An integrated boundary approach for colloidal suspensions simulated using smoothed dissipative particle dynamics

Abstract

In particle-based continuum solvers such as smoothed particle hydrodynamics (SPH) and smoothed dissipative particle dynamics (SDPD), one of the most significant challenges is the treatment of solid boundaries like walls and colloidal particles, whose presence leads to a truncation of the integral approximation, and hence, error in the numerical solution. In this work, we describe an integrated boundary framework for modeling colloidal suspensions composed of rigid spherical particles. The integral corresponding to the colloid's contribution is analytically evaluated, giving a simple and computationally inexpensive approach relative to conventional boundary particle techniques. We formulate a thermodynamically-consistent version of this top-down method for mesoscale simulations, in which the fluid exchanges momentum with the suspended particles due to thermal fluctuations, giving a framework for modeling the dynamics of colloids at arbitrary Reynolds and Péclet numbers. The resulting evolution equations are validated for a single colloidal particle in a fluid at constant temperature. This simple approach requires ∼Nc(ρ/m)Rc2 fewer pair force calculations relative to traditional boundary particle strategies, where Nc is the number of colloids in the system, Rc is the colloid radius, ρ is the colloid mass density, and m is the mass of the SDPD particles. In addition, the use of integrated boundaries removes the need for rigidbody constraint dynamics, giving an elegant and efficient basis for large-scale simulations of colloidal suspensions that is general and does not make any physical assumptions about the flow.