Capillarity driven spreading of circular drops of shear-thinning fluid

Analysis of the self-similar spreading of power law fluids

We consider the equation that models the spreading of thin liquid films of power-law rheology. In particular, we analyze the existence and uniqueness of source-type self-similar solutions in planar and circular symmetries. We find that for shear-thinning fluids there exist a family of such solutions representing both finite and zero contact angle drops and that the solutions with zero contact angle are unique. We also prove the existence of traveling waves in one space dimension and classify them.