Electrophoresis of Dielectric and Hydrophobic Spherical Fluid Droplets Possessing Uniform Surface Charge Density

Droplet Electrophoresis with Internal Free Ions: Effect of Permittivity Changes in the Electric Double Layer

Droplet electrophoresis (EP) is of interest in biological systems, microfluidics, and separation techniques. We investigate EP of an oil droplet that contains free ions and is stabilized in an electrolyte solution through an amphoteric surfactant. The presence of mobile ions within the droplet leads to the creation of a distinct nonzero space charge density inside the droplet and consequently, formation of an inner EDL inside the droplet in addition to the traditionally considered outside EDL. While we assume the permittivity inside the inner EDL to remain constant, we consider both the case of constant and variable permittivity in the outer EDL. Our findings demonstrate a change in the droplet direction of motion in the electric field when transitioning from acidic to alkaline pH, regardless of permittivity and ionic strength in both oil and electrolyte. We further find a significant reduction in the magnitude of droplet velocity in the case of a variable permittivity due to reduction of the local space charge density within the EDL surrounding the droplet. When decreasing the viscosity ratio of the oil to the electrolyte, in all cases we find a reduction in droplet velocity. This decline is attributed mostly to the formation and strength of a vortex around the droplet. We finally demonstrate that with constant permittivity in the outer EDL, the variation in κaouter has a more significant effect on the droplet's EP velocity than altering κainner. However, in cases where the body forces inside of the droplet dominate, minor changes in the outer electrolyte concentration have no influence on the droplet motion, which is relevant for biological colloids that can contain significant free internal charges. Our results are important for the manipulation of biological colloids, water and waste treatment such as lubricant removal from processing streams.

Effect of the Surface Charge-Dependent Boundary Slip on the Electrophoresis of a Hydrophobic Polarizable Rigid Colloid

The electrophoresis of a hydrophobic charged rigid colloid is studied by considering the lateral movement of the adsorbed surface charge. The slip velocity condition at the hydrophobic surface is modified to take into account the impact of the frictional and electric forces created by the adsorbed laterally mobile surface charge. Though the dependency of the surface charge on the slip velocity in the context of electrophoresis has been addressed before, the effect of the laterally mobile adsorbed surface charge on the electrophoresis of hydrophobic colloids has not been studied. The dielectric colloid is considered to polarize and create an induced immobile surface charge when subjected to an imposed electric field. The impact of the mobile surface charge along with the immobile induced surface charge on electrophoresis of a hydrophobic colloid is elucidated by numerically solving the governing electrokinetic equations in their full form. We have also developed a simplified model under a weak applied field consideration, which can be further reduced to a closed-form analytic expression for the mobility under the Debye-Hückel approximation. This analytic model for mobility is in excellent agreement with the exact numerical solution for an entire range of the Debye length when the ζ-potential is in the order of the thermal potential. One of the notable features of this closed-form mobility expression is that it accounts for the mobile adsorbed surface charge on the hydrodynamic slip condition and the dielectric polarization of the particle. We find that the mobility of the surface charge decreases the electrophoretic mobility of the hydrophobic dielectric colloid. However, the mobile surface charge enhances the mobility of a conducting hydrophobic colloid.

Electrophoresis of a dielectric droplet with constant surface charge density

Electrophoresis of a dielectric fluid droplet with constant surface charge density is investigated theoretically in this study. A pseudo-spectral method based on Chebyshev polynomials is adopted to solve the governing electrokinetic equations. It is found, among other things, that the larger the electrolyte strength in the ambient solution is, the slower the droplet moves in general. This is due to the strong screening effect of the large amount of indifferent counterions in the neighborhood of the droplet, with no reinforcement of potential-determining ions adsorbing to the droplet surface. The droplet comes to a complete halt eventually. Critical points are discovered for highly charged droplets, at which the droplet surface becomes immobile and the interior fluid stops recirculating. The droplet moves like a rigid particle with constant mobility regardless of its viscosity, a situation referred to as the "solidification phenomenon." The deadlock between the spinning motions on the charged droplet surface induced by the electric driving force and the hydrodynamic driving force respectively is responsible for this peculiar phenomenon. This is also observed for a dielectric droplet with constant surface electric potential. We demonstrate here that it occurs in the constant surface charge density situation as well.

Dynamic Electrophoresis of a Hydrophobic and Dielectric Fluid Droplet

Dynamic electrophoresis is the foundation for electroacoustical measurements, in which the electroacoustical signals may be used to analyze the size and electrostatic charge of colloidal entities by means of the results for dynamic electrophoretic mobility. Thus, the electrophoresis under an alternating electric field is the key foundation for electroacoustic theory. In this article, we develop a tractable analytical theory for the dynamic electrophoresis of hydrophobic and dielectric fluid droplets possessing uniform surface charge density. The tiny fluid droplets possess charged mobile surfaces and have found widespread applications in our day-to-day life. For dielectric fluid droplets (e.g., oil-water emulsions), the tangential electric stress at the interface is nonzero, which significantly affects its electrohydrodynamics under an oscillatory electric field, which has, however, a negligible impact on the electrophoretic motion of conducting droplets (e.g., mercury droplets). Besides, the micro/nanoscale fluid droplets often show hydrophobicity when they are immersed in an aqueous medium, and the impact of the electric field on hydrophobic surfaces remains a research frontier in the chemical discipline. Whereas a number of approximate expressions for electrophoretic mobility have been derived for the conducting droplet, none of them are applicable to such generic hydrophobic fluid droplets with dielectric permittivity that is significantly lower than or comparable to that of an aqueous medium. In this work, within the Debye-Hückel electrostatic framework, we elaborate an original analytical expression of dynamic electrophoretic mobility for this generic dielectric fluid droplet with a hydrophobic surface considering that the droplet retains its spherical shape during its oscillatory motion. We further derived a set of simplified expressions for dynamic electrophoretic mobility deduced under several limiting cases. The results are further illustrated, indicating the impact of pertinent parameters.

Diffusiophoresis of Weakly Charged Fluid Droplets in a General Electrolyte Solution: An Analytical Theory

Owing to the importance of analytical results for electrokinetics of colloidal entities, we performed a mathematical analysis to determine the closed form analytical results for the diffusiophoretic velocity of a hydrophobic and polarizable fluid droplet. A comprehensive mathematical model is developed for diffusiophoresis, considering the background aqueous medium as general electrolytes (e.g., binary valence-symmetric/asymmetric electrolytes and a mixed solution of binary electrolytes). We performed our analysis under a weak concentration gradient, and the analytical results for diffusiophoretic velocity are calculated within the Debye-Hückel electrostatic framework. The exact form of the diffusiophoretic velocity is further approximated with negligible error, and the approximate form is found to be free from any of the cumbersome exponential integrals and thus very convenient for practical use. The present theory also covers the diffusiophoresis of perfectly dielectric as well as perfectly conducting droplets as its limiting case. In addition, we have further derived a number of closed form expressions for diffusiophoretic velocity pertaining to several particular cases, and we observed that the derived limit correctly recovers the available existing analytical results for diffusiophoretic velocity. Thus, the present analytical theory for diffusiophoresis can be applied to a wide class of fluidic droplets, e.g., hydrophobic and dielectric oil/conducting mercury droplets, air bubbles, nanoemulsions, as well as any polarizable and hydrophobic fluidic droplet suspended in a solution of general electrolytes.

Electropatterning-Contemporary developments for selective particle arrangements employing electrokinetics

The selective positioning and arrangement of distinct types of multiscale particles can be used in numerous applications in microfluidics, including integrated circuits, sensors and biochips. Electrokinetic (EK) techniques offer an extensive range of options for label-free manipulation and patterning of colloidal particles by exploiting the intrinsic electrical properties of the target of interest. EK-based techniques have been widely implemented in many recent studies, and various methodologies and microfluidic device designs have been developed to achieve patterning two- and three-dimensional (3D) patterned structures. This review provides an overview of the progress in electropatterning research during the last 5 years in the microfluidics arena. This article discusses the advances in the electropatterning of colloids, droplets, synthetic particles, cells, and gels. Each subsection analyzes the manipulation of the particles of interest via EK techniques such as electrophoresis and dielectrophoresis. The conclusions summarize recent advances and provide an outlook on the future of electropatterning in various fields of application, especially those with 3D arrangements as their end goal.

pH-Tunable electrokinetic movement of droplets

Manipulation and control of droplet motion in an electric field is of interest in biological systems, microfluidics and electrokinetic (EK) separation techniques. In this work, we show that the electrokinetic motion of oil-in-water (O/W) emulsions stabilized by an amphoteric surfactant can be controlled by changing the pH. Amphoteric surfactants carry both positive and negative head groups and change charge under the influence of changing pH, which allows them to impact the surface charge of droplets as a function of pH, and in extension their direction of motion in an electric field. Using a microfluidic system, we evaluate the effect of pH, surfactant concentration and droplet size on the EK velocity of droplets, which is a combination of electrophoresis (EP) and electro-osmotic flow (EOF). We show that by changing the pH from acidic to alkali, the direction of droplet motion in an external electric field changes. The magnitude of the EK velocity at acidic and neutral pH is not significantly altered as a result of the competition of the EP and EOF in the system, which generally have opposite directions. Our results are in good agreement with theoretical predictions for the droplet EP mobility and can thus serve as a verification of the theoretical descriptions. In addition to the pH, the surfactant concentration affects droplet EK velocity, most specifically at pH of 7 which is close to the isoelectric point of the surfactant monomers. At this pH, changing the surfactant concentration changes the direction of droplet motion due the competing effect of the EP and EOF at different surfactant concentrations. By increasing the droplet size, the magnitude of the EK velocity increases because of the larger local ζ-potential of the larger droplets as well as the wall-enhanced effect in the system. The results from this work can be applied to design on-chip droplet separation strategies based on pH variations and are relevant for systems in which pH gradients naturally occur, such as the human body.