On the application of a three-dimensional boundary integral method to compute distortion of magnetic drops

Couto, H.L.G.; Oliveira, Taygoara Felamingo de; Cunha, Francisco Ricardo

doi:10.22364/mhd.44.1.7

Cited by 2 publications

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“…From the 90s, three-dimensional BI methods have been successfully used to study different complex multiphase flows, such as drop deformation and drop breakup [22][23][24], hydrodynamics interactions between two or more drops [25][26][27][28], rheological properties of emulsions at both dilute and concentrated regimes [16,[29][30][31][32][33], and flow of viscous drops through constricted capillaries and granular materials to investigate the potential applications of emulsion injection in porous media in enhanced oil recovery methods [34][35][36][37][38][39]. Some modified BI formulations have also been proposed to analyze the densification of concentrated emulsions [40], emulsions in compressible Stokes' flows [41], and magnetic drops under the action of external magnetic fields [42]. More recently, boundary integral methods have been used to analyze the dynamics of acoustic microbubbles near solid boundaries, which is associated with important applications in biomedical ultrasonics, cavitation cleaning, and sonochemistry [43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

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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“…For emulsions at the dilute regime, that is, with dispersed phase concentration less than 20% in volume, the hydrodynamic interactions between two or more drops can be neglected, and studies of a single droplet – as the present one – applies straightforwardly to numerical investigations on emulsion rheology. Some modified BI formulations have also been proposed to investigate emulsions in compressible Stokes' flows and emulsions of magnetic drops under the action of external fields . Also, recent advances have been made in order to compute the dynamics of deformable particles including drops, vesicles, and capsules using the BI method .…”

Section: Introductionmentioning

confidence: 99%

A new mesh relaxation approach and automatic time‐step control method for boundary integral simulations of a viscous drop

Siqueira

Rebouças

Oliveira

et al. 2016

Numerical Methods in Fluids

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Summary We present a numerical methodology for the simulation of a viscous drop under simple shear flows by using the boundary integral method. The present work treats only a single drop in an unbounded fluid‐flow, but the results can be directly applied to studies on the rheology of dilute emulsions, in which the hydrodynamic interactions between two or more drops can be neglected. Singular and non‐singular integral representations of the velocity field are considered. Several aspects of the method are presented, including a new mesh relaxation approach and an automatic time‐step control method. The relaxation strategy is used in order to contain the distortion of the mesh and is performed by using relaxation iterations in a virtual temporal march between each physical time step of the simulation and monitoring the standard deviation of the areas of the elements. The automatic time‐step control method uses a global quantity related to the drop deformation in order to automatically set the temporal integration time step. It is carried out in a way to keep the local integration error less than a given tolerance. This strategy reduces the computational cost of the simulation by dramatically reducing the number of time steps in the temporal integration process. Copyright © 2016 John Wiley & Sons, Ltd.

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On the application of a three-dimensional boundary integral method to compute distortion of magnetic drops

Cited by 2 publications

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On the volume conservation of emulsion drops in boundary integral simulations

On the volume conservation of emulsion drops in boundary integral simulations

A new mesh relaxation approach and automatic time‐step control method for boundary integral simulations of a viscous drop

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