Capillarity driven spreading of power-law fluids

Abstract

We investigate the spreading of thin liquid films of power-law rheology. We construct an explicit travelling wave solution and source-type similarity solutions. We show that when the nonlinearity exponent $\lambda$ for the rheology is larger than one, the governing dimensionless equation $h_t+(h^{\lambda+2}|h_{xxx}|^{\lambda-1}h_{xxx})_x=0$ admits solutions with compact support and moving fronts. We also show that the solutions have bounded energy dissipation rate.