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It is known that the microstructure and thereby the mechanical properties of membranes constituting microcapsules are sensitive to parameters such as precursor concentration and pH. In the case of polysiloxane microcapsules, the oligomers, which are already formed in the continuous oil phase, because of the inherent moisture content in the oil phase, deposit on the membrane surface, resulting in the formation of a microstructure with a hairy layer. An electrodeformation investigation shows that the deposition of these oligomers is predominant in the smaller microcapsules compared to the larger ones and results in strain hardening and plasticity in the microcapsule membrane at high deformation. However, if the hydrolysis time during the synthesis of microcapsules is controlled, a smooth morphology (with a diminished hairy layer) can be realized for smaller capsules, as well. This work, using the electrodeformation method, demonstrates significant viscoelasticity and plasticity in the response of the capsules to applied electric stress and establishes an equivalence between simple spring and dashpot element-based phenomenological models with respect to the membrane properties using a linearized viscoelastic elasto-electrohydrodynamic model. The model can capture plasticity and strain hardening that are otherwise missed in simplified elasticity-based models.

The breakup pathway of the Rayleigh fission process observed experimentally using high-speed imaging of a charged drop levitated in an AC quadrupole trap is shown to undergo asymmetric breakup by ejecting a jet in the upward direction ((i.e., opposite to the direction of gravity)). To explain this typical experimental observation, we carry out numerical calculations based on the boundary element method considering inertial droplets levitated electrodynamically using quadrupole electric fields. The simulations show that the gravity-induced downward shift in the equilibrium position of the drop in the trap causes significant, large-amplitude shape oscillations superimposed over the center-of-mass oscillations of the drop. An important observation here is that the shape oscillations due to the applied quadrupole fields, result in sufficient deformations that act as triggers for the onset of the instability below the Rayleigh limit, thereby admitting a sub-critical instability. The center-of-mass oscillations of the droplet within the trap, which follow the applied frequency, are out of phase with the applied AC signal. Thus the combined effect of shape deformations and dynamic position of the drop leads to an asymmetric breakup such that the Rayleigh fission occurs upwards via the ejection of a jet at the north-pole of the deformed drop., Comment: 9 figures, 7 pages

The effect of droplet conductivity on electrocoalescence phenomena is studied experimentally for droplet-in-oil system in an anchored drop setup. Phase diagrams representing the coalescence/non-coalescence behaviour under DC electric field are constructed for three different droplet conductivities. Variation in droplet conductivity and separation distance between droplets do not influence critical electrocapillary number. The critical electrocapillary number varies with oil viscosity. Non-coalescence is not observed for low conductivity (1.5 μ S/cm) droplets for entire range of s 0 / R (initial separation gap to radius ratio), therefore cone angle criteria Bird et al. (2009) does not apply to anchored droplet-in-oil systems. Non-coalescence is observed as bridge vaporization/gas generation due to high current for high s 0 / R in case of moderate conductivity (1244 μ S/cm) droplets and low s 0 / R for high conductivity (89500 μ S/cm) droplets. In addition to coalescence and non-coalescence events, subsequent events after first non-coalescence are studied and an effort is made to explain and categorize the behaviour under different regimes.

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.

The rate of coalescence in an electrocoalescer, which governs the residence time, sensitively depends upon the electrostatic conditions as well as the electrodes arrangement. An experimental study of a cylindrical electrocoalescer vessel for two different modes of operation is reported in this work. The design of the coalescer is optimized for the residence time and water separation. To justify the experimental findings and to unravel more physical insights, the single phase electrostatics is simulated using COMSOL Multiphysics software. The volume of the emulsion under the influence of 0.3–1.0 kV/cm electric field, calculated using COMSOL, correlates well with the water separation. Moreover, the simultaneous measurement of current suggests an ordering, that leads to an increase in size of the droplets and settling of drops in the normal operation. On the other hand, chaining and shorting leads to surge in current at high fields and seems to prevent water separation.

The effect of an electric field on the coalescence of two water droplets suspended in an insulating oil (castor oil) in the non-coalescence regime is investigated. Unlike the immediate breakup of the bridge, as reported in earlier studies, e.g. Ristenpart et al. (Nature, vol. 461 (7262), 2009, pp. 377–380), the non-coalescence observed in our experiments indicate that at strong fields the droplets exhibit a tendency to coalesce, the intervening bridge thickens whereafter the bridge dramatically begins to thin, initiating non-coalescence. Numerical simulations using the boundary integral method are able to explain the physical mechanism of thickening of this bridge followed by thinning and non-coalescence. The underlying reason is the competing meridional and azimuthal curvatures which affect the pressure inside the bridge to become either positive or negative under the effect of electric field induced Maxwell stresses. Velocity and pressure profiles confirm this hypothesis and we are able to predict this behaviour of transitory coalescence followed by non-coalescence.

With an exclusive aim to looking into a mechanism of membrane electroporation on mesoscopic length and time scales, we report the dissipative particle dynamics (DPD) simulation results for systems with and without electrolytes. A polarizable DPD model of water is employed for accurate modeling of long-range electrostatics near the water-lipid interfaces. A great deal of discussion on field induced change in dipole moments of water and lipids together with the special variation of electric field is made in order to understand the dielectrophoretic movement of water, initiating a pore formation via an intrusion through the bilayer core. The presence of salt alters the dipolar arrangement of lipids and water, and thereby it reduces the external field required to create a pore in the membrane. The species fluxes through the pore, distributions for bead density, electrostatic potential, stresses across the membrane, etc. are used to answer some of the key questions pertaining to mechanism of electroporation. The findings are compared with the molecular dynamics simulation results found in the literature, and the comparison successfully establishes an electrostatics paradigm for biomembrane studies using DPD simulations.

The electrocoalescence of aqueous drops in an insulating oil is the fundamental process in the dehydration of emulsions of water in insulating oils, such as crude oils. The great difference in the conductivity of the aqueous droplets and the oil used as the suspending medium suggests that the conductivity of the oil medium should not affect the coalescence process. In this work, contrary to this expectation, we show a very strong dependence of the conductivity of the insulating oil on the mode of droplet coalescence. Experiments are reported using silicone oils, vegetable oils, and hydrocarbons, in the anchored drop setup that also facilitates the use of low viscosity oils. Our study indicates that the droplet undergoes cone-cone mode of interaction at low conductivities of the oil medium. On the other hand, when the conductivity of the oil is increased, the cone-dimple mode of coalescence is observed when the viscosity of the oil phase is higher, while a cone-spray-dimple mode is observed when oils of low viscosity are used.

Polysiloxane microcapsules have emerged as a model system to understand capsule formation and mechanical properties, owing to the simplicity of formation. In this work, we demonstrate that the residual water in the oil phase, that also contains the precursor Octadecyl trichlorosilane (OTS), significantly affects the mechanism of formation of bigger and smaller capsules. While in larger capsules, a smooth morphology is realized, smaller capsules, on the other hand, admit hairy growth at their surface. This leads to a difference in their microstructure as well as their mechanical properties. While the bigger capsules have higher Young's modulus, the smaller capsules are found to be less elastic (low Young's modulus). The kinetics of formation of capsules and their mechanical property estimation are made using a facile method, based on electrohydrodynamics, which was recently suggested by us [1] , [2] . The structure–property relationship demonstrated in this work should be useful in designing these microcapsules for specific applications, wherein either high or low mechanical strength is desired.

The dielectrophoresis of nearly spherical vesicles is commonly modeled using the Dipole Moment Method to estimate the dielectrophoretic force and the drag on the particle is assumed to be the same as the Stokes drag for a rigid spherical particle. We recently (Sinha and Thaokar, J Phys Cond Matt, 2018) showed that this is in agreement with analysis carried out using a more rigorous Maxwell stress method, atleast to the leading order in the shape deformation. This is essentially due to the decoupling of shape deformation and the dielectrophoretic velocity at this order of expansion. In this work, we extend the study to include the effect of shape deformation on the dielectrophoresis of a vesicle in a mixed uniform-quadrupole field. Since the deformation is frequency dependent, the correction to dielectrophoretic force is also expected to be frequency and conductivity dependent. Our analysis shows that the first order corrections are very strong and that the leading order analysis is valid only to very small shape deviations from a spherical vesicle.

Electrocoalescence is an industrially relevant process, especially in oil exploration and petroleum refining industries, and is the working principle of the process equipment, an electrocoalescer. In this work, electrocoalescence is modelled using dipolar electrostatic forces which bring the droplets together but are resisted by Stokesian drag forces. We demonstrate that hydrodynamic interactions are important to model electrocoalescence. Similarly, a multi box methodology is necessary for getting improved statistics for drop size distribution, since any coagulation/coalescence process, typically results in the loss of droplets. Moreover, the process of chaining can be modelled by assuming a “wait-time” on contact of the interacting drops, and n-mer formation can be predicted. Our results show a reasonable agreement between model predictions and experimental data. The simulations also show that an increase in volume fraction, average droplet size, and polydispersity enhance the dynamics of the coalescence process.

The breakup pathway of Rayleigh fission of a charged drop is unequivocally demonstrated by first of its kind, continuous, high-speed imaging of a drop levitated in an AC quadrupole trap. The experimental observations consistently exhibited asymmetric, sub-critical Rayleigh breakup with an upward (i.e. opposite to the direction of gravity) ejection of a jet from the levitated drop. These experiments supported by numerical calculations show that the gravity induced downward shift of the equilibrium position of the drop in the trap cause significant, large amplitude shape oscillations superimposed over the center-of-mass oscillations. The shape oscillations result in sufficient deformations to act as triggers for the onset of instability well below the Rayleigh limit (a subcritical instability). At the same time, the center-of-mass oscillations which are out of phase with the applied voltage, lead to an asymmetric breakup such that the Rayleigh fission occurs upwards via the ejection of a jet at the pole of the deformed drop. As an important application, it follows from corollarial reasoning that the nanodrop generation in electrospray devices will occur, more as a rule rather than as an exception, via asymmetric, subcritical Rayleigh fission events of micro drops due to inherent directionality provided by the external electric fields., 23 pages, 8 figures

The crude oil explored from oil wells is in the form of a water-in-oil emulsion. To process the oil for refining into different useful products, the water needs to be separated from the water-in-oil emulsion. There are several procedures reported for breaking the water-in-oil emulsion. Generally, the water present in crude oil is in the form of brine droplets, and the salt concentration may vary from a few hundred to several thousand ppm. The salts present in the crude oil create severe problems in the downstream processing in refineries such as deactivation or poisoning of the catalyst. Therefore, the removal of water from the emulsion is typically the first unit operation in a crude oil refinery. The overall process of separation of water (brine) from crude oil is generally known as desalting. In this chapter, we give a brief discussion on the stability as well as destabilization of the water-in-oil emulsion system. The mechanism of demulsification and the method of breaking water-in-oil emulsion are also discussed in detail.

In this work, we explore the effect of electric field distribution and incorporating two different frequencies in two different regions of a trigrid coalescer on the electrocoalescer efficiency. Specifically grounding water at the bottom of the coalescer is found to be effective. The effect of frequency on emulsion breakup is essentially due to chaining tendency of water droplets at high frequencies. The reason for this could be reduced electrostatic force between drops at higher frequencies due to higher capacitance of interstitial oil film between two droplets. Moreover, at low frequencies significant bouncing of drops from interface is observed, leading to lower separation rates.

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.

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.

In molecular dynamics simulations of membrane electroporation, the bilayer is subjected to an electric field E either by direct addition of a force f = qE on the charge-bearing species or by imposing an ion imbalance in the salt solutions on the two sides of the bilayer. The former is believed to mimic electroporation with high fields over nanosecond pulse period, during which the membrane is almost uncharged, especially in the low salt limit. Conversely, the ion imbalance method elucidates a low electric field-induced poration over a longer period of micro- to milliseconds with a fully charged membrane. Both these methods of applying electric field have disadvantages while investigating electroporation using dissipative particle dynamics (DPD) simulations. The method involving direct addition of force fails to address the presence of a nonuniform dielectric background for ions embedded in nonpolarizable DPD water and those found in the core of the bilayer. The ion imbalance method in DPD simulations suffers from its unavoidable use of a wall potential to prevent the movement of ions across the periodic boundaries. To address the above issues, we propose a simple method for imposing a desired transmembrane potential (TMV) by placing oppositely but uniformly charged plates on either side of the bilayer. Our DPD simulations demonstrate that the profiles for bead density, mechanical stress, electrical potential, as well as the transient responses in the dipole moment and species fluxes obtained from the proposed method utilizing charged plates are quite similar to those obtained using the ion imbalance method. The proposed protocol is free from the aforementioned drawbacks of the direct force addition and ion imbalance methods.

Natural (red blood cells) and artificial biconcave-discoid-shaped capsules have immense biological (a cellular component of blood) and technological (as drug carrier) relevance, respectively. Their low reduced volume allows significant shape changes under external fields such as extensional flows (encountered at junctions and size-varying capillaries in biological flows) and electric fields (in applications such as electroporation and dielectrophoresis). This work demonstrates biconcave-discoid to capped-cylindrical and prolate-spheroid shape transitions of a capsule in uniaxial extensional flow as well as in DC and AC electric fields. The shape changes of a stress-free biconcave-discoid capsule in external fields are important in determining the momentum and mass transfer between the capsule and the medium fluid as well as dielectrophoresis and electroporation phenomena of a capsule in an electric field. The biconcave-discoid to capped-cylindrical/prolate-spheroid shape transition is demonstrated for both a capsule (with parameters relevant to drug delivery) as well as for a red blood cell (physiological conditions). However, significant differences are observed in this shape transition depending upon the applied external fields. In an extensional flow, the pressure-driven transition shows the equator being squeezed in and the poles being pulled out to deform into a capped cylinder at low capillary number and a prolate spheroid at high capillary number. On the other hand, in the transition driven by electric fields, the shoulders of the capsule seem to play a significant role in the dynamics. The shape transition in the electric fields depends upon the relative magnitude of the electric and the hydrodynamic response times, particularly relevant for the dynamics of red blood cells in physiological conditions. A new method of analysing the shape transition of red blood cells in AC electric fields is suggested, where a large separation of time scales is observed between the hydrodynamic and electric responses.

The effect of an electric field on the coalescence of two water drops suspended in an insulating oil is investigated. We report four new results. (i) The cone angle for the non-coalescence of drops can be significantly smaller (as small as $19^{\circ }$) than the value of $30.8^{\circ }$ reported by Bird et al. (Phys. Rev. Lett., vol. 103 (16), 2009, 164502). (ii) A surprising observation of the dependence of the mode of coalescence/non-coalescence on the type of insulating oil is seen. A cone–cone mode for silicone oil is observed as against cone–dimple mode for castor oil. (iii) The critical capillary number for non-coalescence decreases with increase in the conductivity of the droplet phase. (iv) Systematic experiments prove that the apparent bridge during non-coalescence is indeed transitory and not permanent, as reported elsewhere. Theoretical calculations using analytical theory and the boundary integral method explain the formation of the cone–dimple mode as well as the transitory bridge length. The numerical calculation and thereby the physical mechanism to explain the occurrence of very small non-coalescence angles as well as the dependence of the phenomenon on the conductivity of the insulating oil and the water droplets remain unexplained.

The efficacy of electrocoalescence is critically dependent upon the interfacial tension of the crude–water interface. This study demonstrates the effect of interfacial tension on the electrocoalescence efficiency in crudes with high acidity. The interfacial tension is estimated using spinning drop tensiometer (SDT) and electrocoalescence experiments are performed at an electric field = 1.15 kVrms/cm at a frequency of 50 Hz. It is observed that separation of water from the crude is hindered at high pH for two very different reasons depending upon the source of alkalinity. Calcium hydroxide induced alkalinity leads to more rigid interface, resulting in delayed electrocoalescence. On the other hand, sodium hydroxide based alkalinity leads to ultra-low tension of crude–water interface, thereby causing oil-in-water emulsion. Increase in the pH also leads to poor quality of brine resolution, in case of sodium hydroxide based alkalinity (pH = 10) we get unresolved turbid emulsion.

Seeded growth is one of the most successful and well-studied methods of making nanorods of face-centered cubic (FCC) metals such as Ag, Au, Pt, etc. In this method separately prepared tiny metal seeds (typically smaller than 10 nm) are added to a growth solution containing metal precursor, a weak reducing agent such as ascorbic acid, and a capping agent. The mechanisms that lead to specific shape selection and growth of nanoparticles, in this method, are poorly understood. We propose a mechanism of nanorod growth based on the physical phenomenon of twinning and develop a population balance based model. Briefly, on mixing with growth solution, the seeds start growing isotropically, during which some of the seeds undergo twinning and transform their growth habit to form nanorod nuclei. The nanorod nuclei grow along one dimension to form nanorods, and a mixture of nanorods and nanospheres is obtained after a short aging time (typically < 3 h). The simulations capture the salient features of one-dimensional growth of nanorods, along with the kinetics. The trends in experimental data are reproduced well by this model, and we are able to predict the yield of nanorods. Simulations also reveal that the growth of nanospheres competes with the nucleation and growth of nanorods; their relative magnitudes decide the yield of specific shapes in the system. The model is quite general and will apply to the seeded growth of nanorods of any material that has an FCC crystal structure.

Wormlike micelles (WLMs) are a special class of surfactants, which due to their peculiar morphology (semi-flexible polymer like), provide an exciting template for synthesis of nanoparticles. In this work, a robust method for synthesis of nanorods, assisted by the templating effect of the WLMs, as well as specific magnetic or electrical dipolar interaction between the particles, is provided. Thereby, nanorods of a variety of materials such as semiconductors, metal halides, magnetic and photovoltaics are synthesized using this method. The generality of this method is established by the use of both cationic and anionic surfactant systems. The method shows a good yield of nanorods when the viscosity of the worm-like micellar phase is reduced. It appears that spherical nanoparticles, assisted by the templating effect of the WLMs, self-assemble into chains, which fuse together by interparticle interaction to yield well formed nanorods. This establishes the method as a fairly reproducible and straight-forward method of synthesizing nanorods, albeit in certain classes of materials.

Nickel nanostructures composed of intercrossed nanoplates have been prepared by a one-pot hydrazine reduction process without use of any surfactant or external magnetic field, in which ionised nickel ions are reduced by hydrazine. XRD analysis indicated that the as-synthesized nanoparticles were pure Ni with face-centered cubic (fcc) crystal structure. Scanning electron microscope (SEM) images show the formation of nickel nanoplates that have a narrow size distribution. Vibrating sample magnetometer (VSM) was also used for the characterization of Ni nanoplates. The as-synthesized nickel nanoplates were highly polycrystalline and exhibited large coercivity as compared to bulk nickel. The size of the nanoplates can be changed by altering the hydrazine hydrate concentration. This synthetic protocol may be extended to the preparation of other magnetic nanoparticles.

Past experimental studies have indicated that the Rayleigh fission of a charged drop occurs via the formation of a jet followed by emission of progeny droplets. In order to understand this process, we model the evolution of a drop using an axisymmetric boundary element method in the viscous limit. In this work, the electrostatic model of a charged viscous liquid drop is modified by including surface charge dynamics. This model accounts for the finite charge relaxation time scales over which the drop surface is charged as well as the convection of charges by the interfacial flow. It is observed that, as the drop deforms with time, the generally applied assumption of an equipotential surface becomes invalid near the conical ends that experience singularly fast dynamics and the associated surface charge dynamics gives rise to tangential electric stresses. These tangential electric stresses exert an axial momentum on the fluid and are responsible for the formation of a jet and progeny droplets. Further, the progeny droplets are found to follow an inverse power-law scaling with the conductivity of the liquid and the smaller sized progenies carry a charge close to its Rayleigh limit.

The experimental demonstration of Rayleigh instability that results in the breakup of a charged droplet, levitated in a quadrupole trap, has been investigated in the literature, but only scarcely. We report here the asymmetric breakup of a charged drop, levitated in a loose trap, wherein the droplet is stabilized at an off-center location in the trap. This aspect of levitation leads to an asymmetric breakup of the charged drop, predominantly in a direction opposite to that of gravity. In the present work, we report the evidence of successive events of the deformation and breakup of a charged drop and its subsequent relaxation after jet ejection using high-speed imaging at a couple of hundred thousand frames per second. Several relevant aspects of this phenomenon such as the effect of the electrodynamic (ED) trap parameters in terms of the applied potential as well as physical parameters such as the size of the drop, gravity, and conductivity on the characteristics of droplet breakup are explored. A clear effect of the trap strength on the deformation (both symmetric and asymmetric) is observed. Moreover, the cone angle at the pole undergoing asymmetric breakup is almost independent of the applied field investigated in the experiments. All of the experimental observations are compared with numerical simulations carried out using the boundary element method (BEM) in the Stokes flow limit. The BEM simulations are also extended to other experimentally achievable parameters. It is observed that the breakup in our study is mostly field-influenced and not field-induced. A plausible theory for the observations is reported, and a sensitive role of the sign of the charge on the droplet and the sign of the end-cap potential, as well as the off-center location of the droplet in the trap, is elucidated.

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.

A charged droplet can be electrodynamically levitated in the air using a quadrupole trap by typically applying a sinusoidal electric field. When a charged drop is levitated it exhibits surface oscillations simultaneously building charge density due to continuous evaporation and subsequently undergoes breakup due to Rayleigh instability. In this work, we examined large-amplitude surface oscillations of a sub-Rayleigh charged drop and its subsequent breakup, levitated by various applied signals such as sine, square and ramp waveform at various imposed frequencies, using high-speed imaging (recorded at 100-130 thousand Frames Per Second (fps)). It is observed that the drop surface oscillates in sphere-prolate-sphere-oblate (SPSO) mode and seldom in the sphere-prolate-sphere (SPS) mode depending on the intricate interplay of various forces due to charge(q), the intensity of applied field ($\Lambda$) and shift of the droplet from the geometric center of the trap ($z_{shift}$). The Fast Fourier Transformation (FFT) analysis shows that the droplet oscillates with the forced frequency irrespective of the type of the applied waveform. While in the sinusoidal case, the nonlinearities are significant, in the square and ramp potentials, there is an admittance of all the harmonic frequencies of the applied potential. Interestingly, the breakup characteristics of a critically charged droplet is found to be unaffected by the type of the applied waveform. The experimental observations are validated with an analytical theory as well as with the Boundary Integral (BI) simulations in the potential flow limit and the results are found to be in a reasonable agreement., Comment: 10 pages, 7 figures

The present work on radial electric field induced jet breakup is an extension of our recent work ( Lakdawala et al., 2015b ) on surface tension force induced jet breakup. A Dual Grid Level Set Method (DGLSM) based numerical study on the non-linear breakup of viscous liquid jets immersed in another viscous fluid under radial electric field is carried out in this work. This leads to a better understanding of the mechanism of electrocapillary jet breakup and subsequent formation of primary and satellite drops, due to the temporal growth of surface perturbation. The influence of the electrical Bond number ( B oe ) and Reynolds number ( Re ) on the growth rate, the breakup time, the volume of the primary and satellite drops, and the charge of both primary and satellite drops is analyzed. An excellent agreement of the present numerical with the published analytical results is obtained for different Reynolds numbers ( Re = 10 , 100 ) , wave numbers ( 0 k ≤ 1 ) and electric Bond number ( 0 B oe 4 ) . The results show that electrostatic stresses stabilize the long waves and destabilize the short waves which are in accord with linear stability theory: confirming the robustness of our DGLSM method in simulating two-phase electrohydrodynamic flow. The results indicate that nonlinear contribution from the electrostatic force is very important in analyzing the mechanism of satellite formation. The numerical results reveal that the satellite formation as well as the breakup time is affected significantly when the effect of conduction is weak. For large conduction, the evolution of the thread is close to those obtained for a perfectly conducting core fluid. Finally, we numerically show that the local dynamics may be altered when the conduction is weak compared to the perfect conductor limit.

A numerical study, employing boundary element method (BEM), on the interaction of two perfectly conducting drops in a perfectly dielectric medium (PCPD), under electric field, is presented here. A scaling analysis is carried out to show that electric stress is balanced by the hydrodynamic stress while the capillary stress becomes subdominant as the drops approach each other under electric field. Parameters such as initial separation distance and electrocapillary number are numerically studied using BEM to see their effects on deformation of drops, characterized by their cone angle β at contact, in pre-contact phase. In the post-contact phase, the drops are bridged using Bird et al. (2009)’s analytical model, which is solved numerically. Thereafter BEM is employed to realize coalescence and non-coalescence as exhibited by the bridged drops, depending on critical cone angle. It is also shown numerically, that electrostatics play no part for PCPD system once the charges at the tips of the drop poles are neutralized on bridging thus validating Bird et al. (2009)’s assumption.

In this work an effort has been made to demonstrate and understand electrocoalescence phenomena in droplet-in-air system using an anchored drop setup. Phase diagrams pertaining to the behaviour of droplet-in-air system is absent in the existing literature, and hence, are constructed for three different droplet conductivities, low (1.5 μS/cm), moderate (1244 μS/cm), and high (89500 μS/cm). The critical electrocapillary number C a c (estimated to be ~ 0.25 ) for anchored droplets is found to be independent of droplet conductivity, cone angle, and separation distance between the droplets. For separation less than s 0 / R = 0.5 , coalescence is observed at all C a > C a c because the cone angle of contact is always less than the critical angle of contact for non-coalescence. Different mechanisms govern non-coalescence behaviour with change in droplet conductivity. In addition to coalescence and non-coalescence events, subsequent events after first non-coalescence are studied and an effort is made to explain and categorize the behaviour under different regimes.

Hierarchical self-assembly is an elegant and energy-efficient bottom-up method for the structuring of complex materials. We demonstrate the synthesis of maghemite nanorods via directed self-assembly, assisted by wormlike micelles, under controlled shear. The experimental data are analyzed by formulating a "slithering snake" mechanism and simulating it on a cubic lattice, using a coarse-grained Monte Carlo framework. The influence of shear rate, precursor concentration, and length of Kuhn segment on the morphology of the nanorods is examined. Experiments indicate that the shear is necessary for the formation of nanorods, although diameter and length of the nanorods are insensitive to the shear rate, within the range of shear rates investigated. The model adequately captures the features of directional aggregation of particles, and the computed length and diameter correspond to the typical dimensions of the nanorods obtained experimentally. The protocol has considerable potential for producing nanorods of several materials simply by changing the precursors.

The present work on downward injection of non-Newtonian jet is an extension of our recent work (Lakdawala et al, Int. J. Multiphase Flow. 59: 206-220, 2014) on upward injection of Newtonian jet. The non-Newtonian rheology of the jet is described by a Carreau type generalized Newtonian fluid (GNF) model, which is a phenomenological constitutive equation that accounts for both rate-thinning and rate-thickening. Level set method based numerical study is done for Newtonian as well as various types of shear thinning and thickening jet fluid. Effect of average injection velocity (V (av, i) ) is studied at a constant Reynolds number Re = 14.15, Weber number We = 1, Froude number Fr = 0.25, density ratio chi = 0.001 and viscosity ratio eta = 0.01. CFD analysis of the temporal variation of interface and jet length (L (j) ) is done to propose different types of jet breakup regimes. At smaller, intermediate and larger values of V (av, i) , the regimes found are periodic uniform drop (P-UD), quasi-periodic non-uniform drop (QP-NUD) and no breakup (NB) regimes for a shear thinning jet; and periodic along with Satellite Drop (P +S), jetting (J) and no breakup (NB) regimes for a shear thickening jet, respectively. This is presented as a drop-formation regime map. Shear thickening (thinning) is shown to produce long (short) jet length. Diameter of the primary drop increases and its frequency of release decreases, due to increase in stability of the jet for shear thickening as compared to thinning fluid.

Non-uniform fields are commonly used to study vesicle dielectrophoresis and can be used to hitherto relatively unexplored areas of vesicle deformation and electroporation. A common but perplexing problem in vesicle dynamics is the cross over from the entropic to enthalpic (stretching) tension during vesicle deformation. A lucid demonstration of this concept is provided by the study of vesicle deformation and dielectrophoresis under axisymmetric quadrupole electric field. Small deformation theory incorporating the Maxwell stress approach is used (employing area and volume conservation constraints) to estimate the dielectrophoretic velocity. The entropic and enthalpic tensions are implemented to understand vesicle electrohydrodynamics in low and high tension limits. The shapes 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 which could be used to estimate electromechanical properties of the vesicle. Moreover, an excess area dependent transition between the entropic and enthalpic regimes is observed. The Maxwell stress approach, used in this work, indicates that Clausius-Mossotti factor obtained by the dipole moment method together with the drag on a rigid sphere explains vesicle dielectrophoresis. Interestingly, the coupling of hydrodynamic and electric stress, important in drops is absent in vesicle dielectrophoresis to linear order.

An accurate description of long-ranged electrostatics in molecular simulations necessitates the solvent models that respond in accordance with the local electric fields. Given this fact, many polarisable versions of water models exist for molecular dynamics simulations. However, there is only one model of water which is polarisable available for dissipative particle dynamics (DPD) simulations, and it is based on three-to-one coarse-graining scheme. The recent coarse-grained models of lipids meant for biomembrane studies using DPD are MARTINI-like models and have level of coarse-graining four-to-one. So a polarisable model of water needed to study the biological processes in conjunction with these lipid models should also be of the same degree of coarse-graining. Therefore, we present a DPD model of polarisable water with degree of coarse-graining four-to-one. By reflecting the positions of two Drude oscillators, the model responds to local electric fields, setting up induced polarisation locally. The model parameters are to reproduce the relative dielectric permittivity and compressibility of water at room temperature. The validity and applicability of the water model have been ascertained through in-silico evidences presented.

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 ($\text{Mn}$), 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 $\text{Mn}$. 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.

Electrodynamic (ED) levitation of one or a few charged droplets using Paul traps offers opportunities to understand the Rayleigh instability as well as the role of various inter-particle forces on pattern formations. In this work, we develop a theory for two-dimensional patterns formed during levitation of two to a few droplets in an ED balance, based on an extension of the classical Dehmelt approximation to interacting particle systems. The theory presents closed-form solutions to the inter-particle separations, secular frequencies, orientation stabilities of two-drop systems, and collapse of droplets onto the XY plane. Based on symmetry considerations, the theory is extended to predict the sizes and shapes of closed structures formed for few-drop systems. The analysis specifically helps one to understand the charge independence of inter-particle separations for equal charge to mass ratio drops. This and several other results obtained in this analysis provide functional relationships for the various quantities examined in numerical simulations and experiments. The study thus significantly advances our understanding of many-body levitation in electrodynamic balance.

It is well known that a spherical drop charged beyond its Rayleigh limit becomes unstable (when subjected to a small shape perturbation) and ejects a significant fraction of the original charge in the form of a jet. To understand the detailed mechanism of this process, we model a charged drop of a perfectly conducting viscous liquid numerically using the boundary-element method. It is found from the simulations that the drop progressively deforms into a conical shape with pointed ends just prior to breakup. For ethylene glycol droplets suspended in air, the drop attains an aspect ratio of 3.86 at its critical shape, close to the observed value of 3.85 in the experimental images available in the literature. As the numerical approach fails to predict charge ejection due to the occurrence of a singularity at this point, the charge loss fraction is estimated by determining how much minimum charge must be removed if the drop is to relax back to a spherical shape. In this manner, the charge loss due to Rayleigh fission (the difference between the original charge and the minimum charge removed) is estimated to be about 39%, which falls within the range of experimental data lying between 20% and 50%. The results on scaling laws, time scales of the process, and the role of various stresses on the dynamics of the drop are discussed.

The dynamics of a spherical elastic capsule, containing a Newtonian fluid bounded by an elastic membrane and immersed in another Newtonian fluid, in a uniform DC electric field is investigated. Discontinuity of electrical properties such as conductivities of the internal and external fluid media as well as capacitance and conductance of the membrane lead to a net interfacial Maxwell stress which can cause the deformation of such an elastic capsule. We investigate this problem considering well established membrane laws for a thin elastic membrane, with fully resolved hydrodynamics in the Stokes flow limit and describe the electrostatics using the capacitor model. In the limit of small deformation, the analytical theory predicts the dynamics fairly satisfactorily. Large deformations at high capillary number though necessitate a numerical approach (Boundary element method in the present case) to solve this highly non-linear problem. Akin to vesicles, at intermediate times, highly nonlinear biconcave shapes along with squaring and hexagon like shapes are observed when the outer medium is more conducting. The study identifies the essentiality of parameters such as high membrane capacitance, low membrane conductance, low hydrodynamic time scales and high capillary number for observation of these shape transitions. The transition is due to large compressive Maxwell stress at the poles at intermediate times. Thus such shape transition can be seen in spherical globules admitting electrical capacitance, possibly, irrespective of the nature of the interfacial restoring force., 29 pages, including figure and sub-figures total 93

An accurate time evolution of charged species having exponentially smeared out charge density (Slater type charge distribution) in dissipative particle dynamic (DPD) simulations necessitates the optimal choice of the Ewald splitting parameter (alpha), charge smearing length (lambda), and real space cutoff (c) when the Ewald summation or its variant such as particle-particle particle-mesh or particle-mesh Ewald is employed for long range electrostatics. The present article offers the error estimates in the electrostatic energy and the force as a function of alpha and beta (1/lambda) on account of spherical truncation c in real space. These error estimate formulae are validated by our DPD simulation results. We also give here an Ewald-like derivation for electrostatic energy and force for the Slater type charge density. A quick estimate of the electrostatic pressure without the use of the tedious expression which involves three dimensional Fourier transforms is also presented, and its range of validity is discussed. The basis for the proposed formula for pressure is the fact that the minimum-image truncation in many cases allows one to compute the thermodynamic quantities with reasonable accuracy. Published by AIP Publishing.

Synthesis of giant unilamellar vesicles (GUVs) of charged and uncharged lipids at physiological salt concentration is presented using the starch hydrogel method as an example of the gel assisted synthesis method. The swelling of the gel is assisted by the presence of a high amount of amylopectin in starch and yields giant-sized vesicles, which are unilamellar in nature. This method holds promise since starch is a commonly available cheap bio-compatible material. This work indicates that native starch yields vesicles of better size range as compared to the acid-treated starch. It is demonstrated that contrary to the common belief, pre-hydration of bilayers is not critical to the success of this method. The synthesis of GUVs in physiological salt concentrations is possible since the salt does not produce any osmotic effect on its own. At low starch concentration, the size of the vesicles is found to correlate with the swelling factor. The conjugate effect of the starch concentration and ion leads to the change in the swelling factor of the gel and thereby influence the size and architecture of the vesicles. Also, interactions between starch and lipid play an important role in the formation of the giant vesicles.

In this experimental study we propose the use of highly nonuniform electric field to emulsify a leaky dielectric oil into another oil. Specifically, a pin–plate electrode system is used to emulsify castor oil into silicone oil. The method is suitable for the emulsification of a higher conductivity leaky dielectric oil dispersed in a lower conductivity medium and is suitable for an already existing emulsion, unlike electrospray methods. The process is stabilized by charging of the dispersed phase and the associated electrohydrodynamic flow. A balance of electrocoalescence and breakup leads to a stationary drop size distribution. A short process time indicates its suitability for continuous operation.

The deformation and breakup of a leaky dielectric drop suspended in a leaky dielectric medium subjected to a quadrupole electric field are studied. Analytical (linear and nonlinear asymptotic expansions in the electric capillary number, $C{a}_{Q} $, a ratio of electric to capillary stress) and numerical (boundary element) methods are used. A complete phase diagram for the drop deformation in the $R$–$Q$ plane is presented, where $R$ and $Q$ are the non-dimensional ratios of the resistivities and dielectric constants, respectively, of the drop and the medium phase. The prolate and oblate deformations are mapped in the phase diagram, and the flow contours are also shown. The large deformation and breakup of a drop at higher $C{a}_{Q} $ are analysed using the boundary element method. Several non-trivial shapes are observed at the onset of breakup of a drop. A prolate drop always breaks above a certain critical value of $C{a}_{Q} $. In the oblate deformation cases, breakup as well as steady shapes are observed at a higher value of $C{a}_{Q} $. A detailed study of prolate and oblate deformation tendencies due to the normal and tangential electric stresses and the countervailing role of viscous stresses is presented. The circulation inside a drop is found to be more intense for a quadrupole field as compared with a uniform electric field. More intense internal circulations can lead to enhanced mixing characteristics and will have implications in microfluidic devices.