Contact-line motion of shear-thinning liquids

It is demonstrated that, for the slow advance of a viscous liquid onto a previously dry substrate, the well-known moving contact line paradox is alleviated for liquids exhibiting power-law shear-thinning behavior. In contrast to previous models that allow contact-line motion, it is no longer necessary to abandon the no-slip condition at the substrate in the vicinity of’the contact point. While the stress is still unbounded at the contact point, the equations of motion are shown to be integrable. A three-constant Ellis viscosity model is employed that allows a low-shear Newtonian viscosity, and may thus be used to model essentially Newtonian flows where shear thinning only becomes important in the immediate vicinity of the contact point. Calculations are presented for the model problem of the progression of a uniform coating layer down a vertical substrate using the lubrication approximations. The relationship between viscous heating and shear-thinning rheology is also explored.