SPH modeling and simulation of spherical particles interacting in a viscoelastic matrix

Abstract

In this work, we extend the three-dimensional Smoothed Particle Hydrodynamics (SPH) non-colloidal particulate model previously developed for Newtonian suspending media in Vázquez-Quesada and Ellero [“Rheology and microstructure of non-colloidal suspensions under shear studied with smoothed particle hydrodynamics,” J. Non-Newtonian Fluid Mech. 233, 37–47 (2016)] to viscoelastic matrices. For the solvent medium, the coarse-grained SPH viscoelastic formulation proposed in Vázquez-Quesada, Ellero, and Español [“Smoothed particle hydrodynamic model for viscoelastic fluids with thermal fluctuations,” Phys. Rev. E 79, 056707 (2009)] is adopted. The property of this particular set of equations is that they are entirely derived within the general equation for non-equilibrium reversible-irreversible coupling formalism and therefore enjoy automatically thermodynamic consistency. The viscoelastic model is derived through a physical specification of a conformation-tensor-dependent entropy function for the fluid particles. In the simple case of suspended Hookean dumbbells, this delivers a specific SPH discretization of the Oldroyd-B constitutive equation. We validate the suspended particle model by studying the dynamics of single and mutually interacting “noncolloidal” rigid spheres under shear flow and in the presence of confinement. Numerical results agree well with available numerical and experimental data. It is straightforward to extend the particulate model to Brownian conditions and to more complex viscoelastic solvents.