Dynamical density functional theory for colloidal particles with arbitrary shape

Abstract

Starting from the many-particle Smoluchowski equation, we derive a dynamical density functional theory for Brownian particles with an arbitrary shape. Both passive and active (self-propelled) particles are considered. The resulting theory constitutes a microscopic framework to explore the collective dynamical behavior of biaxial particles in non-equilibrium. For spherical and uniaxial particles, earlier derived dynamical density functional theories are recovered as special cases. Our study is motivated by recent experimental progress in preparing colloidal particles with many different biaxial shapes.

Keywords:

• density functional theory
• dynamical density functional theory
• self-propelled biaxial colloidal particles
• active soft matter
• Brownian dynamics of anisotropic particles

Acknowledgements

We dedicate this work to Luciano Reatto. We thank Helmut R. Brand, Henricus H. Wensink, Gerhard Nägele, and Joost de Graaf for helpful discussions. This work has been supported by DFG within SFB TR6 (project D3).

Notes

Note

1. The reason we write instead of in Equation (34) is that one could in principle also describe systems with a space-dependent short-time diffusion tensor. This is especially relevant for fluids with a space-dependent viscosity.