Electrokinetic model for electric-field-induced interfacial instabilities

Electrokinetics at liquid-liquid interfaces: Physical models and transport mechanisms

The electrification effects and electrokinetic flow phenomena at immiscible liquid-liquid interfaces have been a subject of scientific inquiry for over a century. Unlike solid-liquid interfaces, liquid-liquid interfaces exhibit not only multiphysical and cross-scale characteristics but also diffuse soft properties, including finite thickness, fluidity, ion adsorbability, and permeability, which introduces diverse interfacial charging mechanisms and conductive dielectric properties, imparting unique characteristics to electrokinetic multiphase flow systems. Electrokinetic multiphase hydrodynamics (EKmHD), grounded in electrochemistry and colloid and interface science, has experienced renewed interest in recent years. This is particularly evident in systems such as the interface between two immiscible electrolyte solutions (ITIES) in electrochemistry, self-propelling droplets in physicochemical hydrodynamics, and digital microfluidics in electromechanics. The multiphase diffuse soft nature of charged liquid-liquid interfaces introduces novel physical scales and theoretical dimensions, positioning EKmHD as a potential foundation for a new interdisciplinary field rather than merely a cross-disciplinary area. This review highlights the need for an integrated research approach that combines interfacial charging mechanisms with electrokinetic flows, alongside a cross-scale modeling framework for interfacial multiphysical transport. It systematically organizes the characteristics of liquid-liquid interfaces from the perspectives of charging mechanisms and electrokinetic behaviors, with particular emphasis on spontaneous partition- and adsorption-induced charging at the interface, and the strong coupling between multiphase diffuse soft interface flow and ion transport. Furthermore, the paper comprehensively summarizes the transport mechanisms of electrokinetic multiphase flows concerning interfacial ion transport and fluid flow, while refining the corresponding dominant dimensionless parameters. Additionally, it systematically consolidates current understanding of typical electrokinetic multiphase flow scenarios, with special focus on potential future research directions. These include the electrokinetic double-sided coupling effects in ITIES systems, solidification and nonlinear effects in droplet/bubble electrophoresis, the validity of the leaky dielectric model, electrokinetic instabilities of jets and ion-selective soft interfaces, and the active and passive control of two-phase electrokinetic wetting dynamics and displacement.

Interplay of bulk soluble surfactants and interfacial kinetics governs the stability of two-layer channel flows

The linear stability of two-layer channel flows in the presence of bulk-soluble surfactants is investigated here, taking into account the rheological properties of the interface. The interfacial stresses are quantified using the Boussinesq-Scriven model, while the surfactant kinetics is assumed to follow the Frumkin isotherm, which accounts for their non-ideal behavior. Our results show that in general, the bulk solubility of surfactants has a stabilizing effect on the interface, both with and without the presence of inertia. On the other hand, the interfacial viscosities play a more complex role, depending on the viscosity ratios of the two fluids, the thickness of the fluid layers, the strength of the surface tension gradients, and the extent of inertia. We show that depending on the strength of inertia and the variability in the surface tension, the interfacial rheology may either stabilize or destabilize the base flow. However, for sufficiently small Reynolds numbers, the surface viscosity always has a stabilizing influence. Our results may be used to better design stable co-flow systems with applications in various processes such as surface coating, preparation of fluid lenses, as well as in a host of multi-purpose microfluidic devices.

Electrokinetic Thin-Film Model for Electrowetting: The Role of Bulk Charges

The electrowetting behavior of a charge-carrying sessile droplet is relevant to applications such as point-of-care diagnostics. Often biomedical assays involve droplets that contain charged molecules such as dissolved ions, proteins, and DNA. In this work, we develop a reduced-order electrokinetic model for electrowetting of such a charge-carrying droplet under a parallel-plate electrode configuration. An inertial-lubrication model based on the weighted residual integral boundary layer (WRIBL) technique is used to obtain evolution equations that describe the spatiotemporal evolution of the fluid-air interface and the depth-integrated flow rate. The solutions to the evolution equations are obtained numerically by using the spectral collocation method. We investigate the role of domain and surface charges, characterized by the Debye length, on droplet wetting. Under low relaxation timescales, both droplet deformation and wetting alteration under an AC field are shown to be equivalent to that under a root-mean-square (RMS) DC field. We show that an electrolytic sessile droplet can exhibit a larger deformation in comparison to the two asymptotic limits of a perfect conductor and a perfect dielectric droplet, corresponding, respectively, to very low and high Debye lengths. The effects of several other parameters such as the inherent equilibrium wettability, permittivity ratio, and electric field strength are also investigated.

One-Step Fabrication of Three-Dimensional Fibrous Collagen-Based Macrostructure with High Water Uptake Capability by Coaxial Electrospinning

One step fabrication of the three dimension (3D) fibrous structure of Collagen-g-poly(MMA-co-EA)/Nylon6 was investigated by controlling the experimental conditions during coaxial electrospinning. This 3D fibrous structure is the result of interactions of two polymeric systems with a varied capability to be electrostatically polarized under the influence of the external electric field; the solution with the higher conductivity into the inner spinneret and the solution with the lesser conductivity into the outer capillary of the coaxial needle. This set-up was to obtain bimodal fiber fabrication in micro and nanoscale developing a spatial structure; the branches growing off a trunk. The resultant 3D collagen-based fibrous structure has two distinguished configurations: microfibers of 6.9 ± 2.2 µm diameter gap-filled with nanofibers of 216 ± 49 nm diameter. The 3D fibrous structure can be accumulated at an approximate height of 4 cm within 20 min. The mechanism of the 3D fibrous structure and the effect of experimental conditions, the associated hydration degree, water uptake and degradation rate were also investigated. This highly stable 3D fibrous structure has great potential end-uses benefitting from its large surface area and high water uptake which is caused by the high polarity and spatial orientation of collagen-based macrostructure.

Controlled Nanoscale Electrohydrodynamic Patterning Using Mesopatterned Template

We report the path for a possible fabrication of an array of nanogrooves, by electro-hydrodynamic instability-mediated patterning of a thin polymer film using a patterned stamp with much larger features. Using a predictive computational model based on finite element method, we find the route to control the coalescence of initial instabilities that arise with the onset of spatially varying DC electric field generated through topographical patterns in the top electrode. These quasi-steady structures are shown to evolve with the electrostatic and geometric nature of the two-electrode system and are of a stable intermediate during the process of feature replication, under each electrode feature. We identify conditions to obtain nanogrooves for a range of operating conditions. Such simulations are likely to guide experiments, where simultaneous optimization of multiple parameters to fabricate features with lateral dimension smaller than that of the electrode patterns is challenging.

Deformation Hysteresis of Electrohydrodynamic Patterning on a Thin Polymer Film

Electrohydrodynamic patterning is a technique that enables micro/nanostructures via imposing an external voltage on thin polymer films. In this investigation, we studied the electrohydrodynamic patterning theoretically and experimentally, with special interest focused on the equilibrium state. It is found that the equilibrium structure height increases with the voltage. In addition, we have observed, and believe it to be the first time, a hysteresis phenomenon exists in the relationship between the voltage and structure height. With an increase in the voltage, a critical value (the first critical voltage) is noticed, above which the polymer film would increase dramatically until it comes into contact with the template. However, with a decrease in the voltage, a smaller voltage (the second critical voltage) is needed to detach the polymer from the template. The mismatch of the first and second critical voltages distorts the voltage-structure height curve into an "S" shape. Such a phenomenon is verified for three representative templates and also by experiments. Furthermore, the effects of some parameters (e.g., polymer film thickness and dielectric constant) on this hysteresis phenomenon are also discussed.

Compact micro/nano electrohydrodynamic patterning: using a thin conductive film and a patterned template

The influence of electrostatic heterogeneity on the electric-field-induced destabilization of thin ionic liquid (IL) films is investigated to control spatial ordering and to reduce the lateral dimension of structures forming on the films. Commonly used perfect dielectric (PD) films are replaced with ionic conductive films to reduce the lateral length scales to a sub-micron level in the EHD pattering process. The 3-D spatiotemporal evolution of a thin IL film interface under homogenous and heterogeneous electric fields is numerically simulated. Finite differences in the spatial directions using an adaptive time step ODE solver are used to solve the 2-D nonlinear thin film equation. The validity of our simulation technique is determined from close agreement between the simulation results of a PD film and the experimental results in the literature. Replacing the flat electrode with the patterned one is found to result in more compact and well-ordered structures particularly when an electrode with square block protrusions is used. This is attributed to better control of the characteristic spatial lengths by applying a heterogeneous electric field by patterned electrodes. The structure size in PD films is reduced by a factor of 4 when they are replaced with IL films, which results in nano-sized features with well-ordered patterns over the domain.

Electrohydrodynamic patterning of ultra-thin ionic liquid films

In the electrohydrodynamic (EHD) patterning process, electrostatic destabilization of the air-polymer interface results in micro- and nano-size patterns in the form of raised formations called pillars. The polymer film in this process is typically assumed to behave like a perfect dielectric (PD) or leaky dielectric (LD). In this study, an electrostatic model is developed for the patterning of an ionic liquid (IL) polymer film. The IL model has a finite diffuse electric layer which overcomes the shortcoming of assuming infinitesimally large and small electric diffuse layers inherent in the PD and LD models respectively. The process of pattern formation is then numerically simulated by solving the weakly nonlinear thin film equation using finite difference with pseudo-staggered discretization and an adaptive time step. Initially, the pillar formation process in IL films is observed to be the same as that in PD films. Pillars initially form at random locations and their cross-section increases with time as the contact line expands on the top electrode. After the initial growth, for the same applied voltage and initial film thickness, the number of pillars on IL films is found to be significantly higher than that in PD films. The total number of pillars formed in 1 μm(2) area of the domain in an IL film is almost 5 times more than that in a similar PD film for the conditions simulated. In addition, the pillar structure size in IL films is observed to be more sensitive to initial film thickness compared to PD films.

Electrical perturbations of ultrathin bilayers: role of ionic conductive layer

The effect of electrostatic force on the dynamics, morphological evolution, and drainage time of ultrathin liquid bilayers (<100 nm) are investigated for perfect dielectric-perfect dielectric (PD-PD) and ionic liquid-perfect dielectric (IL-PD) bilayers. The weakly nonlinear "thin film" equation is solved numerically to obtain spatiotemporal evolution of the liquid-liquid interface responses to transverse electric field. In order to predict the electrostatic component of conjoining/disjoining pressure acting on the interface for IL-PD bilayers, an analytical model is developed using the nonlinear Poisson-Boltzmann equation. It is found that IL-PD bilayers with electric permittivity ratio of layers (lower to top), εr, greater than one remain stable under an applied electric field. An extensive numerical study is carried out to generate a map based on εr and the initial mean thickness of the lower layer. This map is used to predict the formation of various structures on PD-PD bilayer interface and provides a baseline for unstable IL-PD bilayers. The use of an ionic liquid (IL) layer is found to reduce the size of the structures, but results in polydispersed and disordered pillars spread over the domain. The numerical predictions follow similar trend of experimental observation of Lau and Russel. (Lau, C. Y.; Russel, W. B. Fundamental Limitations on Ordered Electrohydrodynamic Patterning; Macromolecules 2011, 44, 7746-7751).