scholarly journals Liquid toroidal drop under uniform electric field

2017 ◽  
Vol 473 (2202) ◽  
pp. 20160633 ◽  
Author(s):  
Michael Zabarankin
Keyword(s):  
Surface Tension ◽  
Electric Field ◽  
Dielectric Constants ◽  
Uniform Electric Field ◽  
Normal Velocity ◽  
Spherical Drop ◽  
Electric Stress ◽  
Freely Suspended ◽  
Major Radius ◽  
External Forces

The problem of a stationary liquid toroidal drop freely suspended in another fluid and subjected to an electric field uniform at infinity is addressed analytically. Taylor’s discriminating function implies that, when the phases have equal viscosities and are assumed to be slightly conducting (leaky dielectrics), a spherical drop is stationary when Q =(2 R 2 +3 R +2)/(7 R 2 ), where R and Q are ratios of the phases’ electric conductivities and dielectric constants, respectively. This condition holds for any electric capillary number, Ca E , that defines the ratio of electric stress to surface tension. Pairam and Fernández-Nieves showed experimentally that, in the absence of external forces (Ca E =0), a toroidal drop shrinks towards its centre, and, consequently, the drop can be stationary only for some Ca E >0. This work finds Q and Ca E such that, under the presence of an electric field and with equal viscosities of the phases, a toroidal drop having major radius ρ and volume 4 π /3 is qualitatively stationary—the normal velocity of the drop’s interface is minute and the interface coincides visually with a streamline. The found Q and Ca E depend on R and ρ , and for large ρ , e.g. ρ ≥3, they have simple approximations: Q ∼( R 2 + R +1)/(3 R 2 ) and Ca E ∼ 3 3 π ρ / 2   ( 6  ln  ⁡ ρ + 2  ln ⁡ [ 96 π ] − 9 ) / ( 12  ln  ⁡ ρ + 4  ln ⁡ [ 96 π ] − 17 )   ( R + 1 ) 2 / ( R − 1 ) 2 .

scholarly journals Toroidal drop under electric field: arbitrary drop-to-ambient fluid viscosity ratio

2017 ◽  
Vol 473 (2205) ◽  
pp. 20170379 ◽  
Author(s):  
Michael Zabarankin
Keyword(s):  
Electric Field ◽  
Dielectric Constants ◽  
Uniform Electric Field ◽  
Fluid Viscosity ◽  
Ambient Fluid ◽  
Electric Stress ◽  
Freely Suspended ◽  
Two Phases ◽  
Major Radius ◽  
External Forces

In the absence of external forces, a liquid toroidal drop freely suspended in another fluid shrinks towards its centre. It is shown that if the two phases are slightly conducting viscous incompressible fluids with the drop-to-ambient fluid ratios of electric conductivities, dielectric constants and viscosities to be 1/ R , Q and λ , respectively, then the toroidal drop with volume 4 π /3 and having major radius ρ can become almost stationary when subjected to a uniform electric field aligned with the drop’s axis of symmetry. In this case, Q and electric capillary number Ca E that defines the ratio of electric stress to surface tension, are functions of R , ρ and λ and are found analytically. Those functions are relatively insensitive to λ , and for ρ ≥3, they admit simple approximations, which coincide with those obtained recently for λ =1. Streamlines inside and outside the toroidal drop for the same R and ρ but different λ are qualitatively similar.

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.

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.

Breakup of a conducting drop in a uniform electric field

2014 ◽  
Vol 754 ◽  
pp. 550-589 ◽  
Author(s):  
Rahul B. Karyappa ◽  
Shivraj D. Deshmukh ◽  
Rochish M. Thaokar
Keyword(s):  
Steady State ◽  
Numerical Analysis ◽  
Electric Field ◽  
Viscosity Ratio ◽  
Uniform Electric Field ◽  
Shape Prior ◽  
Capillary Stress ◽  
Electric Stress ◽  
Dc Electric Field ◽  
Axisymmetric Shape

AbstractA conducting drop suspended in a viscous dielectric and subjected to a uniform DC electric field deforms to a steady-state shape when the electric stress and the viscous stress balance. Beyond a critical electric capillary number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Ca}$, which is the ratio of the electric to the capillary stress, a drop undergoes breakup. Although the steady-state deformation is independent of the viscosity ratio $\lambda $ of the drop and the medium phase, the breakup itself is dependent upon $\lambda $ and $\mathit{Ca}$. We perform a detailed experimental and numerical analysis of the axisymmetric shape prior to breakup (ASPB), which explains that there are three different kinds of ASPB modes: the formation of lobes, pointed ends and non-pointed ends. The axisymmetric shapes undergo transformation into the non-axisymmetric shape at breakup (NASB) before disintegrating. It is found that the lobes, pointed ends and non-pointed ends observed in ASPB give way to NASB modes of charged lobes disintegration, regular jets (which can undergo a whipping instability) and open jets, respectively. A detailed experimental and numerical analysis of the ASPB modes is conducted that explains the origin of the experimentally observed NASB modes. Several interesting features are reported for each of the three axisymmetric and non-axisymmetric modes when a drop undergoes breakup.

Deformation and breakup of a leaky dielectric drop in a quadrupole electric field

2013 ◽  
Vol 731 ◽  
pp. 713-733 ◽  
Author(s):  
Shivraj D. Deshmukh ◽  
Rochish M. Thaokar
Keyword(s):  
Phase Diagram ◽  
Electric Field ◽  
Boundary Element ◽  
Dielectric Medium ◽  
Dielectric Constants ◽  
Boundary Element Methods ◽  
Uniform Electric Field ◽  
Quadrupole Field ◽  
Capillary Stress ◽  
Leaky Dielectric

AbstractThe deformation and breakup of a leaky dielectric drop suspended in a leaky dielectric medium subjected to a quadrupole electric field are studied. Analytical (linear and nonlinear asymptotic expansions in the electric capillary number, $C{a}_{Q} $, a ratio of electric to capillary stress) and numerical (boundary element) methods are used. A complete phase diagram for the drop deformation in the $R$–$Q$ plane is presented, where $R$ and $Q$ are the non-dimensional ratios of the resistivities and dielectric constants, respectively, of the drop and the medium phase. The prolate and oblate deformations are mapped in the phase diagram, and the flow contours are also shown. The large deformation and breakup of a drop at higher $C{a}_{Q} $ are analysed using the boundary element method. Several non-trivial shapes are observed at the onset of breakup of a drop. A prolate drop always breaks above a certain critical value of $C{a}_{Q} $. In the oblate deformation cases, breakup as well as steady shapes are observed at a higher value of $C{a}_{Q} $. A detailed study of prolate and oblate deformation tendencies due to the normal and tangential electric stresses and the countervailing role of viscous stresses is presented. The circulation inside a drop is found to be more intense for a quadrupole field as compared with a uniform electric field. More intense internal circulations can lead to enhanced mixing characteristics and will have implications in microfluidic devices.

An Investigation of Behaviours of Bubble in Electric Field

2011 ◽  
Vol 347-353 ◽  
pp. 3184-3188
Author(s):  
Zhi Guang Dong ◽  
Zhi Hui Dong
Keyword(s):  
Aspect Ratio ◽  
Electric Field ◽  
Field Intensity ◽  
Bubble Growth ◽  
Electric Field Intensity ◽  
Uniform Electric Field ◽  
Electric Stress

The effects of an ununiform electric field on bubble behaviours such as bubble growth ,deformation and detachment are investigated experimentally.Experimental results show that the bubble elongated along the direction of the electric field.The bubble’s aspect ratio is increased with the increasing of electric field intensity and the ellipse sphere shape is more evident than without electric field,while its departure volume is decreased with that.The case is the bubble comes under the electric stress.The electric stress compressed the bubble in the equatorial direction and extened the bubble along the axial direction.The bubble behaviours influenced in the ununiform electric field is more evident than the uniform electric field.

Axisymmetric deformation and stability of a viscous drop in a steady electric field

2007 ◽  
Vol 590 ◽  
pp. 239-264 ◽  
Author(s):  
ETIENNE LAC ◽  
G. M. HOMSY
Keyword(s):  
Electric Field ◽  
Stable Solution ◽  
Physical Property ◽  
Linear Instability ◽  
Axisymmetric Deformation ◽  
Creeping Flow ◽  
Uniform Electric Field ◽  
Electric Stress ◽  
Wide Range ◽  
Break Up

We consider a neutrally buoyant and initially uncharged drop in a second liquid subjected to a uniform electric field. Both liquids are taken to be leaky dielectrics. The jump in electrical properties creates an electric stress balanced by hydrodynamic and capillary stresses. Assuming creeping flow conditions and axisymmetry of the problem, the electric and flow fields are solved numerically withboundary integral techniques. The system is characterized by the physical property ratios R (resistivities), Q (permitivities) and λ (dynamic viscosities). Depending on these parameters, the drop deforms into a prolate or an oblate spheroid. The relative importance of the electric stress and of the drop/medium interfacial tension is measured by the dimensionless electric capillary number, Cae. For λ = 1, we present a survey of the various behaviours obtained for a wide range of R and Q. We delineate regions in the (R,Q)-plane in which the drop either attains a steady shape under any field strength or reaches a fold-point instability past a critical Cae. We identify the latter with linear instability of the steady shape to axisymmetric disturbances. Various break-up modes are identified, as well as more complex behaviours such as bifurcations and transition from unstable to stable solution branches. We also show how the viscosity contrast can stabilize the drop or advance break-up in the different situations encountered for λ = 1.

Removal of Particles From the Surface of a Droplet

2008 ◽  
Author(s):  
N. Aubry ◽  
P. Singh ◽  
S. Nudurupati ◽  
M. Janjua
Keyword(s):  
Dielectric Constant ◽  
Electric Field ◽  
Strong Electric Field ◽  
Dielectric Constants ◽  
The Other ◽  
Uniform Electric Field ◽  
Drop Deformation ◽  
Ambient Fluid ◽  
Dielectrophoretic Force ◽  
Different Types

We present a technique to concentrate particles on the surface of a drop, separate different types of particles, and remove them from the drop by subjecting the drop to a uniform electric field. The particles are moved under the action of the dielectrophoretic force which arises due to the non-uniformity of the electric field on the surface of the drop. Experiments show that depending on the dielectric constants of the fluids and the particles, particles aggregate either near the poles or near the equator of the drop. When particles aggregate near the poles and the dielectric constant of the drop is greater than that of the ambient fluid, the drop deformation is larger than that of a clean drop. In this case, under a sufficiently strong electric field the drop develops conical ends and particles concentrated at the poles eject out by a tip streaming mechanism, thus leaving the drop free of particles. On the other hand, when particles aggregate near the equator, it is shown that the drop can be broken into three major droplets, with the middle droplet carrying all particles and the two larger sized droplets on the sides being free of particles. The method also allows us to separate particles for which the sign of the Clausius-Mossotti factor is different, making particles of one type aggregate at the poles and of the second type aggregate at the equator. The former are removed from the drop by increasing the electric field strength, leaving only the latter inside the drop.

scholarly journals The Changing Shape of a Liquid Drop in an Electric Field

2013 ◽  
Vol 3 ◽  
pp. 24-40
Author(s):  
A.A.S.N. Jayalal ◽  
K.A.I.L. Wijewardena Gamalath
Keyword(s):  
Surface Tension ◽  
Dielectric Constant ◽  
Aspect Ratio ◽  
Electric Field ◽  
Applied Electric Field ◽  
Applied Field ◽  
Cone Angle ◽  
Constant Ratio ◽  
Spherical Drop ◽  
Fluid Drop

An approximate extension of the slender body theory was used to determine the static shape of a conically ended dielectric fluid drop in an electric field. Using induced surface charge density, hydrostatic pressure and the surface tension of the liquid with interfacial tension stresses and Maxwell electric stresses, a governing equation was obtained for slender geometries for the equilibrium configuration and numerically solved for 3D. For an applied electric field, the electric energy on a spherical drop can be maximized in a weak dielectric by increasing the applied electric field. The minimum dielectric constant ratio needed to produce a conical end is 14.5 corresponding to a cone angle 31.25° .There is a sharp increment of the aspect ratio after reaching the threshold value of the applied field strength and the deformation of the fluid drop increases with the increase in dielectric constant of the fluid drop. For a particular dielectric constant ratio, the threshold electric field producing conical interface increases with the increased surface tension of the liquid. The threshold electric field for a water drop is 1.0854×104 units and the corresponding aspect ratio is 15. For the minimum dielectric ratio the cone angle of the drop decreases with applied field making the drop more stable at higher fields.

Dynamics of freely suspended films with surface tension

1990 ◽  
Vol 51 (19) ◽  
pp. 2143-2152 ◽  
Author(s):  
Yatin Marathe ◽  
Sriram Ramaswamy
Keyword(s):  
Surface Tension ◽  
Freely Suspended ◽  
Freely Suspended Films
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