Lattice Boltzmann method coupled with the Oldroyd-B constitutive model for a viscoelastic fluid

An extensible lattice Boltzmann method for viscoelastic flows: complex and moving boundaries in Oldroyd-B fluids

 Most biological fluids are viscoelastic, meaning that they have elastic properties in addition to the dissipative properties found in Newtonian fluids. Computational models can help us understand viscoelastic flow, but are often limited in how they deal with complex flow geometries and suspended particles. Here, we present a lattice Boltzmann solver for Oldroyd-B fluids that can handle arbitrarily shaped fixed and moving boundary conditions, which makes it ideally suited for the simulation of confined colloidal suspensions. We validate our method using several standard rheological setups and additionally study a single sedimenting colloid, also finding good agreement with the literature. Our approach can readily be extended to constitutive equations other than Oldroyd-B. This flexibility and the handling of complex boundaries hold promise for the study of microswimmers in viscoelastic fluids.

Lattice Boltzmann model for three-phase viscoelastic fluid flow

A lattice Boltzmann (LB) framework is developed for simulation of three-phase viscoelastic fluid flows in complex geometries. This model is based on a Rothman-Keller type model for immiscible multiphase flows which ensures mass conservation of each component in porous media even for a high density ratio. To account for the viscoelastic effects, the Maxwell constitutive relation is correctly introduced into the momentum equation, which leads to a modified lattice Boltzmann evolution equation for Maxwell fluids by removing the normal but excess viscous term. Our simulation tests indicate that this excess viscous term may induce significant errors. After three benchmark cases, the displacement processes of oil by dispersed polymer are studied as a typical example of three-phase viscoelastic fluid flow. The results show that increasing either the polymer intrinsic viscosity or the elastic modulus will enhance the oil recovery.

Prediction of Flow Effect on Crystal Growth of Semi-Crystalline Polymers Using a Multi-Scale Phase-Field Approach

A multi-scale phase-field approach, which couples the mesoscopic crystallization with the microscopic orientation of chain segments and macroscopic viscoelastic melt flow, is proposed to study how the crystal growth of semi-crystalline polymers is affected by flows. To make the simulation feasible, we divide the problem into three parts. In the first part, a finitely extensible nonlinear elastic (FENE) dumbbell model is used to simulate the flow induced molecular structure. In the second part, formulas for estimating the density, orientation and aspect ratio of nuclei upon the oriented molecular structure are derived. Finally, in the third part, a massive mathematical model that couples the phase-field, temperature field, flow field and orientation field is established to model the crystal growth with melt flow. Two-dimensional simulations are carried out for predicting the flow effect on the crystal growth of isotactic polystyrene under a plane Poiseuille flow. In solving the model, a semi-analytical method is adopted to avoid the numerical difficult of a "high Weissenberg number problem" in the first part, and an efficient fractional step method is used to reduce the computing complexity in the third part. The simulation results demonstrate that flow strongly affects the morphology of single crystal but does not bring a significant influence on the holistic morphology of bulk crystallization.

A Phase Field Technique for Modeling and Predicting Flow Induced Crystallization Morphology of Semi-Crystalline Polymers

Flow induced crystallization of semi-crystalline polymers is an important issue in polymer science and engineering because the changes in morphology strongly affect the properties of polymer materials. In this study, a phase field technique considering polymer characteristics was established for modeling and predicting the resulting morphologies. The considered crystallization process can be divided into two stages, which are nucleation upon the flow induced structures and subsequent crystal growth after the cessation of flow. Accordingly, the proposed technique consists of two parts which are a flow induced nucleation model based on the calculated information of molecular orientation and stretch, and a phase field crystal growth model upon the oriented nuclei. Two-dimensional simulations are carried out to predict the crystallization morphology of isotactic polystyrene under an injection molding process. The results of these simulations demonstrate that flow affects crystallization morphology mainly by producing oriented nuclei. Specifically, the typical skin-core structures along the thickness direction can be successfully predicted. More importantly, the results reveal that flow plays a dominant part in generating oriented crystal morphologies compared to other parameters, such as anisotropy strength, crystallization temperature, and physical noise.

Lattice Boltzmann simulations of a viscoelastic shear-thinning fluid

We present a hybrid lattice Boltzmann algorithm for the simulation of flow glass-forming fluids, characterized by slow structural relaxation, at the level of the Navier-Stokes equation. The fluid is described in terms of a nonlinear integral constitutive equation, relating the stress tensor locally to the history of flow. As an application, we present results for an integral nonlinear Maxwell model that combines the effects of (linear) viscoelasticity and (nonlinear) shear thinning. We discuss the transient dynamics of velocities, shear stresses, and normal stress differences in planar pressure-driven channel flow, after switching on (startup) and off (cessation) of the driving pressure. This transient dynamics depends nontrivially on the channel width due to an interplay between hydrodynamic momentum diffusion and slow structural relaxation.

Temperature and Concentration Stratification Effects in Mixed Convection Flow of an Oldroyd-B Fluid with Thermal Radiation and Chemical Reaction

This research addresses the mixed convection flow of an Oldroyd-B fluid in a doubly stratified surface. Both temperature and concentration stratification effects are considered. Thermal radiation and chemical reaction effects are accounted. The governing nonlinear boundary layer equations are converted to coupled nonlinear ordinary differential equations using appropriate transformations. Resulting nonlinear systems are solved for the convergent series solutions. Graphs are plotted to examine the impacts of physical parameters on the non-dimensional temperature and concentration distributions. The local Nusselt number and the local Sherwood number are computed and analyzed numerically.