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 parado x is alleviated for liquids exhibiting power-law shear-thinning behavi or. In contrast to previous models that allow contact-line motion, it is no longer necessary to abandon the no-slip condition at the substra te in the vicinity of the contact point. While the stress is still unb ounded at the contact point, the equations of motion are shown to be i ntegrable. A three-constant Ellis viscosity model is employed that all ows a low-shear Newtonian viscosity, and may thus be used to model ess entially Newtonian flows where shear thinning only becomes important i n the immediate vicinity of the contact point. Calculations are presen ted for the model problem of the Progression of a uniform coating laye r down a vertical substrate using the lubrication approximations. The relationship between viscous heating and shear-thinning rheology is al so explored.