Casimir amplitudes and capillary condensation of near-critical fluids between parallel plates: Renormalized local functional theory

Abstract

We investigate the critical behavior of a near-critical fluid confined between two parallel plates in contact with a reservoir by calculating the order parameter profile and the Casimir amplitudes (for the force density and for the grand potential). Our results are applicable to one-component fluids and binary mixtures. We assume that the walls absorb one of the fluid components selectively for binary mixtures. We propose a renormalized local functional theory accounting for the fluctuation effects. Analysis is performed in the plane of the temperature T and the order parameter in the reservoir ψ∞. Our theory is universal if the physical quantities are scaled appropriately. If the component favored by the walls is slightly poor in the reservoir, there appears a line of first-order phase transition of capillary condensation outside the bulk coexistence curve. The excess adsorption changes discontinuously between condensed and noncondensed states at the transition. With increasing T , the transition line ends at a capillary critical point T = T ca c slightly lower than the bulk critical temperature Tc. The Casimir amplitudes are larger than their critical-point values by 10-100 times at off-critical compositions near the capillary condensation line.

Hydrodynamics in bridging and aggregation of two colloidal particles in a near-critical binary mixture

“…Recently, we calculated phase diagrams of capillary condensation 47 and bridging 48 . We stress that the solvent-mediated interaction can be much enhanced near these transitions even in pretransitional states (before local phase separation) 10,13,47,48,50 . We also examined the dynamics of capillary condensation 49 .…”

“…Notice that the fluctuation-induced interaction 65 is much weaker than the adsorption-induced one (with inhomogeneous ψ ) 8,55 . In fact, the Casimir amplitudes at h 1 = 0 (in the Neumann boundary condition) 66 are much smaller than those under strong adsorption by one order of magnitude [9][10][11][12]47,56,57 .…”

“…As the critical point is approached, the strong adsorption regime is eventually realized outside CX due to a nonvanishing surface field h 1 (see eqn (4) and (5)) 47,48,55,[60][61][62] . Here, let ψ be positive near the colloid surfaces.…”

“…where the ratio b ′ /b cx is calculated to be 1.47 in our scheme 47 . We consider negative homogeneous τ with considerably large |τ |/τ a = (ξ ′ 0 a/ξ 0 ξ) 1/ν ≫ 1, so we treat the case ξ ≪ a. Hereafter, we measure time t in our simulation in units of t 0 defined by…”

“…As a theoretical method, we use the renormalized local functional theory 47,48,[55][56][57] to account for the nearcritical fluctuation effect. It is combined with the fluidparticle dynamics (FPD) simulation method 1,7,58,59 to calculate the flow around the particles.…”