Рост давления в плоской щели, заполненной жидкостью при ее замерзании

Abstract

The paper considers the problem of pressure variations in circular and rectangular flat fractures filled with liquid as the liquid crystallises, taking into account rigidity of the solid phase forming. We suppose that as a liquid crystallises, the volume it occupies inside the fracture changes due to the difference in density of the solid and liquid phases, and the fracture walls deform due to the pressure difference between the environment and the internal zone. Assuming that the solid and liquid phases are incompressible, we may equate the change in the internal fracture volume caused by the deformation of the surrounding walls to that in the volume of the liquid undergoing a state transition. We presume that crystallisation occurs at the top of the fracture, the temperature of the liquid is constant and equals its crystallisation temperature, and the phase boundary between the liquid and solid phases is flat. We consider the side walls and the bottom to be thermally insulated and perfectly rigid. We derived analytical expressions for determining the pressure