Multiscale analysis of diffusioosmotic transport of micropolar fluids in microchannels

Abstract

The ability of the applied chemical concentration gradients to move the fluid, i.e., diffusioosmosis, requires a more robust mathematical model to predict the interdependency of the solute dispersion and the fluid movement. The present work illustrates the influence of applied concentration gradient on the movement of micropolar fluid within the microchannel using the mathematical model of diffusioosmosis. The model consists of a rectangular channel filled with micropolar fluid in which the solute concentration gradient is imposed, having a standard Gaussian distribution. The model for combined advection-diffusion, i.e., Taylor's dispersion model, is employed to regulate the solute distribution. The diffusioosmotic pressure gradient purely drives the micropolar fluid through the diffusioosmotic slip flow at the wall. A multi-timescale approach is utilized to obtain the closed-form solution of the flow and concentration profiles. The combined approach of homogenization and the Laplace transformation is used to find the analytical expressions of the concentration profile. The pure diffusion and the solute wall interaction induce the slip flow at the wall, which further contributes to solute dispersion by advection, leading to the combined advection-diffusion process. The two different boundary constraints for microrotation at the wall, including no-spin (NS) and no-couple stress (NCS), have been thoroughly studied. The graphical illustrations of the various dynamic quantities provide a comprehensive analysis of their physical behavior under the influence of relevant flow parameters. It is noted that for stronger diffusioosmosis, all the dynamic quantities, including the velocity profile, rotational velocity, effective diffusivity, wall shear stress (WSS), and mean concentration, are sensitive to micropolar fluid parameters like micro-scale parameter and coupling number. It is observed that the velocity profile and mean concentration show less variation concerning different parameters for no-couple stress at the wall, compared to the no spin of the microparticles at the wall. Further, the outcomes from the mathematical model advance the understanding of fluid flow induced by concentration gradients, which can assist the researchers in analyzing drug delivery, the separation process, and various species transport applications in the novel framework of diffusioosmosis.