# Dissipative particle dynamics: Algorithms and recent<br/><br/>applications<br/><br/>

Friday, October 16, 2009 - 11:00am - 11:40am

EE/CS 3-180

Bruce Caswell (Brown University)

In its original version the governing equations of Dissipative Particle Dynamics (DPD) contain three forces which need to be specified in any application, namely: i. a conservative soft repulsion, ii. a random force, iii. a dissipative force. The required thermostat is enforced by balance of ii. and iii. through the Fluctuation-Dissipation theorem . With about 3 to 4 thousand particles (number densities of 3 to 4) these forces simulate a nearly incompressible fluid whose compressibility is close to water’s, and whose viscosity is constant. When the latter is combined with the self-diffusion coefficient a characteristic radius of the DPD particle can be calculated from the Stokes-Einstein relation. Drag force calculations on single DPD particles imersed in a streaming flow show consistency with Stokes law as the Schmidt numbe increases from one. Thus DPD particles are mesoscopic entities, and are hydrodynamically similar to the beads of Brownian Dynamics (BD). However, the hydrodynamic forces between DPD particles are implicit. Complex fluids such as polymers are modeled by connecting DPD particles with spring forces. Examples include dilute, concentrated and undiluted bead-spring chains in plane Couette and in Poiseulle flow which are simulated with periodic boundary conditions. Real boundaries require carefull treatment to avoid unphysical density fluctuations near a wall. Another application of DPD is in the ‘tripple decker’ which attemps to match regions described by continuum, DPD, and Molecular Dynamics (MD) respectively.

In the original DPD all forces on a particle are central which obviates the need to deal with angular momentum. However, the calculated rotational drag on a single DPD particle was found to deveate subtantially from the Stokes value. The remedy adds a non-central term to the dissipative force, and includes angular momentum explicitly. The new formulation has been used to simulate a colloidal suspension of large hard DPD-particles in a solvent of soft DPD particles. The results show the model to be economical, and to exhibit the same features as those obtained by the Stokesian dynamics method.

A more complex case is the red blood cell (RBC) model with a membrane constructed from DPD particles connected by nonlinear springs and with an extra dissipative force to describe the known viscolelastic properties of the RBC membrane. This model succeeds in describing quantitatively a number of static and dynamic experiments without adjustment of parameters.

The models described above have been developed empirically by intuition. A more rigorous and difficult approach is to attempt to derive DPD from analysis at the molecular level. To this end MD simulations of Lennard-Jonesium (LJ) are interpreted statistically for clusters of O(10) LJ molecules to derive the soft potentials and also the dissipative forces which are found generally to be non-central.

In the original DPD all forces on a particle are central which obviates the need to deal with angular momentum. However, the calculated rotational drag on a single DPD particle was found to deveate subtantially from the Stokes value. The remedy adds a non-central term to the dissipative force, and includes angular momentum explicitly. The new formulation has been used to simulate a colloidal suspension of large hard DPD-particles in a solvent of soft DPD particles. The results show the model to be economical, and to exhibit the same features as those obtained by the Stokesian dynamics method.

A more complex case is the red blood cell (RBC) model with a membrane constructed from DPD particles connected by nonlinear springs and with an extra dissipative force to describe the known viscolelastic properties of the RBC membrane. This model succeeds in describing quantitatively a number of static and dynamic experiments without adjustment of parameters.

The models described above have been developed empirically by intuition. A more rigorous and difficult approach is to attempt to derive DPD from analysis at the molecular level. To this end MD simulations of Lennard-Jonesium (LJ) are interpreted statistically for clusters of O(10) LJ molecules to derive the soft potentials and also the dissipative forces which are found generally to be non-central.

MSC Code:

70Fxx

Keywords: