Moving contact line hydrodynamics for power-law fluids

Contact line motion plays a fundamental role in many dynamic wetting processes such as coating, printing, and spreading. It is well known that a spreading Newtonian liquid drop on a no-slip substrate possesses a stress singularity at the three-phase moving contact line. For this reason, a microscopic cutoff is often introduced to relieve this contact line singularity. Here we show that such microscopic cutoff is not always necessary for power-law fluids. For shear-thinning fluids, we find that the viscous braking force on the contact line does not diverge at all. As viscous dissipation in this case is mainly through the bulk instead, the contact line dynamics no longer separates from the bulk flow, making the dynamic contact angle depend on the extent of spreading. For shear-thickening fluids, on the contrary, the contact line singularity becomes much severer than that in Newtonian fluids. Similar to the Newtonian case, the molecular-force-induced precursor film ahead of the contact line can render a natural microscopic cutoff to relieve the contact line singularity. But unlike the Newtonian case, this microscopic cutoff can explicitly enter the apparent dynamic contact angle relationship to strongly influence the global spreading behavior. Along the above lines, distinct dynamic contact angle relationships are also derived respectively for shear-thinning fluids and shear-thickening fluids, and found to be very different from the classical Tanner-Cox-Voinov law for Newtonian fluids. Further compared with experiments, these relationships are able to fairly capture measured data, reverberating critical roles of nonlinear fluid rheology in dynamic wetting and spreading.