Nonequilibrium fluctuation-induced Casimir pressures in liquid mixtures

In this article we derive expressions for Casimir-like pressures induced by nonequilibrium concentration fluctuations in liquid mixtures. The results are then applied to liquid mixtures in which the concentration gradient results from a temperature gradient through the Soret effect. A comparison is made between the pressures induced by nonequilibrium concentration fluctuations in liquid mixtures and those induced by nonequilibrium temperature fluctuations in one-component fluids. Some suggestions for experimental verification procedures are also presented.

Figure 1

${〈{\left[\delta w\left(z\right)\right]}^2〉}_{\mathrm{NE}}$ as a function of $z$ obtained from Eq. (3.6) with Eq. (3.13) (red curve). For comparison we also show ${〈{\left[\delta T\left(z\right)\right]}^2〉}_{\mathrm{NE}}$ for a one-component fluid in the presence of a temperature gradient obtained for rigid boundary conditions [11] and infinite Prandtl number (blue curve). Both curves are normalized independently, so that the average value in the fluid layer for both types of fluctuations is unity. The horizontal line indicates the value of the $z$-independent approximation obtained by retaining only the constant $F_0$ in Eq. (3.13) for $F\left(z\right)$, with the same normalization as the concentration fluctuation (red) curve [21].

Figure 2

NE fluctuation-induced (Casimir) pressures as a function of the (average) molar fraction $x$ of tetralin in a binary mixture with $n$-dodecane at atmospheric pressure, for $\mathrm{\Delta }T=25$ K and $L=1$ mm. The red curve represents the pressure induced by NE concentration fluctuations, Eq. (4.9). The blue curve represents the pressure induced by NE temperature fluctuations.

Figure 3

Schematic of an NE Casimir pressure ${\overline{p}}_{\mathrm{NE}}>$ 0 on a plate at temperature $T_2$ located in a liquid between two walls at temperature $T_1$. For ${\overline{p}}_{\mathrm{NE}}<$ 0, the plate would be pulled to the closest wall.