Coating of shear-thinning and shear-thickening liquids on rotating cylinders

The coating of discrete objects with shear-thinning and shear-thickening liquids is important for many industrial products. To develop fundamental understanding of the influence of rheological effects on discrete-object coating, a model problem involving the flow of power-law liquids on rotating cylinders is considered here. Using the lubrication approximation, a semi-analytical expression is derived for the critical rotation rate above which the liquid film does not drain. The critical rotation rate is found to increase for shear-thinning liquids and decrease for shear-thickening liquids, relative to that for a Newtonian liquid with the same characteristic viscosity, due to weaker and stronger viscous forces, respectively. To understand the temporal evolution of the film along with surface-tension effects, the full two-dimensional equations are solved using finite element simulations. At the critical rotation rate for a Newtonian liquid, a shear-thinning liquid drains, whereas for a shear-thickening liquid a liquid lobe is found to rotate with a smaller oscillation amplitude compared to the Newtonian liquid. The predictions of the critical rotation rate from the lubrication-theory-based model are found to be in good agreement with those obtained from the full two-dimensional model. Flow visualization experiments with shear-thinning liquids reveal that shear thinning leads to thinner entrained films and a wider range of rotation rates over which a smooth coating is obtained, relative to Newtonian liquids of the same zero-shear viscosity. The thinner entrained films lead to a slower development of axially spaced rings from a Rayleigh–Plateau-like instability due to increased viscous stresses within the film, which suppress the growth of perturbations. Critical rotation rates predicted by the models agree well with experimental observations for shear-thinning liquids.