CONICET | Buscador de Institutos y Recursos Humanos

Using the lubrication approximation we investigate the self-similar axisymmetric ﬂow of a power-law liquid towards a central circular cavity. It is shown that this problem has a self-similar solution of the second kind. The self-similarity exponent is found by solving a non-linear eigenvalue problem arising from the requirement that the integral curve that represents the solution must join the appropriate singular points in the phase plane of the governing equation. The eigenvalues for different values of the rheological index are computed. Numerical integration of the equations allows us to determine the shape of the solution in terms of the physical variables. We make a detailed analysis of the inﬂuence of the rheology on the properties of the solutions.