Electrohydrodynamics of a compound drop

From shaping to functionalization of micro-droplets and particles

The structure of microdroplet and microparticle is a critical factor in their functionality, which determines the distribution and sequence of physicochemical reactions. Therefore, the technology of precisely tailoring their shape is requisite for implementing the user demand functions in various applications. This review highlights various methodologies for droplet shaping, classified into passive and active approaches based on whether additional body forces are applied to droplets to manipulate their functions and fabricate them into microparticles. The passive approaches cover batch emulsification, solvent evaporation and diffusion, micromolding, and microfluidic methods. In active approaches, the external forces, such as electrical and magnetic fields or optical lithography, are applied to microdroplets. Special attention is also given to latest technologies using microdroplets and microparticles, especially in the fields of biological, optical, robotic, and environmental applications. Finally, this review aims to address the advantages and disadvantages of the introduced approaches and suggests the direction for further development in this field.

Electro-Hydrodynamics of Emulsion Droplets: Physical Insights to Applications

The field of droplet electrohydrodynamics (EHD) emerged with a seminal work of G.I. Taylor in 1966, who presented the so-called leaky dielectric model (LDM) to predict the droplet shapes undergoing distortions under an electric field. Since then, the droplet EHD has evolved in many ways over the next 55 years with numerous intriguing phenomena reported, such as tip and equatorial streaming, Quincke rotation, double droplet breakup modes, particle assemblies at the emulsion interface, and many more. These phenomena have a potential of vast applications in different areas of science and technology. This paper presents a review of prominent droplet EHD studies pertaining to the essential physical insight of various EHD phenomena. Here, we discuss the dynamics of a single-phase emulsion droplet under weak and strong electric fields. Moreover, the effect of the presence of particles and surfactants at the emulsion interface is covered in detail. Furthermore, the EHD of multi-phase double emulsion droplet is included. We focus on features such as deformation, instabilities, and breakups under varying electrical and physical properties. At the end of the review, we also discuss the potential applications of droplet EHD and various challenges with their future perspectives.

Numerical simulation of electrohydrodynamics of a compound drop based on the ternary phase field method

Analytical and numerical methods are often used to study the behavior of multiphase fluid under electric field. Compared with analytical methods, numerical methods can simulate the real physical phenomenon of multiphase fluid dynamics in a large deformation range. The finite element method is mainly applied in two-phase fluid currently, although it can be used to analyze the small and large deformation of multiphase fluid under electric field. This article attempts to develop a finite element model of a concentric compound drop immersed in continuous medium under electric field based on the ternary phase field method and simulate the electrohydrodynamics of the compound drop whose core phase, shell phase, and continuous phase are different. The small deformation simulation results of the compound drop under weak electric field are compared with the analytical results of previous researchers from the three aspects, namely, deformation, free charge distribution, and flow pattern. This model is proved to be effective under certain conditions. Based on this premise, the large deformation and breakup of the compound drop under high electric field are further simulated to investigate the mechanism of compound drop breakup preliminarily.

Breakups of an encapsulated surfactant-laden aqueous droplet under a DC electric field

We investigate the breakups of an encapsulated conducting aqueous droplet under a direct-current electric field via extensive experiments and theoretical analysis. The encapsulating shell phase and the ambient phase consist of leaky dielectric liquids. We change the surface tension by using an aqueous core with different surfactant (Tween 80) concentrations. Moreover, we vary the core size under different electric-field conditions and observe the core dynamics. We present three different breakup modes of the encapsulated droplet. In the first mode, the encapsulated core forms asymmetric Janus shapes after breakup. In the second and third breakup modes, stable and unstable ternary droplets are formed, respectively. We show that the surfactant molecules significantly alter the dynamics of core stretching. According to the theoretical analysis, we identify the critical conditions of instability leading to breakup. We plot the breakup modes in the form of a phase diagram in the electric capillary number (Ca₂₃ = ε₃r_sE_o²/γ₂₃; ratio of interfacial electric to capillary stresses) vs. radius ratio of the core to the shell (β = r_c/r_s) parametric space at different nondimensional surfactant concentrations (C* = C_Tween 80/C_CMC, where C_CMC represents the critical micellar concentration). The study provides essential physical insight into encapsulated emulsions and is useful for their application in various areas of science and technology.

Mono-emulsion droplet stretching under direct current electric field

We study the mechanism of stretching and breaking of a mono-emulsion droplet under a direct current electric field using theoretical and experimental approaches aided by numerical simulation. Axisymmetric straining flow driven by an electric field results in the equilibrium deformation of the droplet along the direction of the electric field if the electric capillary number Cae that is the ratio of electric stresses to capillary stresses, is less than a critical value (Cae)crit. At (Cae)crit, the droplet breaks either before showing the slow deformation stage or rapidly. Furthermore, we developed a theoretical model to understand the mechanism of the transition from equilibrium deformation to non-equilibrium breaking. The Cae that can induce Taylor's deformation D = (α - β)/(α + β) ≈ 0.295; where α and β are the lengths of semi-major and semi-minor axes of the droplet, corresponds to (Cae)crit. At this stage, the maximum flow velocity shifts to the outside of the droplet along the electric field direction and large electric stresses are mainly concentrated at the droplet's side apex causing daughter droplet ejection. Finally, we compare the values of (Cae)crit obtained from the theoretical model ((Cae)crit ≈ 0.25) for which the conductivity ratio (R) between the droplet and ambient liquid i.e., R ∼ O(10) with our experimental results ((Cae)crit ≈ 0.245) and realize that (Cae)crit decreases as R increases. We also observe that even though the viscosity ratio can alter the emulsion breakup modes, it has no effect on (Cae)crit for the onset of breaking.

Multimodal breakup of a double emulsion droplet under an electric field

We investigate the hydrodynamic deformation and breakup of double emulsion droplets under a uniform DC electric field. Based on comprehensive experiments, we observe four different breakup modes for the double emulsion droplet by varying the viscosity of shell liquid, and conductivity, permittivity or volume fraction of the core liquid. The breakup modes are classified as a unidirectional breakup mode, two different bidirectional breakup modes, and a tip-streaming breakup mode. We performed scaling analysis and numerical simulation to explain the experimental observations. We believe that this study could provide insight for the comprehension of double emulsion droplet functionalities in various applications, including drug delivery, materials science, biological and chemical engineering, and lab-on-a-chip applications.

Electric field-induced circulation and vacuolization regulate enzyme reactions in coacervate-based protocells

Artificial protocells operating under non-equilibrium conditions offer a new approach to achieve dynamic features with life-like properties. Using coacervate micro-droplets comprising polylysine (PLL) and a short single-stranded oligonucleotide (ss-oligo) as a membrane-free protocell model, we demonstrate that circulation and vacuolization can occur simultaneously inside the droplet in the presence of an electric field. The circulation is driven by electrohydrodynamics and applies specifically to the major components of the protocell (PLL and ss-oligo). Significantly, under low electric fields (E = 10 V cm^-1) the circulation regulates the movement of the vacuoles, while high levels of vacuolization produced at higher electric fields can deform or reshape the circulation. By taking advantage of the interplay between vacuolization and circulation, we achieve dynamic localization of an enzyme cascade reaction at specific droplet locations. In addition, the spatial distribution of the enzyme reaction is globalized throughout the droplet by tuning the coupling of the circulation and vacuolization processes. Overall, our work provides a new strategy to create non-equilibrium dynamic behaviors in molecularly crowded membrane-free synthetic protocells.

Electrohydrodynamics of a compound vesicle under an AC electric field

Compound vesicles are relevant as simplified models for biological cells as well as in technological applications such as drug delivery. Characterization of these compound vesicles, especially the inner vesicle, remains a challenge. Similarly their response to electric field assumes importance in light of biomedical applications such as electroporation. Fields lower than that required for electroporation cause electrodeformation in vesicles and can be used to characterize their mechanical and electrical properties. A theoretical analysis of the electrohydrodynamics of a compound vesicle with outer vesicle of radius R _o and an inner vesicle of radius [Formula: see text], is presented. A phase diagram for the compound vesicle is presented and elucidated using detailed plots of electric fields, free charges and electric stresses. The electrohydrodynamics of the outer vesicle in a compound vesicle shows a prolate-sphere and prolate-oblate-sphere shape transitions when the conductivity of the annular fluid is greater than the outer fluid, and vice-versa respectively, akin to single vesicle electrohydrodynamics reported in the literature. The inner vesicle in contrast shows sphere-prolate-sphere and sphere-prolate-oblate-sphere transitions when the inner fluid conductivity is greater and smaller than the annular fluid, respectively. Equations and methodology are provided to determine the bending modulus and capacitance of the outer as well as the inner membrane, thereby providing an easy way to characterize compound vesicles and possibly biological cells.