Nonequilibrium Casimir-like Forces in Liquid Mixtures

Abstract

In this Letter, we consider a liquid mixture confined between two thermally conducting walls subjected to a stationary temperature gradient. While in a one-component liquid nonequilibrium fluctuation forces appear inside the liquid layer, nonequilibrium fluctuations in a mixture induce a Casimir-like force on the walls. The physical reason is that the temperature gradient induces large concentration fluctuations through the Soret effect. Unlike temperature fluctuations, nonequilibrium concentration fluctuations are also present near a perfectly thermally conducting wall. The magnitude of the fluctuation-induced Casimir force is proportional to the square of the Soret coefficient and is related to the concentration dependence of the heat and volume of mixing. When large and long-range fluctuations are present, they will induce forces in confined fluids [1]. These are commonly referred to as Casimir-like forces in analogy to forces induced by vacuum fluctuations between two conducting plates [2,3]. A well-known example is the Casimir force induced by critical fluctuations in fluids [4][5][6][7]. Apart from critical systems, long-range correlations also exist in equilibrium systems with Goldstone modes [1] and in many nonequilibrium systems, where even longerrange correlations can exist [8][9][10][11].In this Letter, we consider a liquid mixture in a nonequilibrium steady state (NESS) between two parallel thermally conducting plates subjected to a uniform temperature gradient ∇T. In a liquid mixture a temperature gradient induces large concentration fluctuations through the Soret effect [12,13]. These nonequilibrium concentration fluctuations vary with the 4th power of the inverse of the wave number k of the fluctuations, just as the nonequilibrium temperature fluctuations in a one-component fluid [8,14]. However, there is a principal difference between the Casimir pressures induced by nonequilibrium concentration fluctuation and those induced by nonequilibrium temperature fluctuations. In thin fluid layers, fluctuations not only may induce a force on the walls, but also may introduce an effective potential inside the fluid layer causing a modification of the density or composition profile [15]. While in a one-component fluid nonequilibrium fluctuations induce the latter phenomenon yielding a rearrangement of the density profile [16], the purpose of the present Letter is to demonstrate that nonequilibrium concentration fluctuations induce an actual Casimir pressure on the walls directly.It is well known that in considering the dynamics of fluctuations around thermal equilibrium, nonlinear terms in the hydrodynamic equations serve to renormalize various terms in the linearized hydrodynamic equations [17][18][19][20][21][22][23][24].Here we show that in a NESS the nonlinear terms cause a most important renormalization of the nonequilibrium (NE) pressure or normal stresses in a binary fluid. To determine the nonequilibrium induced pressure in a liquid mixture, we need to consider the pressure p as a function of the fl...

Nonequilibrium forces following quenches in active and thermal matter

“…[47,53]). Equation (20) is then still expected to hold as the initial density, but the hard inclusion 2 now modifies the density in its vicinity (as corrected for by a reflection term). The force remains proportional to the density gradient of ρ 1 at the origin of inclusion 2, but the reflection modifies its amplitude, introducing a more complicated dependence on V 2 (x).…”

Confinement effect on the dynamics of non-equilibrium concentration fluctuations far from the onset of convection

“…(20) are the inverse of the eigenvalues Γ N (q) = 1/τ N (q) from solving Eqs. (16)- (17). The amplitudes A N are analytically related to Γ N and q.…”

“…Thus, understanding NEFs is a basic question in the physics of non-equilibrium fluids and can lead not only to a deeper insight of transport phenomena like free diffusion or thermodiffusion [12][13][14], but also of new phenomena like NE fluctuation-induced (Casimir) forces [15][16][17][18].…”

Correlations and scaling properties of nonequilibrium fluctuations in liquid mixtures

“…Therefore, the Fickean flux can be decomposed into a superposition of the microscopic currents generated by nonequilibrium fluctuations. A very recent advancement in the understanding of nonequilibrium fluctuations has been the theoretical prediction that long-range nonequilibrium fluctuations occurring in diffusive processes give rise to giant nonequilibrium Casimir forces that are orders of magnitude larger than those present in a mixture close to its critical point [21][22][23]. Earlier studies of nonequilibrium fluctuations relied on the investigation of their average static and dynamic structure factors, due to the fact that these quantities can be accessed easily by using optical techniques such as small-angle light scattering and a quantitative shadowgraph.…”