Electro-osmotic flow in coated nanocapillaries: a theoretical investigation

Marconi, Umberto Marini Bettolo; Monteferrante, Michele; Melchionna, Simone

doi:10.1039/c4cp03680h

Cited by 23 publications

(22 citation statements)

References 30 publications

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“…where γ is the friction constant of the Brownian particles against the (implicit) solvent. This framework is formally exact and goes beyond dynamical density functional theory [11][12][13]; the latter follows from neglecting the excess dissipation, P exc t [ρ, J] = 0. In this Letter we apply the general framework of power functional theory to treat phase coexistence of nonequilibrium steady states.…”

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confidence: 99%

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Nonequilibrium Phase Behavior from Minimization of Free Power Dissipation

2016

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We develop a general theory for describing phase coexistence between nonequilibrium steady states in Brownian systems, based on power functional theory [M. Schmidt and J. M. Brader, J. Chem. Phys. 138, 214101 (2013)]. We apply the framework to the special case of fluid-fluid phase separation of active soft sphere swimmers. The central object of the theory, the dissipated free power, is calculated via computer simulations and compared to a simple analytical approximation. The theory describes well the simulation data and predicts motility-induced phase separation due to avoidance of dissipative clusters. DOI: 10.1103/PhysRevLett.117.208003 Phase transitions in soft matter occur both in equilibrium and in nonequilibrium situations. Examples of the latter type include the glass transition [1], various types of shearbanding instabilities observed in colloidal suspensions [2,3], shear-induced demixing in semidilute polymeric solutions [4], and motility-induced phase separation in assemblies of active particles [5,6]. In contrast to phase transitions in equilibrium, which obey the statistical mechanics of Boltzmann and Gibbs, very little is known about general properties of transitions between out-of-equilibrium states. A corresponding universal framework for describing nonequilibrium soft matter is lacking at present.Theoretical progress has recently been made for the case of many-body systems governed by overdamped Brownian dynamics, encompassing a broad spectrum of physical systems [7]. It has been demonstrated that the dynamics of such systems can be described by a unique time-dependent power functional R t ½ρ; J, where the arguments are the space-and time-dependent one-body density distribution, ρðr; tÞ, and the one-body current distribution, Jðr; tÞ, in the case of a simple substance [8,9]. Both these fields are microscopically sharp and act as trial variables in a variational theory. The power functional theory is regarded to be "important, [as it] provides (i) a rigorous framework for formulating dynamical treatments within the [density functional theory] formalism and (ii) a systematic means of deriving new approximations" [10].The physical time evolution is that which minimizes R t ½ρ; J at time t with respect to Jðr; tÞ, while keeping ρðr; tÞ fixed. Hence,at the minimum of the functional. Here the variation is performed at fixed time t with respect to the positiondependent current. The density distribution is then obtained from integrating the continuity equation, ∂ρðr; tÞ=∂t ¼ −∇ · Jðr; tÞ, in time. The power functional possesses units of energy per time and can be split according towhere P t ½ρ; J accounts for the irreversible energy loss due to dissipation, _ F½ρ is the total time derivative of the intrinsic (Helmholtz) free energy density functional [7,11], and X t ½ρ; J is the external power, given bywhere _ V ext ðr; tÞ is the partial time derivative of the external potential V ext ðr; tÞ, and F ext ðr; tÞ is the external one-body force field, which in general consists of a sum of a conservative c...

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“…This implies that (i) the internal dissipation is negligible, I t ≈ 0 (cf. (12)) and (ii) that the value of the power functional for active particles is a known quantity. We have systematically studied the variation with temperature (as is analogous to varying Pe [14,15]).…”

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Nonequilibrium Phase Behavior from Minimization of Free Power Dissipation

2016

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“…(1) and (2) then describes how the system relaxes to its final equilibrium state whose mean profile and covariance are n eq (r) and σ eq (k; r). Describing this response at the level of the mean local concentration profile n(r, t w ) is precisely the aim of dynamic density functional theory (DDFT) [25][26][27], whose central equation is recovered from Eq. (1) in the limit in which we neglect the friction effects embodied in b(r, t w ) by setting b(r, t w ) = 1 (see Eq.…”

Section: Fundamental Basis Of the Ne-scgle Theorymentioning

confidence: 99%

Crossover from equilibration to aging: Nonequilibrium theory versus simulations

et al. 2017

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Understanding glasses and the glass transition requires comprehending the nature of the crossover from the ergodic (or equilibrium) regime, in which the stationary properties of the system have no history dependence, to the mysterious glass transition region, where the measured properties are nonstationary and depend on the protocol of preparation. In this work we use nonequilibrium molecular dynamics simulations to test the main features of the crossover predicted by the molecular version of the recently developed multicomponent nonequilibrium self-consistent generalized Langevin equation theory. According to this theory, the glass transition involves the abrupt passage from the ordinary pattern of full equilibration to the aging scenario characteristic of glass-forming liquids. The same theory explains that this abrupt transition will always be observed as a blurred crossover due to the unavoidable finiteness of the time window of any experimental observation. We find that within their finite waiting-time window, the simulations confirm the general trends predicted by the theory.

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“…II A. The non-equilibrium properties as well as the interfacial structures of colloidal fluids can be described simultaneously within dynamic density functional theory (DDFT) [14][15][16][17][18][19], the relevant concepts of which are summarized in Sec. II B.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium interfacial tension during relaxation

Bier

2015

Phys. Rev. E

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The concept of a non-equilibrium interfacial tension, defined via the work required to deform the system such that the interfacial area is changed while the volume is conserved, is investigated theoretically in the context of the relaxation of an initial perturbation of a colloidal fluid towards the equilibrium state. The corresponding general formalism is derived for systems with planar symmetry and applied to fluid models of colloidal suspensions and polymer solutions. It is shown that the nonequilibrium interfacial tension is not necessarily positive, that negative non-equilibrium interfacial tensions are consistent with strictly positive equilibrium interfacial tensions, and that the sign of the interfacial tension can influence the morphology of density perturbations during relaxation.

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Electro-osmotic flow in coated nanocapillaries: a theoretical investigation

Cited by 23 publications

References 30 publications

Nonequilibrium Phase Behavior from Minimization of Free Power Dissipation

Nonequilibrium Phase Behavior from Minimization of Free Power Dissipation

Crossover from equilibration to aging: Nonequilibrium theory versus simulations

Nonequilibrium interfacial tension during relaxation

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