Modelling inelastic Granular Media Using Dynamical Density Functional Theory

Goddard, Benjamin D.; Hurst, T.; Ocone, Raffaella

doi:10.1007/s10955-020-02675-0

Cited by 6 publications

(4 citation statements)

References 53 publications

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“…where p 0 = (k B T/m) ρ is the ideal gas pressure and F exc [ρ] = ´dr u is the excess free energy (including the external field), where, in case of a CDFT-based free energy, u is defined by equation (45). Furthermore, D is the viscous stress, and…”

Section: Discussionmentioning

confidence: 99%

“…The early versions of the theory provided a single equation of motion for over-damped Brownian systems, while inertial effects were incorporated later [33][34][35][36][37][38][39][40]. The most recent versions of the theory operate with momentum and energy-type fields in addition to the one-particle density, for which closed hydrodynamic equations are developed [41][42][43][44][45]. For colloidal systems with small (but still moderate) friction coefficients, significant discrepancies have been found between the theory and experiments [46], which can be eliminated by applying systematic corrections [38][39][40].…”

Section: Introductionmentioning

confidence: 99%

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Hydrodynamic density functional theory of simple dissipative fluids

Tóth

2024

New J. Phys.

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In this paper, a statistical physical derivation of thermodynamically consistent fluid mechanical equations is presented for non-isothermal viscous molecular fluids. The coarse-graining process is based on (i) the adiabatic expansion of the one-particle probability density function around Local Thermodynamic Equilibrium, (ii) the assumption of decoupled particle positions and momenta, and (iii) the variational principle. It is shown that there exists a class of free energy functionals for which the conventional thermodynamic formalism can be naturally adopted for non-equilibrium scenarios, and describes entropy monotonic fluid flow in isolated systems. Furthermore, the analysis of the general continuum equations revealed the possibility of a non-local transport mode of energy in highly compressible dense fluids.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hydrodynamic density functional theory of simple dissipative fluids

Tóth

2024

New J. Phys.

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“…Relevant applications of the pseudospectral framework include the solution of different DDFT models 19,20 , DFT problems 54,55 , and other PDE applications 8,60 . The methods have also been extended to solving three-dimensional problems and optimal control problems 2 .…”

Section: A Pseudospectral and Spectral Element Methodsmentioning

confidence: 99%

Dynamic density functional theory for sedimentation processes on complex domains: Modelling, spectral elements, and control problems

Roden,

Goddard,

Pearson

2023

The Journal of Chemical Physics

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Modelling of many real-world processes, such as drug delivery, wastewater treatment, and pharmaceutical production, requires accurate descriptions of the dynamics of hard particles confined in complicated domains. In particular, when modelling sedimentation processes or systems with driven flows, it is important to accurately capture volume exclusion effects. This work applies Dynamic Density Functional Theory to the evolution of a particle density under diffusion, external forces, particle–particle interaction, and volume exclusion. Using a spectral element framework, for the first time it is possible to include all of these effects in dynamic simulations on complex domains. Moreover, this allows one to apply complicated no-flux, and other non-local, non-linear, boundary conditions. The methodology is also extended to control problems, addressing questions of how to enhance production set-up in industrially-motivated processes. In this work the relevant models are introduced, numerical methods are discussed, and several example problems are solved to demonstrate the methods’ versatility. It is shown that incorporating volume exclusion is crucial for simulation accuracy and we illustrate that the choice of boundary conditions significantly impacts the dynamics.

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“…Building up on earlier work [134,135], Fang [136,137,164] has recently derived a DDFT for ferrofluids. Another example is the development of a DDFT for granular media [165,166]. Stanton et al [167] have modeled cellular membranes in DDFT.…”

Section: Applications In New Physical Contextsmentioning

confidence: 99%

Perspective: New directions in dynamical density functional theory

Vrugt

Wittkowski

2022

J. Phys.: Condens. Matter

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Classical dynamical density functional theory (DDFT) has become one of the central modeling approaches in nonequilibrium soft matter physics. Recent years have seen the emergence of novel and interesting fields of application for DDFT. In particular, there has been a remarkable growth in the amount of work related to chemistry. Moreover, DDFT has stimulated research on other theories such as phase field crystal models and power functional theory. In this perspective, we summarize the latest developments in the field of DDFT and discuss a variety of possible directions for future research.

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Modelling inelastic Granular Media Using Dynamical Density Functional Theory

Cited by 6 publications

References 53 publications

Hydrodynamic density functional theory of simple dissipative fluids

Hydrodynamic density functional theory of simple dissipative fluids

Dynamic density functional theory for sedimentation processes on complex domains: Modelling, spectral elements, and control problems

Perspective: New directions in dynamical density functional theory

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