Two typical time scales of the piston effect

The existence of a fourth mode of heat transfer near the critical point, named the piston effect, has been known for more than a decade. The typical time scale of temperature relaxation due to this effect was first predicted by Onuki et al. [Phys. Rev A 41, 2256 (1990)], and this author’s formula has been extensively used since then to predict the thermal behavior of near-critical fluids. Recent studies, however, pointed out that the critical divergence of the bulk viscosity could have a strong influence on piston-effect-related processes. In this paper, we conduct a theoretical analysis of near-critical temperature relaxation showing that the piston effect is not governed by one (as was until now believed) but by two typical time scales. These two time scales exhibit antagonistic asymptotic behaviors as the critical point is approached: while the classical piston-effect time scale (as predicted by Onuki et al.) goes to zero at the critical point (critical speeding up), the second time scale (related to bulk viscosity) goes to infinity (critical slowing down). Based on this property, an alternative method for measuring near-critical bulk viscosity is proposed.

Figure 1

System under study.

Figure 2

Classical time scale (dark full line) and viscous time scale (dark dotted line) of the piston effect, compared with the typical time scales of heat diffusion (gray dotted line) and of acoustic properties.

Figure 3

Time evolution of the bulk temperature after a quench of the fluid cell of amplitude $\delta T$, for different reduced temperatures in the classical regime of the piston effect (the fluid cell is 1 mm long and filled with ${}^3\mathrm{He}$).

Figure 4

Time evolution of the bulk temperature after a quench of the fluid cell of amplitude $\delta T$, for different reduced temperatures in the viscous regime of the piston effect (the fluid cell is 1 mm long and filled with ${}^3\mathrm{He}$).

Figure 5

Ratio of the amplitudes and phase lag between the wall and the bulk temperature oscillations in the viscous regime of the piston effect; the fluid cell is 1 mm long, filled with ${}^3\mathrm{He}$, and subjected to a boundary temperature oscillation of pulsation $\omega$.