Journal of Statistical Physics

, Volume 164, Issue 4, pp 785–809 | Cite as

Dynamical Density Functional Theory for Orientable Colloids Including Inertia and Hydrodynamic Interactions

  • Miguel A. Durán-Olivencia
  • Benjamin D. Goddard
  • Serafim KalliadasisEmail author


Over the last few decades, classical density-functional theory (DFT) and its dynamic extensions (DDFTs) have become powerful tools in the study of colloidal fluids. Recently, previous DDFTs for spherically-symmetric particles have been generalised to take into account both inertia and hydrodynamic interactions, two effects which strongly influence non-equilibrium properties. The present work further generalises this framework to systems of anisotropic particles. Starting from the Liouville equation and utilising Zwanzig’s projection-operator techniques, we derive the kinetic equation for the Brownian particle distribution function, and by averaging over all but one particle, a DDFT equation is obtained. Whilst this equation has some similarities with DDFTs for spherically-symmetric colloids, it involves a translational-rotational coupling which affects the diffusivity of the (asymmetric) particles. We further show that, in the overdamped (high friction) limit, the DDFT is considerably simplified and is in agreement with a previous DDFT for colloids with arbitrary-shape particles.


Dynamical density functional theory Colloidal fluids Arbitrary-shape particles Orientable colloids 



We are grateful to the anonymous referees for useful comments and suggestions and to Andreas Nold for stimulating discussions that led to the scaling arguments in Appendix 2. We acknowledge financial support from the European Research Council via Advanced Grant No. 247031 and from EPSRC via Grant Nos. EP/L020564 and EP/L025159.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Miguel A. Durán-Olivencia
    • 1
  • Benjamin D. Goddard
    • 2
  • Serafim Kalliadasis
    • 1
    Email author
  1. 1.Department of Chemical EngineeringImperial College LondonLondonUK
  2. 2.School of Mathematics and the Maxwell Institute for Mathematical SciencesUniversity of EdinburghEdinburghUK

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