Capillarity driven spreading of circular drops of shear-thinning fluid

We investigate the spreading of thin, circular liquid drops of powerlaw rheology. We derive the equation of motion using the thin film approximation, construct source-type similarity solutions and compute the spreading rate, aparent contact angles and height profiles. In contrast with the spreading of newtonian liquids, the contact line paradox does not arise for shear thinning fluids. In this work we study the spreading of circular drops of power-law rheology fluids, also known as Ostwald-de Waele fluids [1]. The power-law rheology is one of the simplest generalizations of the Newtonian one, in which the effective viscosity is assumed to be a power law of the local rate of deformation γ̇ as μ = m|γ̇|. The values of m and λ depend on the physical properties of the liquid. When λ > 1, the fluid is called shear-thinning and the viscosity tends to zero at high strain rates [1]. The problem of drop spreading has been intensively studied in the last decades (see [2, 3, 4, 5, 6]). The motivation is that this class of flows plays a very important role in processes such as coating and painting. One reason for our study is that while the past work considers only newtonian fluids, most of the fluids of technological interest are non-newtonian. There is also a theoretical motivation: one modelling difficulty for newtonian fluids is the paradox of the contact line, that states that the dissipation of energy is unbounded near the advancing contact line of a newtonian fluid. This paradox may be solved, for example, by introducing the effect of the intermolecular forces, or abandoning the no-slip boundary condition at the substrate. Here