Numerical Modeling of Viscoelasticity in Particle Suspensions Using the Discrete Element Method

The rheological behavior of particle suspensions is a challenging problem because its description depends on the interaction of two phases with different material properties. This interaction can lead to complex behavior because of acting forces at the solid–liquid interface such as lubrication. The goal of this work is to propose a method for the modeling of fluids viscoelasticity in the presence of spherical particles including fluid–particle interactions. To accomplish this, we employed a simplified approach using the discrete element method (DEM) coupled with computational fluid dynamics (CFD) to simulate a suspension of particles under oscillatory flow in a three-dimensional computational domain. The choice of DEM provides versatility to customize the constitutive relations of particle–particle and fluid–particle interactions. Particularly, we focused on studying the effect of solid–liquid interaction (lubrication forces) on the viscoelasticity of the particulate system. To analyze the effect of this interfacial force, we simplified the particle–particle interaction to a nonadhesive elastic contact, thus avoiding aggregation of the particles. The work consists of two parts: the first one is a pure CFD model of the oscillatory motion applied to a Newtonian fluid (without particles), and the second is an extended version including DEM to simulate the viscoelasticity of the particle suspension. In this way, we can isolate the effect of fluid inertia on the viscoelasticity of the particulate system. The obtained results show that the model is capable to reproduce qualitatively the increase of the storage modulus as a function of the solid volume fraction and the dependence of dynamic moduli on the applied shear strain. The presented methodology provides a new insight into modeling of rheology by customizing interactions at the particle level based purely on first-principles with model parameters including solely material properties and physically identifiable quantities.