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# Dissipative particle dynamics

Dissipative particle dynamics (DPD) has become over the last decade a popular method for simulating dynamical and rheological properties of both simple and complex fluids. It is a stochastic simulation technique, which was initially devised by Hoogerbrugge and Koelman [1] [2] to avoid the lattice artifacts of Lattice Gas Automata and to tackle hydrodynamic time and space scales beyond those available with molecular dynamics (MD). It was subsequently reformulated and slightly modified by Espanol [3] to ensure the proper thermal equilibrium state.

DPD is an off-lattice mesoscopic simulation technique which involves a set of particles moving in continuous space and discrete time. Particles represent whole molecules or fluid regions, rather than single atoms, and atomistic details are not considered relevant to the processes addressed. The particles’ internal degrees of freedom are then integrated out and replaced by simplified pairwise dissipative and random forces, so as to locally conserve momentum and ensure correct hydrodynamic behaviour. The main advantage of this method is that it gives access to longer time and length scales compared to what is achievable by conventional MD simulations.

The total force acting on a DPD particle i is expressed as a summation over all the other particles, j, of three forces of the pairwise-additive type:

$f_i =\sum_{j \ne i}(F^C_{ij} + F^D_{ij} + F^R_{ij})$

where the first term in the above equation refers to a conservative force, the second to a dissipative force and the third to a random force.

## Applications

A wide variety of complex hydrodynamic phenomena have been simulated using DPD. The goal of these simulations often is to relate the macroscopic non-Newtonian flow properties of the fluid to its microscopic structure. Such DPD applications range from modelling the rheological properties of concrete[4] to simulating liposome formation in biophysics[5]. Other recent applications involve three-phase phenomena such as dynamic wetting.[6]

## References

1. ^ P. J. Hoogerbrugge and J. M. V. A. Koelman. Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhysics Letters, 19(3):155–160, JUN 1 1992
2. ^ J. M. V. A. Koelman and P. J. Hoogerbrugge. Dynamic simulations of hard-sphere suspensions under steady shear. Europhysics Letters, 21(3):363–368, JAN 20 1993
3. ^ P. Espanol and P. B. Warren. Statistical-mechanics of dissipative particle dynamics. Europhysics Letters, 30(4):191–196, MAY 1 1995
4. ^ James S. Sims and Nicos S. Martys: Modelling the Rheological Properties of Concrete
5. ^ Petri Nikunen, Mikko Karttunen, and Ilpo Vattulainen: Modelling Liposome formation in biophysics
6. ^ B. Henrich, C. Cupelli, M. Moseler, and M. Santer": An adhesive DPD wall model for dynamic wetting, Europhysics Letters 80 (2007) 60004, p.1