Critical dynamics of an isothermal compressible nonideal fluid

Groß, Markus; Varnik, Fathollah

doi:10.1103/physreve.86.061119

Cited by 9 publications

(15 citation statements)

References 130 publications

(262 reference statements)

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“…Furthermore, there is a strong, intrinsically theoretical, interest in such analyses, in particular stemming from numerical methods. Molecular dynamics simulations [26] as well as lattice gas [27] or lattice Boltzmann simulations [28] naturally operate in the canonical ensemble and have been applied for studying static and dynamic critical phenomena [29][30][31][32][33][34][35][36]. In order to properly extract physical properties of bulk * gross@is.mpg.de systems from such simulations, a detailed understanding of finite-size effects in the canonical ensemble is required [6,7,10,[37][38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Critical adsorption and critical Casimir forces in the canonical ensemble

et al. 2016

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Critical properties of a liquid film between two planar walls are investigated in the canonical ensemble, within which the total number of fluid particles, rather than their chemical potential, is kept constant. The effect of this constraint is analyzed within mean field theory (MFT) based on a Ginzburg-Landau free energy functional as well as via Monte Carlo simulations of the threedimensional Ising model with fixed total magnetization. Within MFT and for finite adsorption strengths at the walls, the thermodynamic properties of the film in the canonical ensemble can be mapped exactly onto a grand canonical ensemble in which the corresponding chemical potential plays the role of the Lagrange multiplier associated with the constraint. However, due to a non-integrable divergence of the mean field order parameter (OP) profile near a wall, the limit of infinitely strong adsorption turns out to be not well-defined within MFT, because it would necessarily violate the constraint. The critical Casimir force (CCF) acting on the two planar walls of the film is generally found to behave differently in the canonical and grand canonical ensembles. For instance, the canonical CCF in the presence of equal preferential adsorption at the two walls is found to have the opposite sign and a slower decay behavior as a function of the film thickness compared to its grand canonical counterpart. We derive the stress tensor in the canonical ensemble and find that it has the same expression as in the grand canonical case, but with the chemical potential playing the role of the Lagrange multiplier associated with the constraint. The different behavior of the CCF in the two ensembles is rationalized within MFT by showing that, for a prescribed value of the thermodynamic control parameter of the film, i.e., density or chemical potential, the film pressures are identical in the two ensembles, while the corresponding bulk pressures are not.

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Section: Introductionmentioning

confidence: 99%

Critical adsorption and critical Casimir forces in the canonical ensemble

et al. 2016

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“…This issue has prompted the development of canonical density functional methods [7][8][9][10] which explicitly take fluctuation corrections into account. Recently, static and dynamic critical phenomena have been investigated also within molecular dynamics [11][12][13][14][15][16][17] or lattice Boltzmann simulations [18,19]. These simulation methods typically operate in the canonical ensemble and require finite-size corrections in order to extract physical properties of bulk systems [3,[20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Statistical field theory with constraints: Application to critical Casimir forces in the canonical ensemble

2017

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The effect of imposing a constraint on a fluctuating scalar order parameter field in a system of finite volume is studied within statistical field theory. The canonical ensemble, corresponding to a fixed total integrated order parameter (e.g., the total number of particles), is obtained as a special case of the theory. A perturbative expansion is developed which allows one to systematically determine the constraint-induced finite-volume corrections to the free energy and to correlation functions. In particular, we focus on the Landau-Ginzburg model in a film geometry (i.e., in a rectangular parallelepiped with a small aspect ratio) with periodic, Dirichlet, or Neumann boundary conditions in the transverse direction and periodic boundary conditions in the remaining, lateral directions. Within the expansion in terms of ε=4-d, where d is the spatial dimension of the bulk, the finite-size contribution to the free energy of the confined system and the associated critical Casimir force are calculated to leading order in ε and are compared to the corresponding expressions for an unconstrained (grand canonical) system. The constraint restricts the fluctuations within the system and it accordingly modifies the residual finite-size free energy. The resulting critical Casimir force is shown to depend on whether it is defined by assuming a fixed transverse area or a fixed total volume. In the former case, the constraint is typically found to significantly enhance the attractive character of the force as compared to the grand canonical case. In contrast to the grand canonical Casimir force, which, for supercritical temperatures, vanishes in the limit of thick films, in the canonical case with fixed transverse area the critical Casimir force attains for thick films a negative value for all boundary conditions studied here. Typically, the dependence of the critical Casimir force both on the temperaturelike and on the fieldlike scaling variables is different in the two ensembles.

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“…A more direct test of our predictions can be achieved via simulations, for which non-symmetry breaking BCs are easily realizable. Recently, progress has been made, e.g., within molecular dynamics [93,94] and within the lattice Boltzmann method [95][96][97] towards simulation of critical dynamics and determining CCFs [98]. Moreover, these simulation methods typically realize the canonical ensemble and thus allow one to test the ensemble differences of the CCF [52,53].…”

Section: Discussionmentioning

confidence: 99%

Dynamics of the critical Casimir force for a conserved order parameter after a critical quench

2019

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Fluctuation-induced forces occur generically when long-ranged correlations (e.g., in fluids) are confined by external bodies. In classical systems, such correlations require specific conditions, e.g., a medium close to a critical point. On the other hand, long-ranged correlations appear more commonly in certain non-equilibrium systems with conservation laws. Consequently, a variety of non-equilibrium fluctuation phenomena, including fluctuation-induced forces, have been discovered and explored recently. Here, we address a long-standing problem of non-equilibrium critical Casimir forces emerging after a quench to the critical point in a confined fluid with order-parameterconserving dynamics and non-symmetry-breaking boundary conditions. The interplay of inherent (critical) fluctuations and dynamical non-local effects (due to density conservation) gives rise to striking features, including correlation functions and forces exhibiting oscillatory time-dependences. Complex transient regimes arise, depending on initial conditions and the geometry of the confinement. Our findings pave the way for exploring a wealth of non-equilibrium processes in critical fluids (e.g., fluctuation-mediated self-assembly or aggregation). In certain regimes, our results are applicable to active matter. * gross@is.mpg.de arXiv:1905.00269v2 [cond-mat.stat-mech]

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Critical dynamics of an isothermal compressible nonideal fluid

Cited by 9 publications

References 130 publications

Critical adsorption and critical Casimir forces in the canonical ensemble

Critical adsorption and critical Casimir forces in the canonical ensemble

Statistical field theory with constraints: Application to critical Casimir forces in the canonical ensemble

Dynamics of the critical Casimir force for a conserved order parameter after a critical quench

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