Electrohydrodynamic interactions of drop pairs

We study the pairwise interactions of drops in an applied uniform DC electric field within the framework of the leaky dielectric model. We develop three-dimensional numerical simulations using the boundary integral method and an analytical theory assuming small drop deformations. We apply the simulations and the theory to explore the electrohydrodynamic interactions between two identical drops with arbitrary orientation of the their line of centers relative to the applied field direction. Our results show complex dynamics depending on the conductivities and permittivities of the drops and suspending fluids, and the initial drop pair alignment with the applied electric field.

[1]  J. Sherwood,et al.  Breakup of fluid droplets in electric and magnetic fields , 1988, Journal of Fluid Mechanics.

[2]  Arturo Ferna ndez.  Response of an emulsion of leaky dielectric drops immersed in a simple shear flow: Drops less conductive than the suspending fluid , 2008 .

[3]  J. M. López-Herrera,et al.  The onset of electrospray: the universal scaling laws of the first ejection , 2016, Scientific Reports.

[4]  David Saintillan,et al.  Electrohydrodynamics of viscous drops in strong electric fields: numerical simulations , 2016, Journal of Fluid Mechanics.

[5]  Lexing Ying,et al.  A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains , 2006, J. Comput. Phys..

[6]  M. Zabarankin.  Small deformation theory for two leaky dielectric drops in a uniform electric field , 2020, Proceedings of the Royal Society A.

[7]  C. Sozou.  Electrohydrodynamics of a pair of liquid drops , 1975 .

[8]  M. Siegel,et al.  Deformation and stability of a viscous electrolyte drop in a uniform electric field , 2018, Physical Review Fluids.

[9]  Rochish M. Thaokar,et al.  Breakup of a conducting drop in a uniform electric field , 2014, Journal of Fluid Mechanics.

[10]  Mojtaba Ghadiri,et al.  Electrostatic enhancement of coalescence of water droplets in oil: a review of the technology , 2002 .

[11]  Juan Fern.  The Fluid Dynamics of Taylor Cones , 2007 .

[12]  A. Esmaeeli,et al.  Transient electrohydrodynamics of a liquid drop. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  George Biros,et al.  A fast algorithm for simulating vesicle flows in three dimensions , 2011, J. Comput. Phys..

[14]  George M. Homsy,et al.  Axisymmetric deformation and stability of a viscous drop in a steady electric field , 2007, Journal of Fluid Mechanics.

[15]  Howard A. Stone,et al.  ENGINEERING FLOWS IN SMALL DEVICES , 2004 .

[16]  E. J. Vega,et al.  Numerical simulation of electrospray in the cone-jet mode. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Petia M. Vlahovska,et al.  Electrohydrodynamics of drops in strong uniform dc electric fields , 2010 .

[18]  Yoichiro Mori,et al.  Electrohydrodynamics of Leaky Dielectrics as the Weak Electrolyte Limit of an Electrodiffusion Model , 2017 .

[19]  Rochish Thaokar,et al.  Electrocoalescence of a drop pair , 2015 .

[20]  P. Vlahovska.  CHAPTER 9:Dynamics of Membrane-Bound Particles: Capsules and Vesicles , 2015 .

[21]  D. Saville.  ELECTROHYDRODYNAMICS:The Taylor-Melcher Leaky Dielectric Model , 1997 .

[22]  J. D. Berry,et al.  Electrokinetics of isolated electrified drops. , 2016, Soft matter.

[23]  Petia M Vlahovska,et al.  Electrohydrodynamic rotations of a viscous droplet. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  R. Collins,et al.  Electrohydrodynamic tip streaming and emission of charged drops from liquid cones , 2008 .

[25]  Petia M. Vlahovska,et al.  Electrohydrodynamics of Drops and Vesicles , 2019, Annual Review of Fluid Mechanics.

[26]  M. Carpenter,et al.  Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations , 2003 .

[27]  A. Carlson,et al.  A phase field model for multiphase electro-hydrodynamic flow , 2012 .

[28]  Seung‐Man Yang,et al.  Electrohydrodynamics and electrorotation of a drop with fluid less conductive than that of the ambient fluid , 2000 .

[29]  A. Sau,et al.  Electrohydrodynamic interaction, deformation, and coalescence of suspended drop pairs at varied angle of incidence , 2018, Physical Review Fluids.

[30]  P. Vlahovska,et al.  Streaming from the Equator of a Drop in an External Electric Field. , 2017, Physical review letters.

[31]  J. M. López-Herrera,et al.  Review on the physics of electrospray: From electrokinetics to the operating conditions of single and coaxial Taylor cone-jets, and AC electrospray , 2018, Journal of Aerosol Science.

[32]  Anna-Karin Tornberg,et al.  A highly accurate boundary integral equation method for surfactant-laden drops in 3D , 2017, J. Comput. Phys..

[33]  G. Taylor.  Studies in electrohydrodynamics. I. The circulation produced in a drop by an electric field , 1966, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[34]  Aditya S. Khair,et al.  The role of surface charge convection in the electrohydrodynamics and breakup of prolate drops , 2017, Journal of Fluid Mechanics.

[35]  Petia M. Vlahovska,et al.  A 3D boundary integral method for the electrohydrodynamics of surfactant-covered drops , 2018, J. Comput. Phys..

[36]  George Biros,et al.  Boundary integral method for the flow of vesicles with viscosity contrast in three dimensions , 2015, J. Comput. Phys..

[37]  Howard A. Stone,et al.  Electrohydrodynamic deformation and interaction of drop pairs , 1998, Journal of Fluid Mechanics.

[38]  R. Thaokar,et al.  Breakup and non-coalescence mechanism of aqueous droplets suspended in castor oil under electric field , 2019, Journal of Fluid Mechanics.

[39]  Aditya S. Khair,et al.  Nonlinear electrohydrodynamics of slightly deformed oblate drops , 2015, Journal of Fluid Mechanics.

[40]  Petia M. Vlahovska,et al.  Electrohydrodynamic model of vesicle deformation in alternating electric fields. , 2008, Biophysical journal.

[41]  J. Sethian,et al.  Numerical study on electrohydrodynamic multiple droplet interactions. , 2019, Physical review. E.

[42]  Geoffrey Ingram Taylor,et al.  Disintegration of water drops in an electric field , 1964, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[43]  Robert T. Collins,et al.  Universal scaling laws for the disintegration of electrified drops , 2013, Proceedings of the National Academy of Sciences.

[44]  Ehud Yariv,et al.  The Taylor–Melcher leaky dielectric model as a macroscale electrokinetic description , 2015, Journal of Fluid Mechanics.

[45]  D. Saintillan.  Nonlinear interactions in electrophoresis of ideally polarizable particles , 2008 .

[46]  Subhankar Roy,et al.  Electrocoalescence of a pair of conducting drops in an insulating oil , 2018, Journal of Fluid Mechanics.

[47]  Petia M. Vlahovska,et al.  Electrohydrodynamic instabilities of viscous drops , 2016 .

[48]  R. G. Cox,et al.  Electrohydrodynamic deformation and bursts of liquid drops , 1971, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[49]  Petia M. Vlahovska,et al.  Electric-field-induced transitions from spherical to discocyte and lens-shaped drops , 2020, Journal of Fluid Mechanics.