Fully-resolved simulations of particle-laden viscoelastic fluids using an immersed boundary method

Abstract

This study reports the development of a direct simulation code for solid spheres moving through viscoelastic fluids with a range of different rheological behaviors. The numerical algorithm was implemented on an opensource finite-volume solver coupled with an immersed boundary method, and is able to perform fully-resolved simulations, wherein all flow scales associated with the particle motion are resolved. The formulation employed exploits the log-conformation tensor to avoid high Weissenberg number issues when calculating the polymeric extra stress. A number of benchmark flows were simulated using this method, to assess the accuracy of the newlydeveloped solver. First, the sedimentation of a sphere in a bounded domain surrounded by either Newtonian or viscoelastic fluid was computed, and the numerical results were verified by comparison with experimental and computational data from the literature. Additionally, the spatial and temporal accuracies of the algorithm were evaluated, and different transient and advection discretization schemes were investigated. Second, the rotation of a sphere in a homogeneous shear flow was studied, and again the numerical results obtained were compared to those from the literature. Good agreement is obtained for the variation in the particle rotation rate as a function of Weissenberg number, using both the newly implemented algorithm and an alternative fixed-mesh approach. Finally, the cross-stream migration of a neutrally buoyant sphere in a steady Poiseuille flow, consisting of either a Newtonian or viscoelastic suspending fluid was investigated. For the Newtonian fluid good agreement was obtained for the particle equilibrium position when compared to the well known Segré-Silberberg effect, and for the viscoelastic fluid the effect of the retardation ratio on the final particle equilibrium position was studied. Additionally, the newly-developed solver capabilities were tested to study the shear-induced particle alignment in wall-bounded Newtonian and viscoelastic fluids. The role of the fluid rheology and finite gap size on both the rate and approach pathways of the solid particles is illustrated.

Convergent solutions of Stokes Oldroyd-B boundary value problems using the Immersed Boundary Smooth Extension (IBSE) method

“…Significant effort has been expended on improving the accuracy of embedded boundary schemes [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], an overview is provided in [18]. In addition, methods which build on the IB or Immersed Finite Element (IFEM) method but with modifications such as the use of one-sided interpolation and spread operators near to boundaries have been used to model flow past fixed objects and deformable particles in a viscoelastic fluid [41][42][43]; these works have shown that averaged flow features are resolved but convergence of the stress at and near boundaries is not considered. A subset of these improved embedded boundary methods [18,19,39] generate solutions to the fluid equations that are globally smooth in a simple domain, and as such allow discretizations of more complicated, nonlinear equations to be constructed in a way that is nearly unaltered from solvers used on simple geometries.…”

Verification and Validation of openInjMoldSim, an Open-Source Solver to Model the Filling Stage of Thermoplastic Injection Molding

“…In those cases, instead of using Equation (A1), a different variation of the method could be used. Assuming that ap was the order of accuracy of the discretization schemes used in the calculation procedure, instead of using three meshes, the extrapolated value could be obtained by Equation (A1) using only the two most refined meshes [32].…”

A Meta-Model to Predict the Drag Coefficient of a Particle Translating in Viscoelastic Fluids: A Machine Learning Approach

“…The flow of particle-laden complex fluids has been the centerpiece of many well-documented experimental, theoretical, and numerical approaches [ 1 , 2 , 3 , 4 ]. These fluids are non-Newtonian in character showing shear thinning, shear thickening, viscoplastic, time-dependent and viscoelastic behaviors under different flow conditions.…”