Modelling multi-viscosity systems with dissipative particle dynamics

Dissipative particle dynamics (DPD) is a particle-based simulation technique. It is applicable on time and length scales in-between those typical for molecular modelling and continuum mechanics. These features make DPD an interesting tool in the area of multiphase flows. So far, multiphase DPD simulations were restricted to fluids with the same viscosity, because it was unclear how one could model phases with a different viscosity together. Here, we show how to deal with more than one viscosity in the system. The viscosity of a DPD fluid can be controlled with the friction factor, an input parameter in DPD that characterises the strength of the drag force between interacting particles. So, in a multiphase system each fluid has its own friction factor, yielding the viscosity of that fluid. Now, the problem is to define the friction factor for the interaction between particles of unlike fluids. This factor has a significant effect on flow dynamics, but lacks a related physical property such as interfacial tension or solubility to specify its value. Three methods are presented to calculate the friction factor between particles of unlike fluids. One of these methods only involves the friction factors of the individual fluids and is of most practical use in real applications. The methods are validated for steady and unsteady flow of two adjacent immiscible fluids. Results from these two-phase test cases are consistent with theory. This opens the door to more extensive modelling of multi-viscosity systems with DPD.