Compound giant unilamellar vesicles as a bio-mimetic model for electrohydrodynamics of a nucleate cell.

The understanding obtained by studies on the electrohydrodynamics (EHD) of single giant unilamellar vesicles (sGUVs) has contributed significantly towards a better comprehension of the response of biological cells to electric fields. This has subsequently helped in developing technologies such as cell dielectrophoresis and cell electroporation. For nucleate eukaryotic cells though, a vesicle-in-vesicle compound giant unilamellar vesicle (cGUV) is a more appropriate bio-mimic than a sGUV. In this work, we present an improvised method for the formation of cGUVs, wherein the electrical conductivities of the inner, annular and outer regions of the cGUVs can be modified. A comprehensive experimental study is presented on the EHD of these cGUVs under weak AC fields over a wide range of frequencies, and an encouraging agreement is observed between the experiments and earlier published theoretical studies on concentric cGUVs. The spherical, prolate or oblate spheroidal deformations of a cGUV under AC electric fields depend upon the membrane electromechanical properties as well as the magnitude and direction of the electric traction at the membrane produced by the Maxwell stress that varies with the relative timescales associated with the frequency of the applied AC electric field and that of the membrane charging time and the Maxwell-Wagner relaxation time. This work establishes cGUVs as appropriate bio-mimics for conducting EHD studies relevant to eukaryotic cells.

Effect of the Waveform of the Pulsed Electric Field on the Cylindrical Deformation of Uncharged Giant Unilamellar Vesicles.

High-speed imaging of giant unilamellar vesicles (GUVs) in recent years has shown significant shape deformation of these vesicles under electroporating direct current (DC) pulsed electric fields, possibly altering the surface distribution of transmembrane potential (TMP) and, thereby, the location and extent of electroporation on the bilayer membrane. The development of TMP, the corresponding shape deformation, and the extent of electroporation depend upon the waveform of the applied electric field. In this work, the deformation of vesicles was carried out under a high-intensity, single cycle of a sinusoidal pulsed electric field (SSPEF) and a square wave pulsed electric field (SWPEF). The cylindrical shape deformations of vesicles were observed for both SSPEF and SWPEF and were dependent upon the ratio of conductivity of the inner medium to the outer medium, α. For α = 1 and α > 1, the vesicles deformed into prolate cylinders as a result of Maxwell stress, whereas they were compressed into oblate cylinders for α < 1. Vesicles subjected to a SSPEF relaxed following either the pore closure dominated t2 or the efflux and lipid loss dominated, slow t3 mechanism depending upon the value of α. For α = 1 and α < 1, the relaxation of the vesicles was found to be predominantly dependent upon pore closure. On the other hand, a majority of vesicles gained excess area during poration when α > 1, which can be attributed to a higher TMP and faster charging of the membrane. The predictions of the approximate model for the deformation of vesicles agreed with the experiment, with deviations between the two as a result of the simplicity of the model. Moreover, the degree of deformation of vesicles [measured by the aspect ratio (AR)] and shape deformations of vesicles were found to be dependent upon the pulse width (TP) and amplitude (E0) of the SSPEF. The specific temporal variation of pore-forming tendencies of SSPEF and SWPEF, with their associated peculiarities, can be judiciously used for controlling electroporation in cells and vesicles.

Study of the interfacial viscoelasticity of human serum albumin microcapsules using a viscoelasto-electrohydrodynamic technique.

Crosslinked proteins are widely used as the encapsulating membranes in microcapsules for many biomedical and food industries. The interfacial rheological properties of these capsules are due to the complex microstructure of cross-linked globular proteins owing to structural changes at quaternary, tertiary and secondary levels. These changes in structure can be induced by high protein concentration, hydrophobic-hydrophillic interfaces, and pH. In this work, the interfacial viscoelastic rheological properties of human serum albumin (HSA) microcapsules are estimated using a novel electrodeformation technique exhibiting creep and oscillatory responses. Insights into the microstructure-rheology relationship are obtained using FTIR and SEM studies. The results show a complex dependence of the interfacial properties on the size, concentration and pH of the capsules. An interplay of inter-molecular interactions, adsorption and multilayer formation, accessibility to reactive functional groups, and dependence on the relative content of alpha helix, beta sheet and beta turn is observed. The interfacial rheological properties are estimated using the Burger model and creep is found to sensitively affect the rheological properties due to irreversible changes in microstructure. Furthermore, the electrodeformation technique allows analysis of interfacial rheology at high frequencies, 10 Hz to 1 kHz, which is otherwise not easily possible with conventional rheometers.

Electrohydrodynamics of Vesicles and Capsules.

Giant unilamellar vesicles (GUVs) made up of phospholipid bilayer membranes (liposomes) and elastic capsules with a cross-linked, polymerized membrane, have emerged as biomimetic alternatives to investigating biological cells such as leukocytes and erythrocytes. This feature article looks at the similarities and differences in the electrohydrodynamics (EHD) of vesicles and capsules under electric fields that determines their electromechanical response. The physics of EHD is illustrated through several examples such as the electrodeformation of single and compound, spherical and cylindrical, and charged and uncharged vesicles in uniform and nonuniform electric fields, and the relevance and challenges are discussed. Both small and large deformation results are discussed. The use of EHD in understanding complex interfacial kinetics in capsules and the synthesis of nonspherical capsules using electric fields are also presented. Finally, the review looks at the large electrodeformation of water-in-water capsules and the relevance of constitutive laws in their response.

Coalescence, Partial Coalescence, and Noncoalescence of an Aqueous Drop at an Oil-Water Interface under an Electric Field.

Drop-interface interaction under an electric field is relevant in commercial desalters wherein water droplets suspended in oil coalesce under an electric field, move down under gravity, and eventually coalesce with the water pool at the bottom of the desalter. In this work, we report our observation that the transition from coalescence to partial coalescence can be described by a critical electrocapillary number and is independent of the Ohnesorge number. On the other hand, the partial coalescence to noncoalescence transition depends upon both the electrocapillary number and the Ohnesorge number. The bridge during partial coalescence exhibits an electrocapillary-number-independent growth and collapse dynamics, although the transition time for growth to collapse depends upon the electrocapillary number (CaE). Lastly, contrary to previous studies, our results indicate that the secondary droplet size varies as CaE3/2 unlike the CaE1/2 reported in the literature.

A theoretical study on the dynamics of a compound vesicle in shear flow.

The dynamics of nucleate cells in shear flow is of great relevance in cancer cells and circulatory tumor cells where they determine the flow properties of blood. Buoyed by the success of giant unilamellar vesicles in explaining the dynamics of anucleate cells such as red blood cells, compound vesicles have been suggested as a simple model for nucleate cells. A compound vesicle consists of two concentric unilamellar vesicles with the inner, annular and outer regions filled with aqueous Newtonian solvents. In this work, a theoretical model is presented to study the deformation and dynamics of a compound vesicle in linear shear flow using small deformation theory and spherical harmonics with higher order approximation to the membrane forces. A coupling of viscous and membrane stresses at the membrane interface of the two vesicles results in highly nonlinear shape evolution equations for the inner and the outer vesicles which are solved numerically. The results indicate that the size of the inner vesicle (χ) does not affect the tank-treading dynamics of the outer vesicle. The inner vesicle admits a greater inclination angle than the outer vesicle. However, the transition to trembling/swinging and tumbling is significantly affected. The inner and outer vesicles exhibit identical dynamics in the parameter space defined by the nondimensional rotational (Λan) and extensional (S) strength of the general shear flow. At moderate χ, a swinging mode is observed for the inner vesicle while the outer vesicle exhibits tumbling. The inner vesicle also exhibits modification of the TU mode to IUS (intermediate tumbling swinging) mode. Moreover, synchronization of the two vesicles at higher χ and a Capillary number sensitive motion at lower χ is observed in the tumbling regime. These results are in accordance with the few experimental observations reported by Levant and Steinberg. A reduction in the inclination angle is observed with an increase in χ when the inner vesicle is replaced by a solid inclusion. Additionally, a very elaborate phase diagram is presented in the Λan-S parameter space, which could be tested in future experiments or numerical simulations.

Large deformation electrohydrodynamics of a Skalak elastic capsule in AC electric field.

The axisymmetric electrohydrodynamic deformation of an elastic capsule with a capacitive membrane obeying the Skalak law under a uniform AC electric field is investigated using analytical and boundary integral theory. The low capillary number (the ratio of destabilizing shear or electric force to the stabilizing elastic force) regime shows that time-averaged prolate and oblate spheroid deformations, and the time-periodic prolate-sphere, oblate-sphere breathing modes are commensurate with the time averaged-deformation. A novel prolate-oblate breathing mode is observed due to an interplay of finite membrane charging time and the field reversal of the AC field. The study, when extended to high capillary numbers, shows new breathing modes of cylinder-prolate, cylinder-oblate, and biconcave-prolate deformation. These are the results of highly compressive normal Maxwell stress at the poles and are aided by a weak compressive equatorial stress, characteristic of a capacitive membrane. The findings of this work should form the basis for the understanding of more complex biological cells and synthetic capsules for industrial applications.

Electroemulsification in a Uniform Electric Field.

Emulsification using electric fields is an easy alternative to flow-induced drop breakup, and the former is reported to be more effective and economical than the latter, especially when the medium phase is poorly conducting and highly viscous. The emulsification of a coarse water-in-oil emulsion in a uniform electric field is studied. We perform a detailed experimental analysis of the effect of applied electric field strength and the duration of applied electric field on the drop size distribution. The average diameter as well as the time for emulsification decreases with an increase in the intensity of the electric field. Moreover, a narrow size distribution is observed. An average size of a few microns of the dispersed phase could be achieved. New breakup mechanisms at play in the emulsification process are discussed. Identified mechanisms involve charged lobe disintegration, charged drop breakup, chain formation in which several water droplets are interconnected by thin water bridges, electrospraying and charge transfer, and coalescence. The study shows that charged drop disintegration could be the key mechanism of fine emulsification of an initially electrically neutral coarse emulsion.

Electric-field-assisted formation of nonspherical microcapsules.

A new method for studying the effect of pH on the polysiloxane network formation using electric fields is presented. The kinetic data obtained using these experiments indicates that the two-step interfacial polycondensation of silanes is strongly dependent on the pH, and the mechanism is essentially different at low and neutral to high values of pH. Very rapid hydrolysis followed by moderate rates of condensation are observed at neutral and high pH. The rate of hydrolysis is drastically reduced, while that of condensation is slightly lowered at low pH as compared to that at high values of pH. The slow hydrolysis reaction at low pH is then exploited to synthesize nonspherical microcapsules. Nonspherical polysiloxane microcapsules with varying aspect ratios from 1.05to 1.97 are synthesized by controlling the applied electric field.

Forecasting the Problem of Excessive Oil Entrainment in a Desalter Using Spinning Drop Method.

Frequent desalter upsets in the refineries processing opportunity crude oils are often triggered by a rapid and uncontrollable buildup of the rag layer, a thick water-in-oil emulsion, at the oil-brine interface. This is caused by spontaneous emulsification of brine in oil. This study investigates a unique observation from a spinning drop (SD) tensiometer, revealing the low apparent interfacial tension and rigidity of SD caused by spontaneous emulsification. Fine droplets of brine generated through spontaneous emulsification decorate the SD surface and form a stable, low-energy bilayer. Simulated rag layers using the brines from upset incidences exhibit similar behavior, indicating that spontaneous emulsification is driven by chemical species in brine, which promote osmotic water transport. The rate of rag layer buildup correlates with the rate of spontaneous emulsification, with the temperature coefficient of interfacial tension reduction serving as a sensitive indicator. An imminent upset in the operation can be forecasted by measuring this temperature coefficient, enabling preventive measures.

Development of transmembrane potential in concentric spherical, confocal spheroidal, and bispherical vesicles subjected to nanosecond-pulse electric field.

Electroporation of concentric compound spherical and confocal spheroidal as well as eccentric compound spherical vesicles, considered to be good models for corresponding nucleate cells, are investigated with an emphasis on their response to nanosecond pulse electric field (nsPEF). Analytical models are developed for the estimation of the transmembrane potential (TMP) across the bilayers of the inner and the outer vesicles and finite-element simulations are also carried out for the eccentric case. Our calculations show that with an increase in the aspect ratio, while the TMP decreases when nsPEF is used, it increases for confocal spheroids when the pulse width is greater than the membrane charging time, leading to fully charged vesicles. Bipolar pulses are shown to effectively control the TMP for a desired time period in the nsPEF regime, and a fast decay of the TMP to zero can be achieved by judicious use of pulse polarity. The external conductivity is found to significantly influence the TMP in nsPEF, unlike millisecond pulses where its effect is insignificant. Additionally the critical electric field required to induce a TMP of 1 V at the inner vesicle is presented for different pulse widths, rise time, as well as membrane capacitance, and the TMP of the outer vesicle is found to be within limits of reversible poration. It is found that the maximum TMP has a roughly linear dependence on the outer aspect ratio of the vesicle. We also introduce a new method to obtain the particular solution to the Laplace equation for bispherical system, and it is validated with finite-element simulations. Our study on nsPEF electroporation of bispherical vesicles shows that the north pole TMP is typically greater than the south pole, thereby suggesting the typical pathway a charged species might take inside an eccentric nucleate cell under electroporation.

Shape deformation of a vesicle under an axisymmetric non-uniform alternating electric field.

We suggest that non-uniform electric fields that are commonly used to study vesicle dielectrophoresis can be employed in hitherto relatively unexplored areas of vesicle deformation (for electromechanical characterization) and electroporation. Conventionally, the tension generated in vesicles is commonly modeled to be entropic or enthalpic in origin. A comparison of the configuration of a vesicle in the enthalpic and entropic regimes as well as the cross over between the two regimes during vesicle deformation has eluded understanding. A lucid demonstration of this concept is provided by the study of vesicle deformation under axisymmetric quadrupole electric field and the shapes of the vesicles obtained using the entropic and the enthalpic approaches, show significant differences. A strong dependence of the final vesicle shapes on the ratio of electrical conductivities of the fluids inside and outside the vesicle as well as on the frequency of the applied quadrupole electric field is observed. A comparison with experimental data from the literature is also made. Moreover, an excess area dependent transition between the entropic and enthalpic regimes is observed. The method could be used to estimate electromechanical properties of the vesicle.

Effect of ac electric field on the dynamics of a vesicle under shear flow in the small deformation regime.

Vesicles or biological cells under simultaneous shear and electric field can be encountered in dielectrophoretic devices or designs used for continuous flow electrofusion or electroporation. In this work, the dynamics of a vesicle subjected to simultaneous shear and uniform alternating current (ac) electric field is investigated in the small deformation limit. The coupled equations for vesicle orientation and shape evolution are derived theoretically, and the resulting nonlinear equations are handled numerically to generate relevant phase diagrams that demonstrate the effect of electrical parameters on the different dynamical regimes such as tank treading (TT), vacillating breathing (VB) [called trembling (TR) in this work], and tumbling (TU). It is found that while the electric Mason number (Mn), which represents the relative strength of the electrical forces to the shear forces, promotes the TT regime, the response itself is found to be sensitive to the applied frequency as well as the conductivity ratio. While higher outer conductivity promotes orientation along the flow axis, orientation along the electric field is favored when the inner conductivity is higher. Similarly a switch of orientation from the direction of the electric field to the direction of flow is possible by a mere change of frequency when the outer conductivity is higher. Interestingly, in some cases, a coupling between electric field-induced deformation and shear can result in the system admitting an intermediate TU regime while attaining the TT regime at high Mn. The results could enable designing better dielectrophoretic devices wherein the residence time as well as the dynamical states of the vesicular suspension can be controlled as per the application.

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.

Time-dependent electrohydrodynamics of a compressible viscoelastic capsule in the small-deformation limit.

A theoretical analysis of the time-dependent electrohydrodynamics of a viscoelastic compressible capsule, characterized by the two-dimensional Young's modulus and surface viscosity, is studied in the small-deformation limit. A systematic ac electrohydrodynamics analysis is conducted, and time-independent and time-periodic deformations are related to the electric capillary number and the membrane properties. Additionally, the relaxation of a capsule stretched by a dc electric field is also presented. This necessitates an accurate estimation of the initial strain field in the stretched capsule. Both an oscillatory analysis and an analysis of the relaxation of a stretched capsule are presented for a capsule containing an aqueous phase, modeled as a perfect conductor, and suspended in a perfect dielectric with an infinitesimally thin viscoelastic membrane separating the two. The membrane is assumed to be a perfect dielectric with no electrical contrast with the suspending fluid.