Hyper-pore model of liquid migration in porous materials

A. Czachor and J. J. Milczarek

Institute of Atomic Energy, Świerk, 05-400 Otwock, Poland

Abstract. The equation of motion for a wetting liquid moving along the round tube under capillary forces have been re-derived and completed with a special attention to viscosity forces. The adhesion-driven sticking of the liquid meniscus to the tube wall ( the liquid rolling) has been found to be the only logical mechanism of the force pulling the liquid along the tube. This mechanism is consistent with the Poiseuille boundary condition of the liquid longitudinal velocity at the wall equal to zero. The tendency of the wetting liquid to extend the coverage of the solid surface is shown to be the essential capillary mechanism to pull the wetting liquid from the broad to the narrow tube. The transition from the initial, inertia- dominated movement of the liquid front in a tube, z t, to the long-time viscosity-dominated flow, z , has been emphasized.

The equation of motion has been applied to study the liquid movement in a hyper-pore – the model porous system consisting of interconnected pores, characterized statistically at any cross section by the density (per cm² ) of the pores boundary length L and the density of the pores surface area S. The time (t) dependence of the liquid front position in the so modeled porous system is shown to be qualitatively such as in the tube of the effective radius ; in particular, at long times of liquid imbibition the front goes as . However, due to the variety of pore radii the front movement is slowed down by a factor of the order of (R_min/R_max)^k, k<3 , as compared to the liquid motion in a smooth tube of fixed radius along its length.