On the use of a diffuse-interface model for the simulation of rigid particles in two-phase Newtonian and viscoelastic fluids

For the simulation of particles in two-phase flows, the diffuse-interface model is frequently employed to describe the fluid-fluid interface. The diffuse-interface model can naturally handle moving contact lines and topological changes, but the thickness of the interface is in general chosen larger than the physical one. We systematically investigated the effect of both the interface thickness and the diffusion of the fluids on the motion of rigid particles in two-phase flows, using a diffuse-interface model for the fluid-fluid interface. A sharp- interface model is considered for the fluid-fluid interface as well, which is expected to behave as the limiting case of the interface thickness going to zero.\u3cbr/\u3eThe first case that was investigated is a spherical particle in a closed cylindrical container filled with two Newtonian fluids, where the particle is moved toward the fluid-fluid interface by a force. The second case that was investigated is that of the migration of a rigid particle in a two-phase viscoelastic shear flow. The migration of the particle is due a contrast in the viscoelastic properties of the fluids, a phenomenon that was not reported before in the literature. For both cases, the results for the diffuse-interface model converge to the sharp- interface model when the interface thickness is decreased. However, it is shown that both the interface thickness and the diffusion of the fluids play crucial roles in the resulting dynamics\u3cbr/\u3eof a particle interacting with a diffuse fluid-fluid interface

A comparison between the XFEM and a boundary-fitted mesh method for the simulation of rigid particles in Cahn-Hilliard fluids

Two distinct numerical methods are compared for the simulation of rigid particles sus- pended in Cahn-Hilliard fluids: a boundary-fitted mesh method (BFMM) and an extended finite element method (XFEM). In the BFMM, meshes are generated that cover only the fluid domain and are aligned with the particle boundary, thus boundary conditions can be imposed directly in the nodes on the particle boundary. In the XFEM, a mesh is generated that covers both the fluid and particle domain, and accurate integration is performed by subdividing elements that are intersected by the particle boundary. Furthermore, boundary conditions on the particle boundary are imposed in a weak sense.\u3cbr/\u3eIn the BFMM, locally refined meshes are generated, and remeshing is performed when the fluid-fluid interface moves out of the refined region. In the XFEM, a grid deformation technique is used to locally refine the mesh. This approach avoids the generation of new meshes, but allows for less control over the local element size. Excellent agreement was found between the two methods. In terms of accuracy, both methods perform similar, with the BFMM being slightly more accurate when studying mesh-convergence and the XFEM being slightly more accurate when studying time-convergence

Simulations of the start-up of shear flow of 2D particle suspensions in viscoelastic fluids : structure formation and rheology

We present simulations of the start-up of shear flow of 2D suspensions of rigid particles in viscoelastic fluids. A novel numerical method is applied that makes use of biperiodic domains, which act as representative volume elements of the suspension. Local mesh refine- ment ensures the method is both accurate and efficient, without the need for a repulsive potential between the particles. By averaging many simulations for random initial positions of the particles, we obtain the true rheological bulk response of the material. At Weissenberg numbers of 1 and higher, particle chaining is observed that leads to a decrease in bulk viscos- ity, an effect that was observed experimentally in [1]. Increasing the solid area fraction leads to the particle alignment occuring faster and the particles forming longer chains, causing a stronger decrease in bulk viscosity. In addition, at solid area fractions of 0.3 and higher, an increase of the bulk first normal stress difference is observed, which may be attributed to an increase in local shear rate in between the particle chains. Finally, flow cessation is simulated and it is found that the particle chains are preserved until all elastic stresses in the fluid have relaxed

Direct numerical simulation of particle alignment in viscoelastic fluids

Rigid particles suspended in viscoelastic fluids under shear can align in string-like struc- tures in the flow direction. Although this phenomenon was first reported almost four decades ago by Michele et al. [1], the exact mechanism of particle alignment is not completely un- derstood. Initially, it was believed that normal stress differences are responsible for the alignment of particles, but recent experimental work by van Loon et al. [2] showed particle alignment in a shear-thinning fluid without significant normal stress differences.\u3cbr/\u3eTo unravel the phenomenon of particle alignment, we present for the first time 3D direct numerical simulations of the alignment of two and three rigid, non-Brownian particles in a viscoelastic shear flow, with the shear rate denoted by γ ̇. The equations are solved on moving, boundary-fitted meshes, which are locally refined to accurately describe the polymer stresses around and in between the particles. A small minimal gap size between the particles is introduced. The Giesekus model, with a relaxation time λ, is used for the viscoelastic fluid, and the effect of the Weissenberg number Wi = λγ ̇ , shear thinning parameter α and ratio between the solvent viscosity and zero-shear viscosity β is investigated.\u3cbr/\u3eThe numerical method allows for the detailed investigation of particles interacting in viscoelastic flows. Alignment of two and three particles is observed in the simulations. Mor- phology plots were created for various values of α, β and Wi. Alignment is mainly governed by the value of the elasticity parameter S, defined as half of the ratio between the first nor- mal stress difference and shear stress of the suspending fluid. Alignment appears to occur above a critical value of S, which decreases with increasing α, thus shear thinning promotes alignment. Furthermore, three particles align at lower S than two particles. Finally, simula- tions were performed in a shear-thinning Carreau fluid, where we never observed alignment of the particles. These results lead us to the conclusion that the presence of normal stress differences is essential for particle alignment to occur, although it is strongly promoted by shear thinning

A numerical study of particle migration and sedimentation in viscoelastic couette flow

In this work, a systematic investigation of the migration of sedimenting particles in a viscoelastic Couette flow is presented, using finite element 3D simulations. To this end, a novel computational approach is presented, which allows us to simulate a periodic configuration of rigid spherical particles accurately and efficiently. To study the different contributions to the particle migration, we first investigate the migration of particles sedimenting near the inner wall, without an externally-imposed Couette flow, followed by the migration of non-sedimenting particles in an externally-imposed Couette flow. Then, both flows are combined, i.e., sedimenting particles with an externally-imposed Couette flow, which was found to increase the migration velocity significantly, yielding migration velocities that are higher than the sum of the combined flows. It was also found that the trace of the conformation tensor becomes asymmetric with respect to the particle center when the particle is initially placed close to the inner cylinder. We conclude by investigating the sedimentation velocity with an imposed orthogonal shear flow. It is found that the sedimentation velocity can be both higher or lower then the Newtonian case, depending on the rheology of the suspending fluid. Specifically, a shear-thinning viscosity is shown to play an important role, which is in-line with previously-published results

Temperature-dependent sintering of two viscous particles

Selective laser sintering (SLS) is a promising additive manufacturing technique, where powder particles are fused together under the influence of a laser beam. To obtain good material properties in the final product, the powder particles need to form a homogeneous melt during the fabrication process. On the one hand, you want to give the particles enough time to fuse, such that the original shape is no longer visible, and interdiffusion of polymers can take place. On the other hand, you want the process to be as fast as possible. This is contradictory, thus choosing the right conditions is not trivial. We developed a computational model based on the finite element method to study the material and process parameters concerning the melt flow of the powder particles. In this work, we restrict ourselves to varying the temperature-dependent viscosity, the process parameters, and the convective heat transfer coefficient of the sintering of two polymer (polyamide 12) particles. The simulations allow for a quantitative analysis of the influence of the different material and processing parameters. From the simulations follows that an optimal sintering process has a low ambient temperature, a narrow beam width with enough power to heat the particles only a few degrees above the melting temperature, and a polymer of which the viscosity decreases significantly within these few degrees

Head-on collision of Newtonian drops in a viscoelastic medium

Depending on the application one needs to either stabilize or destabilize the interfacial properties of an emulsion. An aspect of the dynamics that governs the stability of emulsions in general is the drainage time of the film that is formed when two drops collide. In this work, we study the effect that viscoelasticity of the matrix fluid has on this drainage time of two Newtonian drops that perform a head-on collision under an applied macroscopic extensional rate. For the modeling of the viscoelastic matrix material the Giesekus model is chosen. A cylindrical coordinate system is applied with imposed axisymmetry and the resulting equations are solved using fully resolved numerical simulations employing a finite element discretization. Our results show that viscoelasticity reduces the drainage time, which is a combined effect of three different stages

Direct numerical simulation of a bubble suspension in small amplitude oscillatory shear flow

Bubble suspensions can be found in many different fields and studying their rheology is crucial in order to improve manufacturing processes. When bubbles are added to a liquid, the magnitude of the viscosity changes and the behavior of the material is modified, giving it viscoelastic properties. For the purpose of this work the suspended bubbles are considered to be monodisperse. It is assumed that Brownian motion and inertia can be neglected and that the fluid of the matrix is Newtonian and incompressible. The suspension is subject to an oscillatory strain while remaining in the linear regime. The resulting equations are solved in 3D with direct numerical simulation using a finite element discretization. Results of an ordered and random distribution of bubbles of volume fractions up to 40% are presented. The presence of bubbles has an opposite effect on the rheology of the suspension depending on the applied frequency. When the frequency is low, bubbles act as rigid fillers giving a rise to viscosity. On the contrary, when the frequency is high the strain rate is being accommodated by the gaseous phase. Hence, bubbles deform, leading to a decrease of the viscosity.\u3cbr/\u3