Capillarity driven spreading of power-law fluids

AbstractWe 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 λ for the rheology is larger than one, the governing dimensionless equation ht + (hλ+2|hxxx|λ−1hxxx)x=0 admits solutions with compact support and moving fronts. We also show that the solutions have bounded energy dissipation rate