Electrophoretically mediated partial coalescence of a charged microdrop

Highlights

• Electrocoalescence of a microdrop with a flat interface is studied numerically.

• Increasing drop charge results in suppression of partial coalescence.

• Residual droplet size and charge varies with separation and ion concentration.

• A scaling relation between residual droplet charge and droplet size is obtained.

Abstract

Coalescence of charged drops in the presence of an electric field has practical applications in microscale lab-on-a-chip devices. Existing studies have focused on macrodrops, but electrophoretic charge behavior differs for microdrops due to the increased thickness of diffuse charge layers relative to drop dimensions. An electrokinetic model is used in this study to numerically investigate the charge transfer dynamics, for the problem of charged microdrop coalescence with an electroneutral bulk liquid. In particular, the focus is on the transition from complete to partial coalescence, and the study of residual droplet formation during partial coalescence. It is found that the increasing drop charge suppresses the formation of residual droplets. The size and charge of residual droplets is shown to vary with bulk ion concentration (represented by a dimensionless inverse Debye length) and initial separation distance, in difference to experimental results obtained for macrodrops. This behavior originates from the unique charge dynamics of microdrops: the electrophoretic lift force at the drop summit varies throughout the coalescence process, affecting the convected charge in this region, which results in a charge-separation dependent residual droplet size. A scaling relation is obtained to relate the size and charge of residual droplets.

Introduction

When an initially electroneutral drop comes into contact with an electrode, it acquires a net charge (Jung et al., 2008). While the precise mechanisms underlying contact charging have not yet been established (Im et al., 2011), it is understood that the drop is, post charging, electrophoretically conducted away from the electrode by the electric field. This phenomenon, known as Contact Charge Electrophoresis (CCEP) (Drews et al., 2015) (alternatively Electrophoresis of a Charged Drop (ECD) (Im et al., 2015)), can be used to perform the precise drop manipulation required in microdrop based lab-on-a-chip (LOC) devices (Jung and Kang, 2009). These devices treat each drop as a microreactor encapsulating a chemical/biological entity of interest (Theberge et al., 2010), which is subsequently transported and analyzed. The contents of the drop are extracted by coalescing it into a bulk liquid (Fidalgo et al., 2009). Thus, the fundamental understanding of electrically induced coalescence of charged microdrops, into an electroneutral bulk liquid, is important for designing LOC devices (Zhao and Middelberg, 2011). It is also relevant for a host of industrial applications, including electrohydrodynamic inkjet printing (Choi et al., 2008) and electrical demulsification (Eow et al., 2001). However, it has received scant attention in the numerical modeling literature, in part due to the complexities involved in modeling two-phase electrophoretic flow (Pagonabarraga et al., 2010).

Surface energy arguments indicate that complete coalescence is energetically favored when an uncharged drop contacts its bulk liquid as it minimizes the total surface area (Charles and Mason, 1960). Sometimes, incomplete or partial coalescence can occur, resulting in the pinching-off of a ‘residual droplet’. This is temporary as the newly-formed residual droplet subsequently proceeds to coalesce with the bulk liquid (Aryafar and Kavehpour, 2006). When a charged drop is conducted towards its bulk liquid in the presence of an external electric field, electrohydrodynamic effects can induce a similar partial coalescence phenomenon (Aryafar and Kavehpour, 2009). However, unlike the hydrodynamic case, the residual droplet moves away from the interface (towards the top electrode) indicating that it has switched charge during the coalescence process (Mousavichoubeh et al., 2011). Despite the charge transference occurring, remarkably, the size and charge of the residual droplet was found to be independent of the ionic conductivity of the original charged (macroscale) drop. Instead, residual droplet formation, for a fixed electric field, was understood to be a pure inertio-capillary process, with convection determining the quantity of charge transferred (Hamlin et al., 2012). At high electric fields, charge transfer can be achieved without coalescence altogether, as the charge is conducted via a temporary meniscus bridge that connects the drops, and the drop appears to bounce off the interface (Bird et al., 2009, Ristenpart and Bird, 2009).

Depending on the application, either complete or partial coalescence can be desirable in microfluidic devices (Minardi et al., 2013). Predicting and controlling the coalescence outcome requires insight into the physics of charge-transfer during microdrop coalescence. As the width of the space charge regions becomes significant in comparison to the drop size (Masliyah, 2006) for microdrops, charged microdrop dynamics differs in important ways from its macroscale counterpart. To date, the phenomenon of charged drop coalescence (into an electroneutral bulk liquid) has been studied exclusively in the context of macroscale drops (Charles and Mason, 1960, Aryafar and Kavehpour, 2009, Mousavichoubeh et al., 2011, Hamlin et al., 2012), where the charge can be assumed to be located entirely on the interfaces; conduction dominates and diffusion can be assumed to be negligible. In contrast, for microdrops, an electrokinetic model that accounts for the diffusive, conductive and advective transport of individual ion species, is needed to accurately capture the essential physics (Delgado and Gonzalez-Caballero, 2007).

Here, the electrophoretic coalescence of a charged microdrop into its electroneutral bulk liquid is studied, using a recently developed multiphase electrokinetic model (Berry et al., 2013). We focus on the transition between complete and partial coalescence. In particular, we seek to shed light on the fundamental questions: when do residual droplets form and what affects their size and charge?