Numerical and asymptotic analysis of the three-dimensional electrohydrodynamic interactions of drop pairs

Sorgentone, Chiara; Kach, Jeremy I.; Khair, Aditya S.; Walker, Lynn M.; Vlahovska, Petia M.

doi:10.1017/jfm.2020.1007

Cited by 18 publications

(23 citation statements)

References 53 publications

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“…These approaches were presented and validated for identical drops in Sorgentone et al. (2021). Here we summarize the extension of the theory and simulations to treat dissimilar drops.…”

Section: Methodsmentioning

confidence: 99%

“…These flows can be either cooperative or antagonistic to the dipolar interactions (Baygents, Rivette & Stone 1998; Saintillan 2008; Park & Saintillan 2010; Sorgentone et al. 2021) and prevent chaining (Ha & Yang 2000). Recently, the three-dimensional interactions of a pair of identical droplets were investigated by means of numerical simulations using the boundary integral method, asymptotic theory for large separations and spherical droplets (Sorgentone, Tornberg & Vlahovska 2019; Sorgentone et al.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, the three-dimensional interactions of a pair of identical droplets were investigated by means of numerical simulations using the boundary integral method, asymptotic theory for large separations and spherical droplets (Sorgentone, Tornberg & Vlahovska 2019; Sorgentone et al. 2021; Sorgentone & Vlahovska 2021) and experiments (Kach, Walker & Khair 2022). The systematic exploration of the effects of fluid properties and the droplet initial configuration revealed intricate relative motions that eventually lead to either droplet coalescence or indefinite repulsion; only if the droplets line-of-centres were initially perpendicular to the applied field direction and the electrohydrodynamic flow along the droplet surface were equator-to-pole, the drops’ motion is eventually arrested and the drops remain at an equilibrium separation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Tandem droplet locomotion in a uniform electric field

Sorgentone

Vlahovska

2022

J. Fluid Mech.

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An isolated charge-neutral droplet in a uniform electric field experiences no net force. However, a droplet pair can move in response to field-induced dipolar and hydrodynamic interactions. If the droplets are identical, the centre of mass of the pair remains fixed. Here, we show that if the droplets have different properties, the pair experiences a net motion due to non-reciprocal electrohydrodynamic interactions. We analyse the three-dimensional droplet trajectories using asymptotic theory, assuming spherical droplets and large separations, and numerical simulations based on a boundary integral method. The dynamics can be quite intricate depending on the initial orientation of the droplets line-of-centres relative to the applied field direction. Drops tend to migrate towards a configuration with line-of-centres either parallel or perpendicular to the applied field direction, while either coming into contact or indefinitely separating. We elucidate the conditions under which these different interaction scenarios take place. Intriguingly, we find that in some cases droplets can form a pair (tandem) that translates either parallel or perpendicular to the applied field direction.

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“…These approaches were presented and validated for identical drops in Sorgentone et al. (2021). Here we summarize the extension of the theory and simulations to treat dissimilar drops.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Tandem droplet locomotion in a uniform electric field

Sorgentone

Vlahovska

2022

J. Fluid Mech.

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“…The second case is when Ω need not be geometrically simple, but f = 0. In this case, well-conditioned boundary integral equation (BIE) methods exist for many commonly studied operators L; spectrally accurate or high-order singular quadratures for the associated Nÿstrom schemes along with kernel-dependent and kernel-independent Fast Multipole Methods (FMMs) enable accurate solutions to be computed and evaluated in optimal time [3][4][5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Spectrally accurate solutions to inhomogeneous elliptic PDE in smooth geometries using function intension

Stein¹

2022

Preprint

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We present a spectrally accurate embedded boundary method for solving linear, inhomogeneous, elliptic partial differential equations (PDE) in general smooth geometries, focusing in this manuscript on the Poisson, modified Helmholtz, and Stokes equations. Unlike several recently proposed methods which rely on function extension, we propose a method which instead utilizes function intension, or the smooth truncation of known function values. Similar to those methods based on extension, once the inhomogeneity is truncated we may solve the PDE using any of the many simple, fast, and robust solvers that have been developed for regular grids on simple domains. Function intension is inherently stable, as are all steps in the proposed solution method, and can be used on domains which do not readily admit extensions. We pay a price in exchange for improved stability and flexibility: in addition to solving the PDE on the regular domain, we must additionally (1) solve the PDE on a small auxiliary domain that is fitted to the boundary, and (2) ensure consistency of the solution across the interface between this auxiliary domain and the rest of the physical domain. We show how these tasks may be accomplished efficiently (in both the asymptotic and practical sense), and compare convergence to several recent high-order embedded boundary schemes.

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“…Boundary integral equations (BIEs) are advantageous for the numerical solution of a wide variety of linear boundary-value problems (BVPs) in science and engineering [59,46]. They include electro/magnetostatics [35,102], acoustics [82,58], electromagnetics/optics [19,18,64], elastostatics/dynamics [42,16], viscous fluid flow [100,78,88,74,73], electrohydrodynamics [89], and many others. BIEs also form a component in solvers for BVPs with volume driving and/or nonlinearities by solving for a homogeneous PDE solution which corrects the boundary conditions [71,11,27,26,1,103].…”

Section: Introductionmentioning

confidence: 99%

Quadrature by fundamental solutions: kernel-independent layer potential evaluation for large collections of simple objects

Stein¹,

Barnett²

2021

Preprint

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Well-conditioned boundary integral methods for the solution of elliptic boundary value problems (BVPs) are powerful tools for static and dynamic physical simulations. When there are many close-to-touching boundaries (eg, in complex fluids) or when the solution is needed in the bulk, nearly-singular integrals must be evaluated at many targets. We show that precomputing a linear map from surface density to an effective source representation renders this task highly efficient, in the common case where each object is "simple", ie, its smooth boundary needs only moderately many nodes. We present a kernel-independent method needing only an upsampled smooth surface quadrature, and one dense factorization, for each distinct shape. No (near-)singular quadrature rules are needed. The resulting effective sources are drop-in compatible with fast algorithms, with no local corrections nor bookkeeping. Our extensive numerical tests include 2D FMM-based Helmholtz and Stokes BVPs with up to 1000 objects (281000 unknowns), and a 3D Laplace BVP with 10 ellipsoids separated by 1/30 of a diameter. We include a rigorous analysis for analytic data in 2D and 3D.

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Numerical and asymptotic analysis of the three-dimensional electrohydrodynamic interactions of drop pairs

Abstract: Abstract

Cited by 18 publications

References 53 publications

Tandem droplet locomotion in a uniform electric field

Tandem droplet locomotion in a uniform electric field

Spectrally accurate solutions to inhomogeneous elliptic PDE in smooth geometries using function intension

Quadrature by fundamental solutions: kernel-independent layer potential evaluation for large collections of simple objects

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