A computational analysis of electrohydrodynamics of a leaky dielectric drop in an electric field

Abstract

Axisymmetric steady flows driven by an electric field about a deformable fluid drop suspended in an immiscible fluid are studied within the framework of the leaky dielectric model. Deformations of the drop and the flow fields are determined by solving the nonlinear free-boundary problem composed of the Navier-Stokes system governing the flow field and Laplace's system governing the electric field. The solutions are obtained by using the Galerkin finite-element method with an elliptic mesh generation scheme. Under conditions of creeping flow and vanishingly small drop deformations, the results of finite-element computations recover the asymptotic results. When drop deformations become noticeable, the asymptotic results are often found to underestimate both the flow intensity and drop deformation. By tracking solution branches in parameter space with an arc-length continuation method, curves in parameter space of the drop deformation parameter D versus the square of the dimensionless field strength E usually exhibit a turning point when E reaches a critical value Ec. Along such a family of drop shapes, steady solutions do not exist for E > Ec. The nonlinear relationship revealed computationally between D and E2 appears to be capable of providing insight into discrepancies reported in the literature between experiments and predictions based on the asymptotic theory. In some special cases with fluid conductivities closely matched, however, drop deformations are found to grow with E2 indefinitely and no critical value Ec is encountered by the corresponding solution branches. For most cases with realistic values of physical properties, the overall electrohydrodynamic behaviour is relatively insensitive to effects of finite-Reynolds-number flow. However, under extreme conditions when fluids of very low viscosities are involved, computational results illustrate a remarkable shape turnaround phenomenon: a drop with oblate deformation at low field strength can evolve into a prolate-like drop shape as the field strength is increased.

Experimental investigation of water droplets' behavior in dielectric medium: the effect of an applied D.C. electric field

“…The ionized aqueous droplet in silicon oil with electrical resistance lower than 10 −5 , is initially elongated into an ellipsoidal shape. By exceeding the, critical Weber number (0.21 which is in a good agreement with the numerical results of Feng and Scott (1966) and experimental results of Ha and Yang, 2000), the drop shape becomes unstable and varies with time. The deformation rate increases moderately until the main drop is broken into several tiny drops.…”

“…Baygents and Saville (1989) replaced leaky dielectric theory by an electrokinetic model to inspect the matters proposed by Torza et al (1971). Feng and Scott (1966), Vizika and Saville (1992) have demonstrated that the leaky dielectric model has the capability to predict the deformation pattern while zero amounts of charges accumulated at the interface.…”

Analysis of partial electrocoalescence by Level-Set and finite element methods

“…Explicit approaches, such as boundary integral and front-tracking methods, track discrete points on the interface surface. The motion and deformation of droplets under the presence of an electric field [8][9][10][11][12] [14][15][16][17][18][19][20]. Each implicit technique to represent the interface has its own advantages and drawbacks.…”

Numerical Study on Deformation and Interior Flow of a Droplet Suspended in Viscous Liquid under Steady Electric Fields

“…However, his analysis was limited to low Reynolds number cases and the viscosities of droplet and surrounding liquid were assumed to be equal [11]. Feng and Scott numerically studied deformation of a single droplet suspended in axisymmetric flow field at low Reynolds number and discussed the effect of electric strength and Reynolds number on the droplet deformation [12]. Tsukada et al presented a finite element computational technique to calculate inside and outside a dielectric droplet suspended in another dielectric fluid under a uniform electric field.…”

“…As presented above, the finite element method and the boundary integral method were used to treat the interface as being infinitely thin and the forces (electric stress and surface tension) that acted at the interface are applied as a boundary condition [11][12][13][14]. But this method is inaccurate for the calculation of surface tension.…”