using membranes, nutrient uptake from soils, contaminant transport in fractured aquifers, and oil recovery from carbonate reservoirs.