Power-law rheology on mass transport of neutral solute induced by mixed electroosmotic flow through rough microtube with porous wall

In this work, the mass transport properties of a neutral solute in a rough microtube with a porous wall under the combined influence of both pressure and electric fields for non-Newtonian power-law fluids are examined. This investigation explores the effect of various microtube roughness patterns, such as sinusoidal, triangular, and rectangular, as well as different flow behavior indices, on solute mass transport behavior. The Poisson–Boltzmann equation, Cauchy momentum equation, and species conservation equation were solved computationally for different roughness profiles to assess the distribution of electric potential, velocity, and concentration fields. Higher relative roughness amplitude (δ = 0.1) and roughness wavenumber (λ = 12) reduced the average cross-sectional velocity by 31% for the dilatant solution, leading to improved permeation. The influence of roughness parameters (δ and λ) and the flow behavior index (n) on solute permeation mass flux was quantified. For the dilatant case, solute mass flux was enhanced by employing rectangular, sinusoidal, and triangular roughness profiles compared to the smooth porous wall by 19%, 9%, and 8% for assisting flow and 16%, 13%, and 11% for opposing flow. In fact, the highest mass flux effectiveness (ξ) for solute delivery was observed for the dilatant fluid with rectangular roughness in assisting flow. It is anticipated that the results of this study will provide valuable insights for the design of specialized drug delivery systems using microfluidic channels and contribute to a better understanding of nutrient transport in physiological systems.