A problem of penetration of a viscous liquid into a porous medium with
simultaneous squeezing along the surface of this medium is formulated
and discussed. The movement of a liquid is initiated by compressing a
viscous drop positioned between the upper plate and the porous medium
. The system of equations determining the changing of pressure and evo
lution of an impregnation front was formulated and discussed in dimens
ionless variables. Typical solutions were obtained for different sets
of characteristic parameters including the case of an anisotropic poro
us medium. Varying the determining parameters leads to different relat
ionships between impregnation and surface squeezing. It was proven tha
t the formulation of the problem under discussion and solutions obtain
ed in dimensionless form are valid for a ''rheokinetic'' liquid (visco
sity changing due to chemical reactions during flow), if an isothermal
situation is considered. However flow of a rheokinetic liquid ceases
due to unlimited growth of its viscosity and necessity to increase pre
ssure if we want to maintain the preset velocity of the upper pressing
plate.