Critical adsorption and critical Casimir forces for geometrically structured confinements

Tröndle, M.; Harnau, Ludger; Dietrich, S.

doi:10.1063/1.2977999

Cited by 32 publications

(39 citation statements)

References 78 publications

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“…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.…”

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confidence: 93%

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Nonequilibrium Casimir-like Forces in Liquid Mixtures

2015

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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...

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confidence: 93%

“…In practice it may be difficult to maintain plates at a close distance parallel to each other [3,34,35] and one may want to replace the plate by a particle. While a geometrical analysis of such a configuration becomes more complicated [5,15], the physical principle remains the same.…”

Section: Prl 115 035901 (2015) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

Nonequilibrium Casimir-like Forces in Liquid Mixtures

2015

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“…Recent theoretical and experimental studies of QED Casimir forces (see, e.g., Ref. [37] and references therein) as well as critical Casimir forces [38] for topologically structured substrates exhibit remarkable deviations from the corresponding ones for planar walls as well as the occurrence of lateral forces. However, only chemically patterned substrates allow for interesting combinations of attractive and repulsive critical Casimir forces so that, among the various realizations of the critical Casimir effect, the force in the presence of a chemically patterned substrate has recently attracted particular interest [15,39].…”

Section: Introductionmentioning

confidence: 99%

Critical Casimir forces between homogeneous and chemically striped surfaces

2013

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Recent experiments have measured the critical Casimir force acting on a colloid immersed in a binary liquid mixture near its continuous demixing phase transition and exposed to a chemically structured substrate. Motivated by these experiments, we study the critical behavior of a system, which belongs to the Ising universality class, for the film geometry with one planar wall chemically striped, such that there is a laterally alternating adsorption preference for the two species of the binary liquid mixture, which is implemented by surface fields. For the opposite wall we employ alternatively a homogeneous adsorption preference or homogeneous Dirichlet boundary conditions, which within a lattice model are realized by open boundary conditions. By means of mean-field theory, Monte Carlo simulations, and finite-size scaling analysis we determine the critical Casimir force acting on the two parallel walls and its corresponding universal scaling function. We show that in the limit of stripe widths small compared with the film thickness, on the striped surface the system effectively realizes Dirichlet boundary conditions, which generically do not hold for actual fluids. Moreover, the critical Casimir force is found to be attractive or repulsive, depending on the width of the stripes of the chemically patterned surface and on the boundary condition applied to the opposing surface.

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“…So far the theoretical investigations of the critical Casimir effect have been focused on the film geometry, realized either by homogeneous, planar, and parallel walls (see, e.g., Refs. [6,7,8,9,10,11,12,13,14,15,16,17] and references therein) or by chemically patterned [18] or geometrically structured substrates [19], as well as on spherical colloidal particles (see, e.g., Refs. [20,21,22,23] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Critical Casimir interaction of ellipsoidal colloids with a planar wall

Kondrat

Harnau

Dietrich

2009

The Journal of Chemical Physics

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Based on renormalization group concepts and explicit mean field calculations we study the universal contribution to the effective force and torque acting on an ellipsoidal colloidal particle which is dissolved in a critical fluid and is close to a homogeneous planar substrate. At the same closest distance between the substrate and the surface of the particle, the ellipsoidal particle prefers an orientation parallel to the substrate and the magnitude of the fluctuation induced force is larger than if the orientation of the particle is perpendicular to the substrate. The sign of the critical torque acting on the ellipsoidal particle depends on the type of boundary conditions for the order parameter at the particle and substrate surfaces, and on the pivot with respect to which the particle rotates.

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Critical adsorption and critical Casimir forces for geometrically structured confinements

Cited by 32 publications

References 78 publications

Nonequilibrium Casimir-like Forces in Liquid Mixtures

Nonequilibrium Casimir-like Forces in Liquid Mixtures

Critical Casimir forces between homogeneous and chemically striped surfaces

Critical Casimir interaction of ellipsoidal colloids with a planar wall

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