Dissipative Particle Dynamics: A Method to Simulate Soft Matter Systems in Equilibrium and Under Flow - Selected Topics of Computational and Experimental Fluid Mechanics - page 51

colloids or amphiphilic molecules (Allen and Tildesley 1987 ; Frenkel and Smit 2002 ).
Liquid mixtures can be also studied by changing the potential among different kind
of particles.
While the original DPD method was thought as a complete simulation procedure,
including the soft potentials and the pair-wise thermostat, it was soon realized that
they do not need to be used together (Soddemann et al. 2003 ; Pastorino et al. 2007 ).
One could use a DPD thermostat with any interaction model (potentials) among
particles or molecules, and not only with soft potentials. This option of using “hard
potentials”, such as Lennard-Jones or any other common potential in MD simula-
tions comes, of course, at the price of reducing the time step in the simulations,
which is one of the original advantages of DPD. However, the correct description
of hydrodynamics can be a highly desirable feature in many physical situations of
interest.
DPD has been used for soft matter systems in many contexts and physical situ-
ations (Murtola et al. 2009 ; Binder et al. 2011 ; Moeendarbary et al. 2010 ). In this
work we review the use of the DPD method with soft and hard potentials for complex
fluids and polymeric systems. In Sect. 2 , we review the DPD method as a variation
of standard MD and Brownian Dynamics simulations. In Sect. 3 , we provide details
of the use of soft and hard potentials to simulate soft matter systems such as poly-
meric systems. In this section we also provide various examples of equilibrium DPD
simulations with soft potentials. We devote Sect. 4 to give examples of the use of
DPD in soft matter systems under flow in order to study the behavior and coupling
of these soft matter systems under non-equilibrium conditions. We also show some
difficulties concerning temperature conservation in strongly out-of-equilibrium sim-
ulations and how to deal with them in Sect. 5 . We provide the final comments and
conclusions in Sect. 6 .

2 Details of the Dissipative Particle Dynamics Method

2.1 Basic Molecular Dynamics Simulation

The DPD simulation scheme can be thought as an extension of the typical MD
algorithm (Allen and Tildesley 1987 ; Frenkel and Smit 2002 ). The basic idea in MD
is integrating numerically the classical equations of motion for a set of N particles.
The Newton equation for each particle i is

− ∂

V ( r )

≡ f i = m i ¨ r i , (1)

∂ r i

where m i is the mass of the particle, f i is the total force on particle i due to other
particles of the system and any external field applied. In a simple bulk simulation,
the evolution is done in a box of a certain volume with periodic boundary conditions,