The dynamics of retraction of an initially highly slender liquid sheet of an incompressible Newtonian fluid the surface of which is covered with a monolayer of insoluble surfactant and that is surrounded by a passive gas is analyzed in the Stokes limit. In this limit, the sheets retract without the formation of a rim or capillary waves along the liquid-gas (L-G) interface. The dynamics of retraction is studied in situations in which surface rheological effects are absent as well as when they are present. Initially, the cross sections of liquid sheets are rectangular in shape albeit with semicircular caps at both ends, i.e. the cross sections resemble elongated two-dimensional (2D) drops. The 2D drops begin to retract due to the capillary pressure difference between their tips and their rectangularly shaped interiors. The free surface flow within the 2D drop is governed by the continuity and the Stokes equations which determine the flow, i.e. the velocity and pressure fields, and the convection-diffusion equation which governs surfactant transport, and hence surfactant concentration, along the L-G interface. Surface tension is related to surfactant concentration by the Szyskowski equation and the surface rheology is described by the Boussinesq-Scriven constitutive equation which involves surface shear and dilatational viscosities that are both functions of surfactant concentration. The dynamics is governed by five dimensionless groups: initial aspect ratio L-0, initial surfactant concentration Gamma(0), surfactant strength parameter beta, surface Peclet number Pe (the dimensionless ratio of surface convection to diffusion of a surfactant), and reference Boussinesq-Scriven number B-0 which measures the relative importance of surface to bulk viscous stresses. Taking advantage of sheet slenderness, a set of one-dimensional (1D) slender-sheet equations is derived using a control volume analysis. The 1D equations are solved numerically by a finite-element-based method and predictions made with the 1D algorithm are shown to accord well with ones in which the 2D free surface flow within the 2D drop is solved numerically without invoking slenderness. The results reveal that the early time retraction dynamics far from the two tips are nearly independent of Pe. Moreover, since the two surfaces of the sheet in this region remain planar for long times after the initiation of retraction, a control volume analysis is used to analytically calculate the maximum film thickness and retraction velocity that are likewise independent of Pe. In the theoretical analysis, advantage is taken of the fact that away from the tips, surfactant concentration and sheet half-thickness are simply functions of time and proportional to one another. The analytical results are expressed as implicit functions of time in terms of the exponential integral function and explicitly if surface tension varies slightly during retraction. It is shown that sheets with B-0 not equal 0 retract slower than ones with B-0 = 0, which in turn retract slower than ones with clean interfaces. The role of finite inertia is also investigated briefly and it is demonstrated that rim formation is suppressed so long as Oh (1 + B-0 Gamma(0)) >> L-0 where Oh is the Ohnesorge number [viscous force/ root(inertia)(surface tension force)].

Drop coalescence plays a crucial role in nature and industry. In continuum theory, after the two drops are taken to touch at a point at the onset of coalescence, two scaling regimes for the temporal growth of the bridge connecting the drops have been identified. Coalescence, however, is initiated at length and timescales at which the discrete nature of matter is of importance. Therefore, a continuum description provides no information about the mechanistic details of the actual initiation of bridge formation. To provide molecular-level insights into bridge formation and growth, we study the initial stages of coalescence using a hybrid Monte Carlo-molecular dynamics (MC-MD) simulation method. We reduce the required computational effort by only simulating those parts of the drops directly facing each other. Particle reservoirs, along with grand-canonical MC steps (GCMC), are used to maintain the bulk densities of the drops at specified values. These GCMC steps also enable the drops to be both thermally and chemically equilibrated prior to coalescence, thereby eliminating any potential evaporative phenomena that may confound the analysis. We identify three distinct regimes of droplet coalescence. In the first regime, the bridge expands linearly with time, t. The new simulations show that this regime is initiated by "molecular jumps" into the bridge, in agreement with the results of prior MD simulations of others, and where the density in the bridge is seen to quickly increase until it reaches nearly the bulk value. Afterwards, the bridge dynamics eventually transition to a second, viscous regime in which the bridge radius appears to scale with time as -tlnt, as also predicted in continuum analyses but which heretofore had not been observed in molecular simulations. Finally, a third, inertial regime is observed at longer times, during which the bridge radius follows a scaling law akin to the t^{1/2} scaling also predicted in continuum analyses.

Liquid sheets are omnipresent in nature and applications. The cross sections of liquid sheets are elongated two-dimensional (2D) drops the two ends of which contract towards each other because of surface tension (sigma ). If sufficiently thin, sheets can rupture due to van der Waals forces. Burton and Taborek, however, have shown that regardless of sheet thickness 2h0, a contracting inviscid liquid sheet can break even in their absence. Here we use 2D simulations and theory to show that for small yet finite viscosity mu, contracting liquid sheets will escape from pinch-off when van der Waals forces are absent due surpris\/ingly to two distinct mechanisms that depend on Ohnseorge number Oh = mu/ rho sigma h0 (rho: density). For Oh -> 0, escape is shown to be due to viscous resistance, while for larger but yet still small Oh, it can be attributed to vorticity generation at the free surface. The distinct mechanisms yield different scaling laws relating minimum sheet thickness when escape occurs to Oh.

Slender-jet equations are a set of nonlinear evolution equations that arise in the analysis of pinch-off singularities and govern the shape of and the axial velocity at leading order within a thinning liquid thread. Moreover, because they are a set of relatively simple transient partial differential equations that depend only on one spatial variable, they are also widely employed in simulating dripping and jetting from nozzles, dynamics of liquid bridges, and contraction of liquid filaments as their use results in drastic reduction in computational effort compared to solving the full set of equations governing such free surface flows. Here, a physically based derivation of the slender-jet equations is presented for situations in which the jet's surface is covered with surfactant and surface rheological (viscous) effects are important and, moreover, both the bulk fluid and the interface can be non-Newtonian. It is worth noting that a derivation of the general slender-jet equations governing the dynamics of jets consisting of arbitrary bulk and surface phases has heretofore been lacking in the literature and this deficiency is hence remedied in this paper. These general equations are then reduced to ones governing the dynamics of what is referred to as a Newtonian jet, i.e., a jet where the bulk liquid is an incompressible Newtonian fluid and its interface is a two-dimensional Newtonian fluid whose rheology is described by the widely used Boussinesq-Scriven constitutive equation. The one-dimensional (1D) slender-jet equations have recently been used to analyze the stability and breakup of primarily Newtonian jets but also of jets of non-Newtonian fluids with a Newtonian surface phase. However, most of the aforementioned studies have been carried out without benchmarking the results obtained from solving the 1D slender-jet equations against full free surface flow simulations or experiments. Therefore, we also present here a comparison of theoretical predictions obtained from slender-jet theory with computational results obtained from the use of a fully three-dimensional, axisymmetric (3DA) algorithm for a breaking surfactant-covered Newtonian jet first when the jet is undergoing Stokes flow and then also when inertia cannot be neglected. For Newtonian jets, analytical results obtained from slender-jet theory are shown to be in excellent accord with predictions obtained from the 3DA simulations.

A common feature of many free surface flows—drop/bubble breakup or coalescence and film/sheet rupture—is the occurrence of hydrodynamic singularities. Accurately computing such flows with continuum mechanical, multidimensional free surface flow algorithms is a challenging task given these problems’ multiscale nature, which necessitates capturing dynamics occurring over disparate length scales across 5–6 orders of magnitude. In drop breakup, the thinning of fluid threads that form and eventually pinch-off must be simulated until the thread's radius is about 10 nm. When two drops approach one another, the thickness of the fluid film separating them must fall below 10 nm before coalescence is said to have occurred. If the initial drop radii are 1 mm, simulations must remain faithful to the physics as thread radius or film thickness falls from 10−3 m to below 10−8 m. Here we review significant findings in interfacial flows with hydrodynamic singularities spearheaded by sharp interface algorithms. These multidimensional algorithms can achieve resolution that to date has only been possible with the use of simple 1D evolution equations.

Liquid filaments surrounded by a gas arise in nature and applications. As filaments contract, they either retract into spheres or disintegrate to form numerous droplets. In most previous computational studies, the filament's initial shape at time t = 0 has been idealized as a perfect cylinder capped off at both ends by identical hemispheres (radii R) and the fluid within which is at rest. Motivated by the fact that in experiments and applications the filament fluid is often not quiescent at t = 0, the effect of a nonzero initial velocity profile is examined for Newtonian filaments. A comprehensive phase diagram is presented in the space of L-0 (initial aspect ratio) and v(z,max) (initial tip velocity) for filaments of intermediate Ohnesorge number Oh equivalent to mu/rho gamma R (density rho, viscosity mu, and surface tension gamma) that delineates regions of the parameter space where breakup occurs from those where filaments contract to spheres without breakup.

The breakup of surfactant-covered liquid jets or threads is central to inkjet printing, microarraying, and crop spraying. During the thinning of the thread, convection and diffusion???the relative importance of which is characterized by a Peclet number Pe??? compete to determine the distribution of surfactant along the interface. As fluid evacuates the thinning neck, surfactant is convected away from that locale. However, the resulting concentration gradient gives rise to diffusion which tries to replenish the neck with surfactant. When surface rheological effects are negligible, regardless of Pe, the dynamics in the vicinity of the finite-time singularity is self-similar and, asymptotically, there is always a transition from a diffusion-dominated scaling regime to a convection-dominated one as the space-time singularity is approached. Theory and simulations are used to show that a highly viscous thread undergoing breakup under conditions in which surface viscous stresses are present gives rise to an exceptional type of dynamics in the vicinity of the neck. In contrast to previous studies of breakup in which there is always a dynamical transition between different scaling regimes as pinch-off nears, the presence of surface viscous stresses results in dynamics that cuts off this universal type of response. It is demonstrated that when Pe Pec, the dynamics is always diffusion-dominated and the rate of thread thinning is exponential in time. If, however, Pe Pec, the dynamics is self-similar and exhibits a power-law dependence on time until pinch-off. The fact that a transition between the two regimes is not possible is also demonstrated.

The thinning of threads of low-viscosity fluids like water in air has been of interest for more than a century and is gaining new importance because of the emergence of applications involving the breakup of drops and jets of liquid metals which have viscosities comparable to but surface tensions and densities much larger than water. The dynamics of thinning and pinch-off is governed by the Ohnesorge number Oh = mu/root rho gamma R, where mu, rho, gamma, and R stand for viscosity, density, surface tension, and nozzle or initial jet radius. When Oh << 1, the thread initially thins as if it were inviscid and its minimum radius (h) over tilde (min) obeys a universal scaling law h similar to min = A(gamma /rho)(1/3)((t) over tilde (b) - (t) over tilde )2/3, where (t) over tilde (b) is the time (t) over tilde at which the thread breaks up and A.= 0.717. As the interface overturns prior to breakup when Oh is sufficiently small, it has proven challenging to observe in simulations and experiments the value of the prefactor A predicted from theory and furthermore the transition of the dynamics as (h) over tilde (min) -> 0 from the inviscid regime to a different scaling regime in which the effect of viscosity is no longer negligible. Here we employ high-accuracy simulation using a sharp-interface algorithm to show that for sufficiently small Oh, the value of A predicted from computations agrees with the theoretical value to three decimal places and the inviscid power-law behavior can be observed over two to three decades in Transition out of the inviscid regime and into a viscous one is also demonstrated from simulations. (h) over tilde (min) as (t) over tilde (b) - (t) over tilde -> 0.

Liquid filaments, which are commonplace in daily life, nature, and technology, including inkjet printing and crop spraying, contract due to surface tension: they either retract into a single sphere or break up to produce a primary drop(s) and several smaller satellites. The latter are undesirable because they reduce printing quality and cause pollution due to spray drift. Surfactants and/or polymer additives can be used to control filament contraction and breakup. It has recently been demonstrated experimentally that the velocity at which the tips of contracting filaments retract can be increased in viscoelastic filaments that contain polymer additives compared to purely Newtonian filaments. Here, simulations are used to investigate the contraction of viscoelastic filaments whose rheology is described by the Oldroyd-B model. Filaments produced from nozzles are expected to be prestressed when they begin to contract. It is shown that the velocity with which the tips of prestressed filaments retract is greatly increased compared to filaments in which the polymer molecules are relaxed. This enhancement is explained by examining the value of sigma : D (sigma: Elastic stress; D: Rate-of-strain tensor), which can be positive or negative. This quantity is positive when the flow does work on the polymer molecules but negative when the molecules do work on the flow, i.e., when elastic recoiling or unloading takes place. In prestressed filaments, elastic unloading takes place because sigma : D < 0: The elastic stresses work by pulling the fluid in axially and pushing it out radially, thereby drastically increasing the tip velocity.

Rupture of liquid sheets of power-law fluids surrounded by a gas is analysed under the competing influences of pressure due to van der Waals attraction, inertia, viscous stress and capillary pressure due to surface tension. Results of a combined theoretical and computational study are presented over the entire range of parameters governing the thinning of a power-law fluid of power-law exponent $0 < n \le 1$ ( $n=1$ : Newtonian fluid) and Ohnesorge number $0 \le Oh < \infty$ , where $Oh \equiv \mu _0/\sqrt {\rho h_0 \sigma }$ , and $\mu _0, \rho, h_0$ and $\sigma$ stand for the zero-deformation-rate viscosity, density, the initial sheet half-thickness and surface tension, respectively. The dynamics in the vicinity of the space–time singularity where the sheet ruptures is asymptotically self-similar, and thus the variation with time remaining until rupture $\tau \equiv t_R - t$ , where $t_R$ is the time instant $t$ at which the sheet ruptures, of sheet half-thickness, lateral length scale and lateral velocity is determined analytically and confirmed by simulations. For sheets for which inertia is negligible ( $Oh^{-1}=0$ ), two distinct viscous scaling regimes are found, one for $0.58 < n \le 1$ and the other for $n \le 0.58$ . The thinning dynamics of inviscid sheets ( $Oh = 0$ ) is identical to that of Newtonian ones. For real fluids for which neither viscosity nor inertia is negligible, it is shown that the aforementioned creeping and inertial flow regimes are transitory and the thinning of power-law sheets exhibits a remarkably richer set of scaling transitions compared with Newtonian sheets.

Rupture of thin free films of Newtonian fluids is analyzed when the sheets' two free surfaces are covered with insoluble surfactant and surface rheological effects are important. The analysis relies on a long-wavelength model composed of a system of one-dimensional evolution equations for film thickness h(z, t), lateral velocity v(z, t), and surfactant concentration Gamma(z, t) (z: lateral coordinate, t: time). As the dynamics near the space-time singularity in sheet rupture is asymptotically self-similar when surfactants are convected away from the rupture point, the partial differential equations are also reduced to a set of ordinary differential equations in similarity space. For both highly viscous fluids in the Stokes limit and moderately viscous fluids, it is shown that the dominant balance involves van der Waals pressure and bulk viscous as well as surface viscous stresses while surface tension pressure and Marangoni stress are negligible. In the Stokes limit, self-similarity is of the second kind and h similar to Gamma similar to tau(1/3), z similar to tau(alpha z), and v similar to tau(alpha z-1) where tau is time remaining until rupture and alpha(z) is the lateral scaling exponent. Although alpha(z) cannot be determined by dimensional arguments, it is shown to equal 0.249. For moderately viscous fluids, inertia also enters the picture and self-similarity is of the first kind (h similar to Gamma similar to tau (1/3), z similar to tau(1/2), and v similar to tau(-1/2)). Scalings determined from theory are confirmed by numerical solution of the evolution equations. Closed-form expressions for the sheet's thinning rate, which have heretofore been lacking, are also reported.

Surfactants at fluid interfaces not only lower and cause gradients in surface tension but can induce additional surface rheological effects in response to dilatational and shear deformations. Surface tension and surface viscosities are both functions of surfactant concentration. Measurement of surface tension and determination of its effects on interfacial flows are now well established. Measurement of surface viscosities, however, is notoriously difficult. Consequently, quantitative characterization of their effects in interfacial flows has proven challenging. One reason behind this difficulty is that, with most existing methods of measurement, it is often impossible to isolate the effects of surface viscous stresses from those due to Marangoni stresses. Here, a combined asymptotic and numerical analysis is presented of the pinch-off of a surfactant-covered Newtonian liquid jet. Similarity solutions obtained from slender-jet theory and numerical solutions are presented for jets with and without surface rheological effects. Near pinch-off, it is demonstrated that Marangoni stresses become negligible compared to other forces. The rate of jet thinning is shown to be significantly lowered by surface viscous effects. From analysis of the dynamics near the pinch-off singularity, a simple analytical formula is derived for inferring surface viscosities. Three-dimensional, axisymmetric simulations confirm the validity of the asymptotic analyses but also demonstrate that a thinning jet traverses a number of intermediate regimes before eventually entering the final asymptotic regime.

Abstract Free drops of uncharged and charged inviscid, conducting fluids subjected to small-amplitude perturbations undergo linear oscillations (Rayleigh, Proc. R. Soc. London, vol. 29, no. 196–199, 1879, pp. 71–97; Rayleigh, Philos. Mag., vol. 14, no. 87, 1882, pp. 184–186). There exist a countably infinite number of oscillation modes, $n=2, 3, \ldots$, each of which has a characteristic frequency and mode shape. Presence of charge ($Q$) lowers modal frequencies and leads to instability when $Q>Q_R$ (Rayleigh limit). The $n=0$ and $n=1$ modes are disallowed because they violate volume conservation and cause centre of mass (COM) motion. Thus, the first mode to become unstable is the $n=2$ prolate–oblate mode. For free drops, there is a one-to-one correspondence between mode number and shape (Legendre polynomial $P_n$). Recent research has shifted to studying oscillations of spherical drops constrained by solid rings. Pinning the drop introduces a new low-frequency mode of oscillation ($n=1$), one associated primarily with COM translation of the constrained drop. We analyse theoretically the effect of charge on oscillations of constrained drops. Using normal modes and solving a linear operator eigenvalue problem, we determine the frequency of each oscillation mode. Results demonstrate that for ring-constrained charged drops (RCCDs), the association between mode number and shape is lost. For certain pinning locations, oscillations exhibit eigenvalue veering as $Q$ increases. While slightly charged RCCDs pinned at zeros of $P_2$ have a first mode that involves COM motion and a second mode that entails prolate–oblate oscillations, the modes flip as $Q$ increases. Thereafter, prolate–oblate oscillations of RCCDs adopt the role of being the first mode because they exhibit the lowest vibration frequency. At the Rayleigh limit, the first eigenmode – prolate–oblate oscillations – loses stability while the second – involving COM motion – remains stable.

Drops subjected to electric fields can deform into singular shapes exhibiting apparent sharp tips. At high field strengths, a perfectly conducting drop surrounded by a perfectly insulating exterior fluid deforms into a prolate-shaped drop with conical ends and can exist in hydrostatic equilibrium. On the conical ends, capillary stress, which is due to the out-of-plane curvature and is singular, balances electric normal stress which is also singular. If the two phases are not perfect conductors/insulators but are both leaky dielectrics and the drop is much more conducting and viscous than the exterior, electric tangential stress disrupts the hydrostatic force balance and leads to jet emission from the cone's apex. If, however, the physical situation is inverted so that a weakly conducting, slightly viscous drop is immersed in a highly conducting, more viscous exterior, the drop deforms into an oblate lens-like profile before eventually becoming unstable. In experiments, the equator of a lenticular drop superficially resembles a wedge prior to instability. Such a drop disintegrates by equatorial streaming by ejecting a thin liquid sheet from its equator. We show theoretically by performing a local analysis that a lenticular drop's equatorial profile can be a wedge only if an approximate form of the surface charge transport equation – continuity of normal current condition – is used. Moreover, we demonstrate via numerical simulation that such wedge-shaped drops do not become unstable and therefore cannot emit equatorial sheets. We then show by transient simulations how equatorial streaming can occur when charge transport along the interface is analysed without approximation.

As two spherical gas bubbles of radii (R) over tilde are brought together inside a liquid of density (rho) over tilde, viscosity (mu) over tilde and surface tension (sigma) over tilde, the liquid sheet separating them drains, thins and ultimately ruptures. The instant and location at which the bubbles make contact, and whereby a circular hole of vanishingly small radius is formed in the thin sheet, represent the occurrence of a finite-time singularity. The large curvature near the edge of the sheet where the hole has just formed, and where the two bubbles are now connected via a microscopic gas bridge, drives liquid to flow radially outward, causing the sheet to retract and the radius of the hole (R) over tilde (min) to increase with time. Recent work in this area has uncovered self-similarity and universal scaling regimes when two bubbles coalesce in a Newtonian fluid. Motivated by applications in which the exterior is a deformation-rate-thinning, power-law fluid, recent studies on bubble coalescence in Newtonian fluids are extended to coalescence in power-law fluids. In such fluids, viscosity decreases with deformation rate (gamma) over tilde raised to the n - 1 power where 0 < n <= 1 (n = 1 for a Newtonian fluid). Attention is focused here on power-law fluids that are slightly viscous at zero deformation rate, i.e. when the Ohnesorge number Oh = <(mu)over tilde>(0)/((rho) over tilde(R) over tilde(sigma) over tilde)(1/2) is small (Oh << 1) and where (mu) over tilde (0) is the zero-deformation-rate viscosity. A combination of thin-film theory and three-dimensional, axisymmetric computations is used to probe the dynamics in the aftermath of the singularity. Heretofore unexplored regimes are uncovered, and criteria are developed for transitions between different regimes. The existence of a truly inviscid regime, predicted long ago by Keller (Phys. Fluids, vol. 26, 1983, pp. 3451-3453) and which comes into play as a purely geometrical limit of the free-surface shape, is also reported. New insights are presented on the much studied Newtonian limit beyond the initial regime reported by Munro et al. (J. Fluid Mech., vol. 773, 2015, R3). The paper concludes with a phase diagram in (n, (R) over tilde (min)/(R) over tilde)-space, where the index n characterizes the fluid and (R) over tilde (min)/(R) over tilde the extent of coalescence, that highlights the various regimes and transitions between them.

When two drops are slowly brought together and first touch, a microscopic liquid neck or a bridge forms between them. The expansion of the neck is controlled by the capillary (Laplace) pressure which diverges when the curvature of the interface is infinite at the point where the drops first touch. The change in topology and the flows that ensue as time advances and the bridge grows from microscopic to macroscopic scales, and the two drops merge into one, are intimately coupled to this singularity in the dynamics. Despite the large volume of work dedicated to this problem, currently experiment, theory, and computation are not in complete agreement with respect to the earliest times following the initial contact of the two drops. Experiments, supported by simulations, report an initial regime where the radius of the connecting bridge grows linearly in time before a transition to either a Stokes regime or an inertial regime where either viscous or inertial force balances capillary (surface tension) force. In the initial linear regime, referred to as the inertially limited viscous (ILV) regime, all three forces are thought to be important. This is in contrast to theory which predicts that all coalescence events begin in the Stokes regime where inertia is negligible. Here we use high-accuracy numerical simulations to show that the ILV regime is only realized when the two coalescing drops are initially separated by a finite distance. Moreover, for two drops that initially just touch at a point, coalescence always begins in the Stokes regime. It is demonstrated that the linear ILV regime is more akin to a Taylor-Culick-type regime whose existence and duration are purely consequences of the use of an initial bridge of finite size that poorly approximates the point contact condition that is a cardinal feature of the coalescence singularity.

In addition to surface tension lowering and Marangoni stresses, surfactants also induce surface rheological effects when they deform against themselves at fluid interfaces. Because surface viscosities are functions of surfactant concentration, surface rheological stresses can compete with capillary, Marangoni, and bulk stresses in surfactant-laden free surface flows with breakup. To elucidate the effects of surface rheology, we examine the breakup of a Stokes thread covered with a monolayer of insoluble surfactant when either surfactants are convected away from the space-time singularity or diffusion is dominant. Surprisingly, in both limits, surface rheological effects always enter the dominant balance of forces and alter the thread's thinning rate. Moreover, if surfactants are convected away from the singularity, we provide an analytical expression for thinning rate that explicitly depends on surface rheological parameters, providing a simple route for measuring surface viscosity.

Highly stretched liquid drops, or filaments, surrounded by a gas are routinely encountered in nature and industry. Such filaments can exhibit complex and unexpected dynamics as they contract under the action of surface tension. Instead of simply retracting to a sphere of the same volume, low-viscosity filaments exceeding a critical aspect ratio undergo localized pinch-off at their two ends resulting in a sequence of daughter droplets - a phenomenon called endpinching - which is an archetype breakup mode that is distinct from the classical Rayleigh-Plateau instability seen in jet breakup. It has been shown that endpinching can be precluded in filaments of intermediate viscosity, with the so-called escape from endpinching being understood heretofore only qualitatively as being caused by a viscous mechanism. Here, we show that a similar escape can also occur in nearly inviscid filaments when surfactants are present at the free surface of a recoiling filament. The fluid dynamics of the escape phenomenon is probed by numerical simulations. The computational results are used to show that the escape is driven by the action of Marangoni stress. Despite the apparently distinct physical origins of escape in moderately viscous surfactant-free filaments and that in nearly inviscid but surfactant-covered filaments, it is demonstrated that the genesis of all escape events can be attributed to a single cause - the generation of vorticity at curved interfaces. By analysing vorticity dynamics and the balance of vorticity in recoiling filaments, the manner in which surface tension gradients and concomitant Marangoni stresses can lead to escape from endpinching is clarified.

Abstract When a poorly conducting drop that is surrounded by a more conducting exterior fluid is subjected to an electric field, the drop can deform into an oblate shape at low field strengths. Such drops become unstable at high field strengths and display two types of dynamics, dimpling and equatorial streaming, the physics of which is currently not understood. If the drop is more viscous, dimples form and grow at the poles of the drop and eventually the discocyte-shaped drop breaks up to form a torus. If the exterior fluid is more viscous, the drop deforms into a lens and sheds rings from the equator that subsequently break into a number of smaller droplets. A theoretical explanation as to why dimple- and lens-shaped drops occur, and the mechanisms for the onset of these instabilities, are provided by determining steady-state solutions by simulation and inferring their stability from bifurcation analysis. For large drop viscosities, electric shear stress is shown to play a dominant role and to result in dimpling. For small drop viscosities, equatorial normal stresses (electric, hydrodynamic and capillary) become unbounded and lead to the lens shape.