Coalescence of charged droplets in outer fluids

Abstract

A controlled technique to produce a precise volume of fluid species, such as water droplets, has critical importance in a variety of industrial applications. Electric field provided a well-established method to produce charged water droplets with a controlled volume. The coalescence of produced charged water droplets, however, impedes the efficiency of electric field-assisted methods. Whereas the coalescence of stationary single droplets, often charged, is overwhelmingly studied in air or vacuum, the effects of surrounding medium and approaching velocity are neglected. Systematic series of experiments and simulations were designed to address the effect of viscosity as well as approaching velocity on the coalescence of charged water droplets in viscous surrounding mediums ($\mu$ = 100 & 1000 cSt). Results suggested that increasing the electrical conductivity of water droplets with lower approaching velocity diminishes the chance of coalescence between water droplets. The higher viscosity of surrounding medium resulted in a lower chance of coalescence between water droplets while droplets with stronger electrical conductivities underwent a lower deformation inside the dielectric medium. Finally, results suggested that water chain formation, which is reportedly a main retarding factor in electrocoalescers, took place for droplets with intermediate sizes in higher viscosities of surrounding medium.

Introduction

Droplet coalescence is a pivotal phenomenon in various technologies ranging from ink-jet printing [1], [2], [3] to emulsion stability [4], [5] and has been utilized in numerous applications including petroleum [6] and food industries [7], among others. Designing tools with higher working efficiencies stipulate better understanding of drop-drop interactions.

Study of underlying physics of drop-drop interactions is an active area of research [8]. Dynamics of droplet coalescence is a long-standing subject of study started with early observations of Osborne Reynolds on droplet coalescence into the pool of water in 1875 [9] followed by the seminal work of Lord Rayleigh on the equilibrium of liquid conducting masses charged with electricity [10]. Generally, dynamics of coalescence of droplets are divided into Stokes regime, inertially limited viscous regime, and inertial regime [11]. In the Stokes regime, the coalescence of droplets is driven by surface-tension forces which provides an inward flow to connect the droplet necks. These local flows come into play substantially in the inertial regime of coalescence. While the coalescence of droplets has been long studied in the air, this phenomenon mostly occurs in dense surrounding fluids. Recently, Paulsen et al. [12] reported that external viscosity of the surrounding fluid plays an important role in determining the regimes of droplet coalescence.

Physicochemical properties of droplets are not the only factors that control the fate of approaching droplets. Manipulation of water droplets by electrical forces, which are essentially the basis for applications such as electrospraying [3], [13] and electrocoalescence [14], [15], has been a long-standing subject which started with pioneering works of Lord Rayleigh in the 19th century [16]. Coalescence of water droplets in the presence of electric field, i.e., electrocoalescence, is mainly dictated by surface tension [17], [18], electric field strength [19], [20], and its frequency for alternative currents [21]. Raisin et al. [22] reported that interfacial tension and initial spacing predominantly influence the coalescence of two anchored droplets. Ristenpart et al. [23] demonstrated that the coalescence of oppositely charged droplets does not occur when the surface charges of the droplets exceed a threshold value. Moreover, Hamlin et al. reported a critical electrical conductivity at which partial coalescence takes place between oppositely charged droplets [24]. This was followed by systematic experiments performed by Aryafar and Kavehpour [25], which demonstrated that a critical electric field is required for partial coalescence, which was later acknowledged by other research groups [26]. Aside from coalescence between charged droplets, periodic non-coalescence, and fuse and split regimes were observed by researchers for charged emulsion droplets. The interplay between surface tension and electrical forces was found to have a pivotal role in determining the regimes of interaction between charged droplets [26]. Despite all efforts that have been made to understand the coalescence of charged droplets, the effect of outer fluid on the dynamics of charged drops is a topic that appears to be severely lacking in the literature. Most of the research in this area was undertaken on stationary water droplets. However, droplets usually possess inertial forces when they come together for coalescence in nature. Thus, the effect of approaching velocity on the dynamics of interaction between water droplets calls for further investigation. In addition, a general mapping of the regimes in the coalescence of charged droplets due to the change in physicochemical properties of both inner and outer fluids which can provide a good roadmap for droplet-based separation devices has still remained obscure.

Here, we have reported general regimes of interactions of two opposing dynamic charged droplets in an outer fluid with different viscosities for the first time, to the best of our knowledge. We have observed four distinct regimes, namely, no-contact, coalescence, non-coalescence, and chain formation. The effect of approaching velocity on the regimes of interaction between charged water droplets was also reported for the first time in this paper. The liquid properties of droplets, i.e., the liquid conductivity, and surrounding medium, i.e., liquid viscosity, were modified to understand their role in the behavior of interacting droplets. The experimentally measured velocity and deformation of the droplet, as well as the numerical simulation results, were employed to better understand the forces exerted on the water droplets. We have concluded that increasing the viscosity of the surrounding medium decreases the chance of coalescence whereas the increase in the electrical conductivity of the electrolyte increases the chance of non-coalescence for the droplet with lower approaching velocities.