In recent years, lubricant-infused superhydrophobic microfluidic surfaces have attracted significant attention for their potential to reduce drag. Motivated by the need to examine how non-Newtonian rheology influences hydrodynamic resistance in such systems, an analytical model for apparent slip is developed for pressure-driven flow of a non-Newtonian primary fluid over a non-Newtonian secondary infused fluid. For analytical tractability, Poiseuille flow in a non-Newtonian liquid-infused microchannel is modelled as two adjacent, immiscible power-law fluids co-flowing between infinite parallel plates under a constant pressure gradient. By enforcing continuity of velocity and tangential shear stress at the flat interface, closed-form expressions are obtained for the velocity distribution and interfacial slip velocity. Indeed, auxiliary two-phase full-field simulations for representative cases are consistent with the analytical predictions of interfacial shear stress and slip velocity. A quantitative analysis of the classical effective slip length reveals that it is governed by the slip-layer thickness, the infused fluid rheology and the interfacial apparent viscosity ratio. Generalised expressions are further obtained for the slip flow-rate ratio and the pressure-drop ratio relative to the classical no-slip channel. Within the present two-layer model, for fixed interfacial apparent viscosity ratio and slip-layer thickness, combinations involving shear-thinning primary and secondary fluids yield better slip-enhancement and drag-reduction trends. These results provide a reduced analytical framework for interpreting rheology-dependent apparent slip behaviour in non-Newtonian liquid-infused microchannels.
Chandran et al. (Mon,) studied this question.