The Overdamped Limit of Dynamic Density Functional Theory: Rigorous Results

Goddard, Benjamin D.; Pavliotis, Grigorios A.; Kalliadasis, Serafim

doi:10.1137/110844659

Cited by 39 publications

(72 citation statements)

References 65 publications

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“…In the large-γ limit, we obtain an analogous DDFT to that of Rex and Löwen [25], but with a modified HI term. See [44]. This in turn, by neglecting HI, recovers the original DDFT of Marconi and Tarazona [21].…”

Section: Equations Of Motionsupporting

confidence: 59%

“…This in turn, by neglecting HI, recovers the original DDFT of Marconi and Tarazona [21]. The passage to the overdamped limit was treated rigorously in [44].…”

Section: Equations Of Motionmentioning

confidence: 62%

“…In Section 6 we show that the kinetic pressure term may be neglected in the limit of large friction, i.e. γ 1; see [44] for a rigorous study of this regime. Assuming for the moment that we may approximate or neglect the term containing f (1) neq , in order to obtain a DDFT, it remains to treat the friction tensor term in (19).…”

Section: Expansion Of the One-body Distributionmentioning

confidence: 99%

“…We first use the results of [44], which show that, at least for two-body potential and friction terms and under the Enskog approximation, terms containing A are negligible in the high-friction limit. At this point we have recovered the corresponding result of [42], but using the rigorous results of [44]. To treat the HI terms, is necessary to find a closure relation, expressing v as a functional of ρ.…”

Section: Reduction To Dynamics Of the Densitymentioning

confidence: 99%

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Unification of dynamic density functional theory for colloidal fluids to include inertia and hydrodynamic interactions: derivation and numerical experiments

Goddard

Nold

Savva

et al. 2012

J. Phys.: Condens. Matter

143

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Abstract. Starting from the Kramers equation for the phase-space dynamics of the N -body probability distribution, we derive a dynamical density functional theory (DDFT) for colloidal fluids including the effects of inertia and hydrodynamic interactions (HI). We compare the resulting theory to extensive Langevin dynamics simulations for both hard rod systems and three-dimensional hard sphere systems with radially-symmetric external potentials. As well as demonstrating the accuracy of the new DDFT, by comparing with previous DDFTs which neglect inertia, HI, or both, we also scrutinise the significance of including these effects. Close to local equilibrium we derive a continuum equation from the microscopic dynamics which is a generalized Navier-Stokes-like equation with additional non-local terms governing the effects of HI. In the overdamped limit we recover analogues of existing configuration-space DDFTs but with a novel diffusion tensor.

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Section: Equations Of Motionsupporting

confidence: 59%

“…This in turn, by neglecting HI, recovers the original DDFT of Marconi and Tarazona [21]. The passage to the overdamped limit was treated rigorously in [44].…”

Section: Equations Of Motionmentioning

confidence: 62%

Section: Expansion Of the One-body Distributionmentioning

confidence: 99%

Section: Reduction To Dynamics Of the Densitymentioning

confidence: 99%

See 2 more Smart Citations

Unification of dynamic density functional theory for colloidal fluids to include inertia and hydrodynamic interactions: derivation and numerical experiments

Goddard

Nold

Savva

et al. 2012

J. Phys.: Condens. Matter

143

View full text Add to dashboard Cite

show abstract

“…The unstable character of these states can be readily confirmed by going beyond the equilibrium theory and considering the dynamics of the system. 8,35,[49][50][51] We also note the existence of a metastable film adsorbed on the walls of the pore. The interval of ∆µ where we find the film phase is rather narrow and has a width ∆ µ ≈ 7.6 × 10 −3 .…”

Section: B Slit Porementioning

confidence: 71%

Wetting of prototypical one- and two-dimensional systems: Thermodynamics and density functional theory

Yatsyshin

Savva

Kalliadasis

2015

The Journal of Chemical Physics

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Consider a two-dimensional capped capillary pore formed by capping two parallel planar walls with a third wall orthogonal to the two planar walls. This system reduces to a slit pore sufficiently far from the capping wall and to a single planar wall when the side walls are far apart. Not surprisingly, wetting of capped capillaries is related to wetting of slit pores and planar walls. For example, the wetting temperature of the capped capillary provides the boundary between first-order and continuous transitions to condensation. We present a numerical investigation of adsorption in capped capillaries of mesoscopic widths based on density functional theory. The fluid-fluid and fluid-substrate interactions are given by the pairwise Lennard-Jones potential. We also perform a parametric study of wetting in capped capillaries by a liquid phase by varying the applied chemical potential, temperature, and pore width. This allows us to construct surface phase diagrams and investigate the complicated interplay of wetting mechanisms specific to each system, in particular, the dependence of capillary wetting temperature on the pore width. C 2015 AIP Publishing LLC. [http://dx

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