Drag Coefficient of a Circular Inclusion in a Near-Critical Binary Fluid Membrane

Tani, Hiroumi; Fujitani, Youhei

doi:10.7566/jpsj.87.104601

Cited by 5 publications

(2 citation statements)

References 68 publications

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“…particle radius and the distance is small, the CCF can be obtained from a 'small-sphere expansion' of the Boltzmann weight [11,[14][15][16]. Recently, the non-equilibrium dynamics of colloidal particles in critical media has received increased attention [17,18], examples including studies of drag forces [18][19][20][21][22][23], aggregation [18,24], diffusion [25][26][27][28][29][30][31], shear flow [32,33], solvent coarsening [34][35][36], and interplay between criticality and activity [37,38].…”

Section: Introductionmentioning

confidence: 99%

Dynamics and steady states of a tracer particle in a confined critical fluid

Groß

2021

J. Stat. Mech.

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The dynamics and the steady states of a point-like tracer particle immersed in a confined critical fluid are studied. The fluid is modeled field-theoretically in terms of an order parameter (concentration or density field) obeying dissipative or conservative equilibrium dynamics and (non-)symmetry-breaking boundary conditions (BCs). The tracer, which represents, e.g., a colloidal particle, interacts with the fluid by locally modifying its chemical potential or its correlations. The coupling between tracer and fluid gives rise to a nonlinear and non-Markovian tracer dynamics, which is investigated here analytically and via numerical simulations for a one-dimensional system. From the coupled Langevin equations for the tracer-fluid system we derive an effective Fokker–Planck equation for the tracer by means of adiabatic elimination as well as perturbation theory within a weak-coupling approximation. The effective tracer dynamics is found to be governed by a fluctuation-induced (Casimir) potential, a spatially dependent mobility, and a spatially dependent (multiplicative) noise, the characteristics of which depend on the interaction and the BCs. The steady-state distribution of the tracer is typically inhomogeneous. Notably, when detailed balance is broken, the driving of the temporally correlated noise can induce an effective attraction of the tracer towards a boundary.

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Section: Introductionmentioning

confidence: 99%

Dynamics and steady states of a tracer particle in a confined critical fluid

Groß

2021

J. Stat. Mech.

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“…By contrast, in the far-distance limit, where the ratio between the particle radius and the distance is small, the CCF can be obtained from a "smallsphere expansion" of the Boltzmann weight [10,[13][14][15]. Recently, the non-equilibrium dynamics of colloidal particles in critical media has received increased attention [16], examples including studies of drag forces [16][17][18][19][20][21], aggregation [16,22], diffusion [23][24][25][26][27][28][29], shear flow [30,31], solvent coarsening [32][33][34], and interplay between criticality and activity [35,36].…”

Section: Introductionmentioning

confidence: 99%

Dynamics and steady states of a tracer particle in a confined critical fluid

Gross

2021

Preprint

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The dynamics and the steady states of a point-like tracer particle immersed in a confined critical fluid are studied. The fluid is modeled field-theoretically in terms of an order parameter (concentration or density field) obeying dissipative or conservative equilibrium dynamics and (non-)symmetrybreaking boundary conditions. The tracer, which represents, e.g., a colloidal particle, interacts with the fluid by locally modifying its chemical potential or its correlation length. The coupling between tracer and fluid gives rise to a nonlinear and non-Markovian tracer dynamics, which is investigated here analytically and via numerical simulations for a one-dimensional system. From the coupled Langevin equations for the tracer-fluid system we derive an effective Fokker-Planck equation for the tracer by means of adiabatic elimination as well as perturbation theory within a weak-coupling approximation. The effective tracer dynamics is found to be governed by a fluctuation-induced (Casimir) potential, a spatially dependent mobility, and a spatially dependent (multiplicative) noise, the characteristics of which depend on the interaction and the boundary conditions. The steadystate distribution of the tracer is typically inhomogeneous.

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Drag coefficient of a rigid spherical particle in a near-critical binary fluid mixture, beyond the regime of the Gaussian model

Yabunaka¹,

Fujitani²

2020

J. Fluid Mech.

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The drag coefficient of a rigid spherical particle deviates from the Stokes law when it is put into a near-critical fluid mixture in the homogeneous phase with the critical composition. The deviation (∆γ d ) is experimentally shown to depend approximately linearly on the correlation length far from the particle (ξ ∞ ), and is suggested to be caused by the preferential attraction between one component and the particle surface. In contrast, the dependence was shown to be much steeper in the previous theoretical studies based on the Gaussian free-energy density. In the vicinity of the particle, especially when the adsorption of the preferred component makes the composition strongly off-critical, the correlation length becomes very small as compared with ξ ∞ . This spacial inhomogeneity, not considered in the previous theoretical studies, can influence the dependence of ∆γ d on ξ ∞ . To examine this possibility, we here apply the local renormalized functional theory, which was previously proposed to explain the interaction of walls immersed in a (near-)critical binary fluid mixture, describing the preferential attraction in terms of the surface field. The free-energy density in this theory, coarse-grained up to the local correlation length, has much complicated dependence on the order parameter, as compared with the Gaussian free-energy density. Still, a concise expression of the drag coefficient, which was derived in one of the previous theoretical studies, turns out to be available in the present formulation. We show that, as ξ ∞ becomes larger, the dependence of ∆γ d on ξ ∞ becomes distinctly gradual and close to the linear dependence.

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Drag Coefficient of a Circular Inclusion in a Near-Critical Binary Fluid Membrane

Cited by 5 publications

References 68 publications

Dynamics and steady states of a tracer particle in a confined critical fluid

Dynamics and steady states of a tracer particle in a confined critical fluid

Dynamics and steady states of a tracer particle in a confined critical fluid

Drag coefficient of a rigid spherical particle in a near-critical binary fluid mixture, beyond the regime of the Gaussian model

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