Capillary imbibition of inelastic non-Newtonian fluids in an asymmetric flow assay

Abstract

Inelastic non-Newtonian fluids are imbibed in a non-uniform conical-shaped microfluidic channel, discussed quantitatively using a theoretical model. We consider the Ostwald–de Waele power-law model to describe the rheology of the inelastic non-Newtonian fluids. Consistent with the reduced order model, the theoretical framework developed here accounts for the coupled effects of fluid rheology, flow configuration, and surface wettability to describe the transient progression of the filling length in the capillary under varied cases. Considering the simultaneously intervening interactions resulting due to rheological effect, geometrical modulation, and surface wetting condition during the imbibition phenomenon, we demonstrate the temporal advancement of the filling phase fluid length in the non-uniform capillary for a set of involving parameters pertinent to this analysis. Non-uniformity in the capillary cross-section gives rise to an alteration in the viscous force acting at the fluid–fluid–solid interface, which in turn, leads to a control over the temporal progression of fluid length, retaining a balance between the capillary and viscous forces. From the predicted relation between filing length and time of filling, we identify three distinct regimes of filling and establish the befitting scaling laws describing the imbibition phenomenon in the respective regimes.