Flow with impregnation of a rheokinetic liquid

Abstract

Flow with impregnation of a porous layer for a special class of non-Newtonian liquids is discussed. The particular feature of the rheological properties is the assumption that the viscosity of a liquid can change due to a chemical reaction. Change in the degree of conversion is described by a standard kinetic equation and the dependence of viscosity on the degree of conversion is written by means of an exponential equation. Moreover, it is assumed that, when approaching some critical degree of conversion, the viscosity grows without limit, i.e. chemical “curing” of the liquid takes place. Flow of such a “rheokinetic” liquid along a plane feeding channel with simultaneous impregnation of a porous layer in contact with this channel is simulated by a system of balance equations (taking into account non-Newtonian effects provided by time-dependent viscosity), supplemented by a kinetic equation. This system of equations is rewritten and solved in a dimensionless form. The principle possible solutions are obtained, including the situation where—due to premature loss of fluidity—a liquid cannot completely impregnate a porous layer. An approximate relationship determining the condition of complete impregnation is formulated.