Critical slowing down and fading away of the piston effect in porous media

TL;DR

This study analyzes how the piston effect's speed and influence diminish near the critical point in porous media, revealing universal crossovers and the fading of the effect due to viscous and boundary layer dynamics.

Contribution

It provides an asymptotic analysis of the piston effect in porous media near the critical point, identifying universal crossovers and explaining the fading of the effect.

Findings

Two universal crossovers depending on porosity, permeability, and viscosity.

The piston effect time scale stops decreasing and tends to a constant near the critical point.

The piston effect ultimately fades away due to boundary layer pressure gradients.

Abstract

We investigate the critical speeding up of heat equilibration by the piston effect (PE) in a nearly supercritical van der Waals (vdW) fluid confined in a homogeneous porous medium. We perform an asymptotic analysis of the averaged linearized mass, momentum and energy equations to describe the response of the medium to a boundary heat flux. While nearing the critical point (CP), we find two universal crossovers depending on porosity, intrinsic permeability and viscosity. Closer to the CP than the first crossover, a pressure gradient appears in the bulk due to viscous effects, the PE characteristic time scale stops decreasing and tends to a constant. In infinitly long samples the temperature penetration depth is larger than the diffusion one indicating that the PE in porous media is not a finite size effect as it is in pure fluids. Closer to the CP, a second cross over appears which is characterized by a pressure gradient in the thermal boundary layer (BL). Beyond this second crossover, the PE time remains constant, the expansion of the fluid in the BL drops down and the PE ultimately fades away.