Asymmetric capillary filling of non-Newtonian power law fluids

A theoretical analysis of the capillary-driven imbibitions of non-Newtonian fluids in conical capillaries is presented. More precisely, the consequences of the variation in the fluid viscosity with the shear rate are investigated by using the inelastic power law model. Novel fluid dynamic behaviors are predicted, notably the asymmetry of filling times measured from different ends of the conical tube. The effect is due to the anisotropy of the flow domain and takes place with simple Newtonian fluids indeed. It is quantitatively described how shear-thinning fluids increase the asymmetry, and shear-thickening fluids decrease it. Relevant applications in microfluidic rheometry are envisaged. In addition, these results are of interest in active fields of research such as passive micropumping and microflow rectification, where the geometric design of microchannels is the key to control fluidic operations.