Spreading of Lava as a Non-Newtonian Fluid in the Conditions of Partial Slip on the Underlying Surface

Abstract

The effect of the boundary condition imposed on the underlying surface on the propagation of lava flows is studied in the case in which the non-Newtonian properties of the medium should be taken into account. The problem of lava spreading over a plane horizontal plane is solved. The no-slip condition on the underlying surface is replaced by the partial slip condition. The lava is modeled as a power-law fluid. The flow is assumed to be axisymmetric. In the thin layer approximation the problem reduces to the solution of one nonlinear partial differential second-order equation with an additional integral condition. In the case of the power-law time dependence of the lava flow rate a self-similar solution is obtained; however, it exists only under some constraints on the problem parameters. The non-self-similar solution is considered numerically. It is shown that the lava propagation velocity can be considerably higher, when the slip is taken into account.