Maximum spreading of electrically charged droplets impacting on dielectric substrates

In this work, the electric charging effect on the spreading of droplet impacting on dielectric substrates has been investigated. The charged water droplets were directed on the paraffin wax and the Teflon-coated plates. The impinging behavior was visualized and recorded using a CCD camera to identify the maximum extent of the flattened droplets. Droplet diameter and velocity approaching the wall were measured as well. The diameter of the electrically charged droplet at the maximum spread turned out to be larger compared to that of neutral droplet (at the maximum spread), and the difference becomes larger with increasing of the electric charge ratio (defined as the ratio of the actual electric charge to the Rayleigh limit). This phenomenon is considered to be due to reduction of effective interfacial tensions between the liquid and the gas and between the liquid and the solid by electric charging. Finally, an improved model was proposed to predict the maximum spreading ratio for electrically charged droplets by introducing correlations on the liquid–gas and the liquid–solid interfacial tensions.     

Electrokinetic Mixing and Displacement of Charged Droplets in Hydrogels

Mixing in droplets is an essential task in a variety of microfluidic systems. Inspired by electrokinetic mixing, electric field-induced hydrodynamic flow inside a charged droplet embedded in an unbounded polyelectrolyte hydrogel is investigated theoretically. In this study, the polyelectrolyte hydrogel is modeled as a soft, and electrically charged porous solid saturated with a salted Newtonian fluid, and the droplet is considered an incompressible Newtonian fluid. The droplet-hydrogel interface is modeled as a surface, which is located at the plane of shear, with the electrostatic potential \(\zeta \) . The fluid inside the droplet attains a finite velocity owing to hydrodynamic coupling with the electroosmotic flow arising from the droplet and polymer charge. The fluid velocity inside the droplet is linearly proportional to the electroosmotic flow velocity in the charged gel and the electroosmotic flow velocity beyond the electrical double layer of a charged interface. It is found that the polymer boundary condition at the droplet surface and the viscosities of the fluids inside and outside the droplet significantly modulate the interior fluid flow. The ionic strength and the permeability of the polymer network impact the flow differently depending on whether the flow arises from the droplet or polymer charge. Finally, the displacement of a charged droplet embedded in a gel under the influence of an external electric field is undertaken. This work is motivated by experimental attempts, which can register sub-nanometer-scale inclusion displacements in hydrogels, to advance electrical microrheology as a diagnostic tool for probing inclusion-hydrogel interfaces. In the absence of polymer charge, a close connection is found between the electrical response of a charged droplet when it is immobilized in an uncharged incompressible gel and when it is dispersed in a Newtonian electrolyte.     

The influence of the curvature dependence of the surface tension on the geometry of electrically charged menisci

We evaluate how the curvature dependence of surface tension affects the shape of electrically charged interfaces between a perfectly conducting fluid and its vapour. We consider two cases: i) spherical droplets in equilibrium with their vapour; ii) menisci pending in a capillary tube in presence of a conducting plate at given electric potential drop. Tolman-like dependence of surface tension on curvature becomes important when the “nucleation radius” is comparable with the interface curvature radius. In case i) we prove existence of the equilibrium minimal radius and estimate its dependence on the electric fields and Tolman-like curvature effects. In case ii) the menisci are subject to the gravitational force, surface tension and electrostatic fields. We determine the unknown surface of the menisci to which the potential is assigned using an iterative numerical method and show that Tolman-like corrections imply: 1) a variation of the height (up to 10% in some cases) of the tip of the menisci; 2) a decrease of the maximum electrical potential applicable to the menisci before their break-down amounting to 40V over 800V in the considered cases. We conjecture that these effects could be used in new experiments based on electric measurements to determine the dependence of the equilibrium surface tension on curvature. Received January 19, 1998     

Capillary instabilities of charged drops and electrical dispersion of liquids

The phenomenology of the instability of charged and uncharged drops and liquid menisci at the end of a capillary through which liquid is fed in constant and variable external electric fields, both uniform and nonuniform, is considered. Methods of investigating such instability are described. The steady-state deformation of drops in electric fields, the critical conditions under which their charged surface loses stability, and the laws of electrical dispersion of liquids in the final stage of instability are discussed.Yaroslavl'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 3–22, May–June, 1994.     

Determination of particle charge and size from the propagation of ultrasound in suspensions

The propagation of small perturbations in raulticomponent disperse media consisting of an uncharged dispersion fluid, positive and negative ions and charged particles or droplets of another fluid is investigated. When weak waves pass through emulsions and suspensions, because of the difference in the velocities of the ions and charged particles a non-uniform distribution of electric potential develops in the medium [1–3]. Expressions relating the amplitude of the electric potential and the amplitude of the fluid velocity in the wave, the particle charge and the parameters characterizing the medium are derived. Relations are obtained for the phase shift between the values of the electric potential and the fluid velocity. It is proposed to use the expressions obtained, which describe the propagation of ultrasound, for the experimental determination of the particle charge and other parameters of the disperse medium, in particular, the particle size.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 122–128, January–February, 1988.     

Numerical study of particle motion near a charged collector

The behavior of particles impacting the surface of a charged droplet involves adhesion, rebound, and submersion. In the present study, a numerical model for simulating particle impacts on charged droplets is presented that takes into account the various impact modes. With the droplet considered as a solid boundary, the criterion for rebounding is that the particle’s impact angle is <85°. The simulated trajectories of the particles are verified by comparing with experimental data for low-velocity particles to assess the reliability of the model. For impact angles >85°, particles undergo three distinct modes depending on normal impact velocities. The critical velocity of adhesion/rebound and rebound/submersion is used to identify the mode that the particles are undergoing. The criteria are also verified by comparing with analytical data. The results show that the impact angle of particles increases with increasing Coulomb number and decreases dramatically with increasing Stokes number, both of which lead to a high probability for particle rebound.     

Statistical fluctuations of the charged surface of an inviscid fluid

A fluctuation mechanism of origin of the deformation of a charged liquid surface, which explains the experimental facts, is proposed. The Hamilton equations that describe the dynamics of an inviscid fluid with electrically charged free surface are formulated. Solutions of these equations, which describe the evolution of the free surface, are found. The spectra of the surface disturbances are investigated.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 117–124, May–June, 1992.     

A Hybrid Boundary/Finite Element Method for Simulating Viscous Flows and Shapes of Droplets in Electric Fields

A mixed boundary element and finite element numerical algorithm for the simultaneous prediction of the electric fields, viscous flow fields, thermal fields and surface deformation of electrically conducting droplets in an electrostatic field is described in this paper. The boundary element method is used for the computation of the electric potential distribution. This allows the boundary conditions at infinity to be directly incorporated into the boundary integral formulation, thereby obviating the need for discretization at infinity. The surface deformation is determined by solving the normal stress balance equation using the weighted residuals method. The fluid flow and thermal fields are calculated using the mixed finite element method. The computational algorithm for the simultaneous prediction of surface deformation and fluid flow involves two iterative loops, one for the electric field and surface deformation and the other for the surface tension driven viscous flows. The two loops are coupled through the droplet surface shapes for viscous fluid flow calculations and viscous stresses for updating the droplet shapes. Computing the surface deformation in a separate loop permits the freedom of applying different types of elements without complicating procedures for the internal flow and thermal calculations. Tests indicate that the quadratic, cubic spline and spectral boundary elements all give approximately the same accuracy for free surface calculations; however, the quadratic elements are preferred as they are easier to implement and also require less computing time. Linear elements, however, are less accurate. Numerical simulations are carried out for the simultaneous solution of free surface shapes and internal fluid flow and temperature distributions in droplets in electric fields under both microgravity and earthbound conditions. Results show that laser heating may induce a non-uniform temperature distribution in the droplets. This non-uniform thermal field results in a variation of surface tension along the surface of the droplet, which in turn produces a recirculating fluid flow in the droplet. The viscous stresses cause additional surface deformation by squeezing the surface areas above and below the equator plane.     

On simulations investigating droplet diameter–charge distributions in electrostatically atomized dielectric liquid sprays

A general procedure has been developed for the simulation of charged liquid and electrostatically atomized sprays. The procedure follows a Lagrangian approach for simulation of spray droplets and a Eulerian approach for gas‐phase variables, including the electric field generated by the charge presence on droplets. Validation of the procedure was examined through simulations of previously published charged spray experiments. Results showed that for the specification of initial droplet charge, modelling the droplet charge–diameter relationship through a scaling law is as reliable a method as using a directly obtained charge–diameter relationship from experimental measurements. The normalized root‐mean‐square errors for sprays using the two methods were shown to be within 12% of one another, for the prediction of spatially averaged profiles of mean droplet diameters, mean axial velocities and mean radial droplet velocities. Results showed that the general spatial characteristics and dynamics of a charged liquid spray can successfully be reproduced, including the axial and radial dispersal pattern of droplets and the distribution of mean droplet diameters throughout the spray plume. For all sprays with droplet charges defined through a scaling law relationship, the normalized root‐mean‐square errors range from 9.0% to 31.6% for mean droplet diameters, 10.4% to 67.9% for mean axial droplet velocities and 16.8% to 38.6% for mean radial droplet velocities. Lastly, we present a brief set of general recommendations for simulating electrostatically atomized dielectric liquid sprays.Copyright © 2013 John Wiley & Sons, Ltd.     

Experimental investigation of the active compensation of the electric charge of a body in a flow with ions and charged drops

Results of experimental investigation of the problem of active control of the charge acquired by a body (sphere) in flow with an electrically charged component (ions) and electrically charged dispersed phase (water drops) are obtained and analyzed. This situation is not uncommon during aircraft flight in a cloud front. Previous experimental studies have mainly considered flows without a dispersed phase. The required flow was created by introducing in a turbulent air-steam jet a corona discharge on whose ions “electric” condensation developed and on the growing drops that arose a charge was accumulated due to diffusion processes and directional ion motion in the electric field. On the sphere which was introduced in the charged jet a discharger (active compensator) with an autonomous high-voltage power source creating a potential difference between the discharger corona needle insulated from the body and the body surface was mounted. Measurements of the size and concentration of the drops ahead of the critical point of the sphere were performed. The electric currents to elements of the experimental electric system and the floating potential of the body were measured for various corona charge parameters and various voltages on the active compensator. An active control of the sphere charge, its complete removal and the recharge of the sphere, is realized.