Algorithm for direct numerical simulation of emulsion flow through a granular material

Zinchenko, Alexander Z.; Davis, Robert H.

doi:10.1016/j.jcp.2008.05.004

Cited by 26 publications

(47 citation statements)

References 51 publications

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“…In [75] the same simplified energy is supplemented by node redistribution, aiming to equalize mesh edge lengths. A modification of this method reducing maximal deviation from average is described in [74]. In Cristini et al [19] a damped relaxation with the energy gradient projected to the surface is used.…”

Section: Related Workmentioning

confidence: 99%

A fast algorithm for simulating vesicle flows in three dimensions

Veerapaneni

Rahimian

Biros

et al. 2011

Journal of Computational Physics

136

143

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Vesicles are locally-inextensible fluid membranes that can sustain bending. In this paper, we extend "A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows", Veerapaneni et al. Journal of Computational Physics, 228(19), 2009 to general non-axisymmetric vesicle flows in three dimensions.Although the main components of the algorithm are similar in spirit to the axisymmetric case (spectral approximation in space, semi-implicit time-stepping scheme), important new elements need to be introduced for a full 3D method. In particular, spatial quantities are discretized using spherical harmonics, and quadrature rules for singular surface integrals need to be adapted to this case; an algorithm for surface reparameterization is neeed to ensure sufficient of the timestepping scheme, and spectral filtering is introduced to maintain reasonable accuracy while minimizing computational costs. To characterize the stability of the scheme and to construct preconditioners for the iterative linear system solvers used in the semi-implicit time-stepping scheme, we perform a spectral analysis of the evolution operator on the unit sphere.By introducing these algorithmic components, we obtain a time-stepping scheme that, in our numerical experiments, is unconditionally stable. We present results to analyze the cost and convergence rates of the overall scheme. To illustrate the applicability of the new method, we consider a few vesicle-flow interaction problems: a single vesicle in relaxation, sedimentation, shear flows, and many-vesicle flows.

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Section: Related Workmentioning

confidence: 99%

A fast algorithm for simulating vesicle flows in three dimensions

Veerapaneni

Rahimian

Biros

et al. 2011

Journal of Computational Physics

136

143

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“…Most typical, we used 8640 triangles on the drop and 5120 triangles on each solid particle, though higher resolution was used for some runs. Simulations have been performed with two, three and four solid particles [27,28], including both spheres and disks.…”

Section: Drop Motion Through a Constrictionmentioning

confidence: 99%

“…The drop is neutrally buoyant and dri- ven by an external flow of velocity U 1 far away and directed perpendicular to the plane containing the sphere centers. The drop motion is directed along the centerline passing between the spheres, though more complicated paths have also been explored [28]. The drop-to-particle diameter ratio is 0.6, and the undeformed drop diameter is about twice as large as the hole size.…”

Section: Drop Motion Through a Constrictionmentioning

confidence: 99%

“…However, continued elongation and potential drop breakup are expected to occur downstream of the cluster for sufficiently high capillary number, in this case slightly greater than 1.3. With multipole acceleration [28] added to the algorithm [27], the high-resolution run for Ca = 1.5 (with 11.5 K elements on the drop and 5 K elements on each solid sphere) took 24 h on an AMD PC.…”

Section: Drop Motion Through a Constrictionmentioning

confidence: 99%

“…10 shows a more recent calculation of a drop squeezing between four fixed spheres. It was performed with the multipoleaccelerated algorithm of Zinchenko and Davis [28], but with additional mesh-topology transformations to handle extreme deformations. Here, the drop passes through two successive constrictions.…”

Section: Drop Motion Through a Constrictionmentioning

confidence: 99%

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Motion of deformable drops through granular media and other confined geometries

Davis

Zinchenko

2009

Journal of Colloid and Interface Science

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On the volume conservation of emulsion drops in boundary integral simulations

Siqueira

Rebouças

Cunha

et al. 2017

J Braz. Soc. Mech. Sci. Eng.

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Boundary Integral simulations are very common to study the microhydrodynamics of viscous drops and predict the rheology of emulsions. The standard boundary integral formulation for the velocity field at the drop surface is given by surface integrals of singular Green's functions in space and depends on geometric quantities of the mesh, as the local mean curvature and the unitary exterior normal vector. Typically, the drops deform and rotate under the flow action, which leads to a great distortion of the computational mesh and, therefore, might produce several numerical errors in the surface velocity calculation. In this work, we investigate the numerical errors in the calculation of the surface velocity in boundary integral simulations of a viscous drop in simple shear flows. Assuming that the flow is incompressible, such that the total volume of the drops must remain constant, we use the net flow rate across the drop surface as a measure of the numerical errors in the simulations. For both small and moderate regimes of drop surface deformation, we show that the net mass flow rate across the drop surface is positive, and strongly depends on the drop-to-basis fluid viscosity ratio, capillary number of the flow, and mesh refinement. These results indicate that the volume of the drops increases continuously during the simulations. To remove the spurious mass flow rate from the simulations, we present a mesh convergence study based on an extrapolation procedure to an almost continuous mesh, so that the results become independent of mesh refinement and recover the theoretical prediction of a null net flow rate and constant drop volume in incompressible flows. The extrapolation method proposed here can be straightforwardly implemented to improve the accuracy of BI simulations used to study drop microhydrodynamics and emulsion rheology. As a matter of example, we applied the method to predict the surface deformation of a high-viscosity emulsion drop, and the result is compared in very good agreement with asymptotic theories available in the related literature.

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Algorithm for direct numerical simulation of emulsion flow through a granular material

Cited by 26 publications

References 51 publications

A fast algorithm for simulating vesicle flows in three dimensions

A fast algorithm for simulating vesicle flows in three dimensions

Motion of deformable drops through granular media and other confined geometries

On the volume conservation of emulsion drops in boundary integral simulations

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