Multi-particle collision dynamics for microflows

Abstract

Multiparticle collision dynamics (MPCD) is a particle based mesoscopic simulation technique for incorporating hydrodynamics and thermal fluctuations in complex fluid simulations. Due to its simplicity, theMPCD algorithm has become quite popular in the study of complex flow problems. In this thesis, kinetic nature of the algorithm is investigated for quantitative accuracy in case of flows at finite Knudsen numbers. In particular, microflow set-ups such as shear, gravity, and pressure driven flows have been used for the study, and the algorithm is benchmarked against the well know analytical and numerical results. In addition, the effectiveness of bounce back and diffuse wall boundary conditions are investigated for the above mentioned canonical flows. Here, we also present a new collision scheme in the framework of MPCD, termed as Pseudo Binary Collision Model (PBCM), which ensures Galilean invariance for the system at small time steps. In standard MPCD, velocity correlations start building up among particles when the time step is small enough that the particles move only a fraction of the cell size of the grid used. These correlations in turn lead to the failure of Galilean invariance, and the system shows unphysical behaviour. By numerical means, we have shown that the performance of MPCD method improves substantially by the use of pseudo binary collision model in simulations with small time steps. Finally, we show how the ideal gas equation of state of an MPCD fluid can be modified to a general non-ideal equation of state. Here, we have used a phenomenological mean field model for incorporating excluded volume effect into the system. In particular, we have used the Van der Waals and Carnahan-Starling equations of state for including the excluded volume effect into the MPCD system, and also the effectiveness of this approach is investigated. In addition, the effect of attraction between molecules is included by considering a Vlasov type force on the particles. With these changes a two phase system, condensation of a gas into liquid, is studied using MPCD. The study of Maxwell construction shows excellent agreement with the theory.