A Leaky Dielectric Drop with Conical Ends in An Electric Field

2019 ◽  
Vol 79 (5) ◽  
pp. 1768-1796
Author(s):  
Michael Zabarankin
Keyword(s):  
Electric Field ◽  
Leaky Dielectric

scholarly journals Sedimentation of a surfactant-laden drop under the influence of an electric field

2018 ◽  
Vol 849 ◽  
pp. 277-311 ◽  
Author(s):  
Antarip Poddar ◽  
Shubhadeep Mandal ◽  
Aditya Bandopadhyay ◽  
Suman Chakraborty
Keyword(s):  
Surface Tension ◽  
Electric Field ◽  
Surfactant Concentration ◽  
Perturbation Technique ◽  
Internal Flow ◽  
Dielectric Fluid ◽  
Regular Perturbation ◽  
Spherical Drop ◽  
Leaky Dielectric ◽  
Marangoni Stress

The sedimentation of a surfactant-laden deformable viscous drop acted upon by an electric field is considered theoretically. The convection of surfactants in conjunction with the combined effect of electrohydrodynamic flow and sedimentation leads to a locally varying surface tension, which subsequently alters the drop dynamics via the interplay of Marangoni, Maxwell and hydrodynamic stresses. Assuming small capillary number and small electric Reynolds number, we employ a regular perturbation technique to solve the coupled system of governing equations. It is shown that when a leaky dielectric drop is sedimenting in another leaky dielectric fluid, the Marangoni stress can oppose the electrohydrodynamic motion severely, thereby causing corresponding changes in the internal flow pattern. Such effects further result in retardation of the drop settling velocity, which would have otherwise increased due to the influence of charge convection. For non-spherical drop shapes, the effect of Marangoni stress is overcome by the ‘tip-stretching’ effect on the flow field. As a result, the drop deformation gets intensified with an increase in sensitivity of the surface tension to the local surfactant concentration. Consequently, for an oblate type of deformation the elevated drag force causes a further reduction in velocity. For similar reasons, prolate drops experience less drag and settle faster than the surfactant-free case. In addition to this, with increased sensitivity of the interfacial tension to the surfactant concentration, the asymmetric deformation about the equator gets suppressed. These findings may turn out to be of fundamental significance towards designing electrohydrodynamically actuated droplet-based microfluidic systems that are intrinsically tunable by varying the surfactant concentration.

Nonlinear electrohydrodynamics of slightly deformed oblate drops

2015 ◽  
Vol 774 ◽  
pp. 245-266 ◽  
Author(s):  
Javier A. Lanauze ◽  
Lynn M. Walker ◽  
Aditya S. Khair
Keyword(s):  
Steady State ◽  
Electric Field ◽  
Surface Charge ◽  
Time Scale ◽  
Applied Field ◽  
Major Axis ◽  
Boundary Integral ◽  
Numerical Results ◽  
Transient Deformation ◽  
Leaky Dielectric

The transient deformation of a weakly conducting (‘leaky dielectric’) drop under a uniform DC electric field is computed via an axisymmetric boundary integral method, which accounts for surface charge convection and a finite relaxation time scale over which the drop interface charges. We focus on drops that attain an ultimate oblate (major axis normal to the applied field) steady-state configuration. The computations predict that as the time scale for interfacial charging increases, a shape transition from prolate deformation (major axis parallel to the applied field) to oblate deformation occurs at intermediate times due to the slow buildup of charge at the surface of the drop. Convection of surface charge towards the equator of the drop is shown to weaken the steady-state oblate deformation. Additionally, convection results in sharp shock-like variations in surface charge density near the equator of the drop. Our numerical results are then compared with an experimental system consisting of a millimetre-sized silicone oil drop suspended in castor oil. Agreement in the transient deformation is observed between our numerical results and experimental measurements for moderate electric field strengths. This suggests that both charge relaxation and charge convection are required, in general, to quantify the time-dependent deformation of leaky dielectric drops. Importantly, accurate prediction of the observed modest deformation requires a nonlinear model. Discrepancies between our numerical calculations and experimental results arise as the field strength is increased. We believe that this is due to the observed onset of rotation and three-dimensional flow at such high electric fields in the experiments, which an axisymmetric boundary integral formulation naturally cannot capture.

Transient Electrohydrodynamic Manipulation of Particles on the Surface of a Drop

2016 ◽  
Author(s):  
Edison C. Amah ◽  
Ian S. Fischer ◽  
Pushpendra Singh
Keyword(s):  
Electric Field ◽  
Applied Electric Field ◽  
Control Parameter ◽  
Transient Behavior ◽  
Uniform Electric Field ◽  
Electrohydrodynamic Flow ◽  
Dielectric Model ◽  
Leaky Dielectric Model ◽  
Leaky Dielectric

In our previous studies we have shown that particles adsorbed on the surface of a drop can be concentrated at its poles or equator by applying a uniform electric field. This happens even when the applied electric field is uniform; the electric field on the surface of the drop is nonuniform, and so particles adsorbed on the surface are subjected to dielectrophoretic (DEP) forces. In this study, we use leaky dielectric model to model the transient behavior of particles at low electric field frequencies. We show that the frequency of the electric field is an important control parameter that under certain conditions can be used to collect particles at the poles or the equator, and to move them from the poles to the equator. The speed with which particles move on the surface depends on the strength of the electrohydrodynamic flow which diminishes with increasing frequency.

Small deformation theory for two leaky dielectric drops in a uniform electric field

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190517
Author(s):  
Michael Zabarankin
Keyword(s):  
Electric Field ◽  
Deformation Theory ◽  
Small Deformation ◽  
Dielectric Constants ◽  
Dynamics Simulation ◽  
Uniform Electric Field ◽  
Fluid Viscosity ◽  
Ambient Fluid ◽  
Drop Dynamics ◽  
Leaky Dielectric

A small deformation theory for two non-identical spherical drops freely suspended in an ambient fluid and subjected to a uniform electric field is presented. The three phases are assumed to be leaky dielectric (slightly conducting) viscous incompressible fluids and the nonlinear effects of inertia and surface charge convection are neglected. The deformed shapes of the drops are linearized with respect to the electric capillary number that characterizes the balance between the electric stress and the surface tension. When the two drops are sufficiently far apart, their deformed shapes are predicted by Taylor’s small deformation theory—depending on Taylor’s discriminating function, the drops may become prolate, oblate or remain spherical. When the two drops get closer to each other, in addition to becoming prolate/oblate, they start translating and developing an egg shape. (Since there is no net charge, the centre of mass of the two drops remains stationary.) The extent of each of these ‘modes’ of deformation depends on the distance between the drops’ centres and on drop-to-ambient fluid ratios of electric conductivities, dielectric constants and viscosities. The predictions of the small deformation theory for two drops perfectly agree with the existing results of two-drop dynamics simulation based on a boundary-integral equation approach. Moreover, while previous works observed only three types of behaviour for two identical drops—the drops may either become prolate or oblate and move towards each other or become prolate and move away from each other—the small deformation theory predicts that non-identical drops may, in fact, become oblate and move away from each other when the drop-to-ambient fluid conductivity ratios are reciprocal and the drop-to-ambient fluid viscosity ratios are sufficiently large. The presented theory also readily yields an analytical insight into the interplay among different modes of drop deformation and can be used to guide the selection of the phases’ electromechanical properties for two-drop dynamics simulations.

scholarly journals Effect of an axial electric field on the breakup of a leaky-dielectric liquid filament

2021 ◽  
Vol 33 (9) ◽  
pp. 092114
Author(s):  
M. Rubio ◽  
A. Ponce-Torres ◽  
M. A. Herrada ◽  
A. M. Gañán-Calvo ◽  
J. M. Montanero
Keyword(s):  
Electric Field ◽  
Dielectric Liquid ◽  
Axial Electric Field ◽  
Leaky Dielectric ◽  
Liquid Filament
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