A number of chemical and physical processes occur at interfaces where solids meet liquids. Among them is heap and in-situ leaching, an important technological process to extract uranium, precious metals, nickel, copper and other compound. To understand the main peculiarities of these processes a general mathematical approach is developed and applied. Its key point is new conditions at the free (unknown) boundary between liquid and solid phases (pore space-solid skeleton). The developed model can be used to analyze the dependence of the dynamics of the free fluid-skeleton interface on the external parameters of the process, like temperature, pressure, reagent concentration and others. Therefore, the overall behavior of the process can be controlled either by the rate of chemical reaction on the free interface via reagent concentration or by the velocity at which dissolved substances are transported to or from the free surface. The special attention is paid to a plausible justification of upscaling from mesoscopic to macroscopic scales and its comparison with approaches usually used at the moment. Several examples illustrate the feasibility of the models.
