Hydrodynamic fluctuation-induced forces in confined fluids

Monahan, Christopher; Naji, Ali; Horgan, R. R.; Lu, Bing-Sui; Podgornik, Rudi

doi:10.1039/c5sm02346g

Cited by 7 publications

(18 citation statements)

References 52 publications

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“…The power-law relations obtained here for the (generally non-thermal) surface-driven stress correlators assimilate to the "secondary" hydrodynamic Casimir-like forces, analyzed previously in the context of thermal fluctuations in a fluid film with fixed boundaries [40]. Such non-equilibrium fluctuation-induced, or Casimirlike effects have been of considerable interest in other soft-matter contexts in recent years [38][39][40][41][42][43][44][45][46][47][48]. It is also important to note that the r.m.s.…”

Section: Discussionmentioning

confidence: 75%

“…where we have defined ∆τ ⊥ = τ ⊥ − τ ⊥ and ∆τ = τ − τ . These time-dependent (real-valued) stress correlators are to be calculated from the Fourier-transform relations (40) and also by making use of the frequency-domain expressions for C (z , z ; ω ) and C ⊥ (z ⊥ , z ⊥ ; ω ⊥ ), themselves following from the dimensionless form of Eq. (26) as…”

Section: Dimensionless Representationmentioning

confidence: 99%

“…The equal-time longitudinal stress correlators defined through Eq. (40), and denoted more compactly as γ⊥ = 2 γ⊥ = 10 γ⊥ = 30 γ⊥ = 100 10 0 10 1 10 2 10 3…”

Section: A Equal-time Longitudinal Stress Correlatorsmentioning

confidence: 99%

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Hydrodynamic stress correlations in fluid films driven by stochastic surface forcing

et al. 2018

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We study hydrodynamic fluctuations in a compressible and viscous fluid film confined between two rigid, no-slip, parallel plates, where one of the plates is kept fixed, while the other one is driven in small-amplitude, translational, displacements around its reference position. This jiggling motion is assumed to be driven by a stochastic, external, surface forcing of zero mean and finite variance. Thus, while the transverse (shear) and longitudinal (compressional) hydrodynamic stresses produced in the film vanish on average on either of the plates, these stresses exhibit fluctuations that can be quantified through their equal-time, two-point, correlation functions. For transverse stresses, we show that the correlation functions of the stresses acting on the same plate (self-correlators) as well as the correlation function of the stresses acting on different plates (cross-correlators) exhibit universal, decaying, power-law behaviors as functions of the inter-plate separation. At small separations, the exponents are given by −1, while at large separations, the exponents are found as −2 (self-correlator on the fixed plate), −4 (excess self-correlator on the mobile plate) and −3 (cross-correlator). For longitudinal stresses, we find much weaker power-law decays in the large separation regime, with exponents −3/2 (excess self-correlator on the mobile plate) and −1 (cross-correlator). The selfcorrelator on the fixed plate increases and levels off upon increasing the inter-plate separation, reflecting the non-decaying nature of the longitudinal forces acting on the fixed plate. * Corresponding author: a.naji@ipm.ir ers may exhibit no equilibrium counterpart as are the hydrodynamic interactions, having significant impact on dynamic properties (e.g., spatiotemporal correlations) of colloids in bulk [1][2][3][4] or strongly confined fluids [10,11]. arXiv:1712.05051v2 [cond-mat.soft]

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Section: Discussionmentioning

confidence: 75%

Section: Dimensionless Representationmentioning

confidence: 99%

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Hydrodynamic stress correlations in fluid films driven by stochastic surface forcing

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“…In this section, we show the derivation of (154). The method of calculation is essentially the same as that in Monahan et al [56]. They claimed that the cross correlations between the random stress tensor and other fluctuating fields vanish.…”

Section: Calculated Quantitiesmentioning

confidence: 98%

Statistical Mechanical Expressions of Slip Length

Nakano

Sasa

2019

J Stat Phys

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We provide general derivations of the partial slip boundary condition from microscopic dynamics and linearized fluctuating hydrodynamics. The derivations are based on the assumption of separation of scales between microscopic behavior, such as collision of particles, and macroscopic behavior, such as relaxation of fluid to global equilibrium. The derivations lead to several statistical mechanical expressions of the slip length, which are classified into two types. The expression in the first type is given as a local transport coefficient, which is related to the linear response theory that describes the relaxation process of the fluid. The second type is related to the linear response theory that describes the non-equilibrium steady state and the slip length is given as combination of global transport coefficients, which are dependent on macroscopic lengths such as a system size. Our derivations clarify that the separation of scales must be seriously considered in order to distinguish the expressions belonging to two types. Based on these linear response theories, we organize the relationship among the statistical mechanical expressions of the slip length suggested in previous studies.

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“…These nonequilibrium LRCs, in turn, give rise to associated non-equilibrium fluctuation-induced forces. Such forces have been studied theoretically for systems with gradients in temperature [22][23][24] or density [25], quenched systems [26,27], stochastically driven systems [28], in systems under shear [29,30], and within fluctuating hydrodynamics [31].…”

Section: Introductionmentioning

confidence: 99%

Correlations and forces in sheared fluids with or without quenching

et al. 2019

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Spatial correlations play an important role in characterizing material properties related to non-local effects. Inter alia, they can give rise to fluctuation-induced forces. Equilibrium correlations in fluids provide an extensively studied paradigmatic case, in which their range is typically bounded by the correlation length. Out of equilibrium, conservation laws have been found to extend correlations beyond this length, leading, instead, to algebraic decays. In this context, here we present a systematic study of the correlations and forces in fluids driven out of equilibrium simultaneously by quenching and shearing, both for non-conserved as well as for conserved Langevin-type dynamics. We identify which aspects of the correlations are due to shear, due to quenching, and due to simultaneously applying both, and how these properties depend on the correlation length of the system and its compressibility. Both shearing and quenching lead to long-ranged correlations, which, however, differ in their nature as well as in their prefactors, and which are mixed up by applying both perturbations. These correlations are employed to compute non-equilibrium fluctuation-induced forces in the presence of shear, with or without quenching, thereby generalizing the framework set out by Dean and Gopinathan. These forces can be stronger or weaker compared to their counterparts in unsheared systems. In general, they do not point along the axis connecting the centers of the small inclusions considered to be embedded in the fluctuating medium. Since quenches or shearing appear to be realizable in a variety of systems with conserved particle number, including active matter, we expect these findings to be relevant for experimental investigations.instance, to uniaxial magnetic systems, model B describes binary alloys, spinodal dynamics of binary liquid mixtures, as well as single-component fluids [32,33]. These models have been applied extensively in describing various dynamical situations, e.g. the approach of the critical point from non-equilibrium initial conditions [34][35][36][37], the coarsening following a temperature quench [38,39], or for driven systems at criticality [40,41]. They have also been used to study shearing of near-critical fluids [42][43][44][45][46][47][48], leading to a large variety of phenomena.The use of such models provides generic scenarios, which we expect to be relevant for physical systems which allow for shearing and/or quenching. Shear is directly experimentally accessible [49]. Quenches can also be realized, for instance by using effective interactions of particles which can be changed suddenly, e.g. by swelling particles [50] or through external fields [51]. Another type of quench concerns a sudden change of temperature, which is a perturbation often employed in order to obtain supercooled liquids [52]. Such quenches of temperature (or of noise strength) may be achieved experimentally also in active fluids [53][54][55], which in many respects can be described by the use of effective temperatures [27,56...

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Hydrodynamic fluctuation-induced forces in confined fluids

Cited by 7 publications

References 52 publications

Hydrodynamic stress correlations in fluid films driven by stochastic surface forcing

Hydrodynamic stress correlations in fluid films driven by stochastic surface forcing

Statistical Mechanical Expressions of Slip Length

Correlations and forces in sheared fluids with or without quenching

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