Derivation of Stokes’ Law from Kirkwood’s Formula and the Green–Kubo Formula via Large Deviation Theory

Itami, Masato; Sasa, Shigehiko

doi:10.1007/s10955-015-1349-z

Cited by 8 publications

(13 citation statements)

References 58 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Because (σ N + p th ) 2 eq depends on ζ, it is necessary for our calculation to introduce ζ. Note that we obtain the same result as (30) when we use the method of [25], where the effect of the volume viscosity ζ is ignored. Unlike the time-averaged normal stress fluctuations in the bulk (7), the shear viscosity η is relevant for describing the time-averaged normal stress fluctuations on the surface.…”

Section: Time-averaged Normal Stress Fluctuationssupporting

confidence: 65%

Singular behaviour of time-averaged stress fluctuations on surfaces

Itami

Sasa

2018

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

We provide a method for calculating time-averaged stress fluctuations on surfaces in a viscous incompressible fluid at equilibrium. We assume that (i) the timeaveraged fluctuating stress is balanced in equilibrium at each position and that (ii) the time-averaged fluctuating stress obeys a Gaussian distribution on the restricted configuration space given by (i). Using these assumptions with the Green-Kubo formula for the viscosity, we can derive the large deviation function of the time-averaged fluctuating stress. Then, using the saddle-point method for the large deviation function, we obtain the time-averaged surface stress fluctuations. As an example, for a fluid between two parallel plates, we study the time-averaged shear/normal stress fluctuations per unit area on the top plate at equilibrium. We show that the surface shear/normal stress fluctuations are inversely proportional to the distance between the plates.

show abstract

Section: Time-averaged Normal Stress Fluctuationssupporting

confidence: 65%

Singular behaviour of time-averaged stress fluctuations on surfaces

Itami

Sasa

2018

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The derivation below can be extended straightforwardly for our problem discussed in the subsequent sections. See Bedeaux & Mazur (1974) for the derivation from the linearized equations in fluctuating hydrodynamics, and Itami & Sasa (2015) for the one from Hamilton dynamics of many particle systems within the linear response regime.…”

Section: Preliminariesmentioning

confidence: 99%

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.

View full text Add to dashboard Cite

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.

show abstract

“…where τ denotes the projected time evolution. Equation (35) contains two elements. The first, i,j e iK·(ri(τ )−R(τ )) e −iK ′ ·(rj (0)−R(0)) , describes the evolution of the solvent density around the Brownian particle.…”

Section: Dynamical Averagesmentioning

confidence: 99%

A microscopic model of the Stokes–Einstein relation in arbitrary dimension

Charbonneau

Szamel

2018

The Journal of Chemical Physics

View full text Add to dashboard Cite

The Stokes-Einstein relation (SER) is one of the most robust and widely employed results from the theory of liquids. Yet sizable deviations can be observed for self-solvation, which cannot be explained by the standard hydrodynamic derivation. Here, we revisit the work of Masters and Madden [J. Chem. Phys. 74, 2450-2459 (1981)], who first solved a statistical mechanics model of the SER using the projection operator formalism. By generalizing their analysis to all spatial dimensions and to partially structured solvents, we identify a potential microscopic origin of some of these deviations. We also reproduce the SER-like result from the exact dynamics of infinite-dimensional fluids.

show abstract

Derivation of Stokes’ Law from Kirkwood’s Formula and the Green–Kubo Formula via Large Deviation Theory

Cited by 8 publications

References 58 publications

Singular behaviour of time-averaged stress fluctuations on surfaces

Singular behaviour of time-averaged stress fluctuations on surfaces

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

A microscopic model of the Stokes–Einstein relation in arbitrary dimension

Contact Info

Product

Resources

About