Imperial College London
Alternate

Dr Miguel A. Durán-Olivencia

Faculty of Engineering, Department of Chemical Engineering

 
 
 
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Contact

 

m.duran-olivencia

 
 
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Location

 

Roderic Hill BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Duran:2017:1367-2630/aa9041,
author = {Duran, Olivencia MA and Yatsyshin, P and Goddard, B and Kalliadasis, S},
doi = {1367-2630/aa9041},
journal = {New Journal of Physics},
title = {General framework for fluctuating dynamic density functional theory},
url = {http://dx.doi.org/10.1088/1367-2630/aa9041},
volume = {19},
year = {2017}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations. We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then, we average out the bath via Zwanzig's projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean-Kawasaki (DK) model, which resembles the stochastic Navier-Stokes (NS) description of a fluid. Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities. We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution, where the former is related to a generalised version of the canonical distribution, we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of the mesoscopic density and momentum fields. Along the way, we outline the connection between the ad-hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory (DFT). The resultant equation has the structure of a dynamical DFT (DDFT) with an additional fluctuating force coming from the random interactions with the bath. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating NS equations, originally derived by Landau and Lifshitz. Our framework thus provi
AU  - Duran,Olivencia MA
AU  - Yatsyshin,P
AU  - Goddard,B
AU  - Kalliadasis,S
DO  - 1367-2630/aa9041
PY  - 2017///
SN  - 1367-2630
TI  - General framework for fluctuating dynamic density functional theory
T2  - New Journal of Physics
UR  - http://dx.doi.org/10.1088/1367-2630/aa9041
UR  - http://iopscience.iop.org/article/10.1088/1367-2630/aa9041
UR  - http://hdl.handle.net/10044/1/51664
VL  - 19
ER  -
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