Multi-Particle Collision Dynamics: A Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids

Abstract

In this review, we describe and analyze a mesoscale simulation method for fluid flow, which was introduced by Malevanets and Kapral in 1999, and is now called multi-particle collision dynamics (MPC) or stochastic rotation dynamics (SRD). The method consists of alternating streaming and collision steps in an ensemble of point particles. The multi-particle collisions are performed by grouping particles in collision cells, and mass, momentum, and energy are locally conserved. This simulation technique captures both full hydrodynamic interactions and thermal fluctuations. The first part of the review begins with a description of several widely used MPC algorithms and then discusses important features of the original SRD algorithm and frequently used variations. Two complementary approaches for deriving the hydrodynamic equations and evaluating the transport coefficients are reviewed. It is then shown how MPC algorithms can be generalized to model non-ideal fluids, and binary mixtures with a consolute point. The importance of angular-momentum conservation for systems like phase-separated liquids with different viscosities is discussed. The second part of the review describes a number of recent applications of MPC algorithms to study colloid and polymer dynamics, the behavior of vesicles and cells in hydrodynamic flows, and the dynamics of viscoelastic fluids.

Shear-induced dynamics of polymeric globules at adsorbing homogeneous and inhomogeneous surfaces

“…This method is practical for small particle numbers and large system volumes, as we have in our study, and thus preferred over alternative LatticeBoltzmann methods [23] or multi-particle collision dynamics [24]. The discretized Langevin equation for particle i and time step Δt = Δt/τ is given by…”

Optimal control of particle separation in inertial microfluidics

“…We determine the flow field within the channel and inertial lift forces acting on suspended particles using a mesoscopic simulation technique called Multi-Particle Collision Dynamics (MPCD) which effectively solves the Navier-Stokes equations [35][36][37]. We have recently used it to study the motion of sheets and active particles as well as the locomotion of the parasite African trypanosome [38][39][40][41].…”

Inertial microfluidics with multi-particle collision dynamics

“…In this section we discuss the details of our implementation of a variant of the original method based on the Andersen thermostat. For an extensive review we refer to the article by Gompper et al where they describe algorithmic details, the resulting fluid properties, and the application of MPCD to a wide range of systems [29].…”

“…We have introduced the number of particles in the cell, N c , the particle position vector r i,c relative to the center of mass of the cell at r c , and the moment of inertia tensor θ of all the particles in the cell again relative to r c . If the mean free path of fluid particles is small compared to the cell size l c , correlations may arise [29]. To remove these correlations and restore Galilean invariance, we perform a random shift of all collision cells.…”