A transient analysis to quantify droplet deformation under DC electric fields is presented. The full Taylor-Melcher leaky dielectric model is employed where the charge relaxation time is considered to be finite. The droplet is assumed to be spheroidal in shape for all times. The main result is an ODE governing the evolution of the droplet aspect ratio. The model is validated by extensively comparing predicted deformation with both previous theoretical and numerical studies, and with experimental data. Furthermore, the effects of parameters and stresses on deformation characteristics are systematically analyzed taking advantage of the explicit formulae on their contributions. The theoretical framework can be extended to study similar problems, e.g., vesicle electrodeformation and relaxation.
When a free-falling liquid droplet is hit by a laser it experiences a strong ablation driven pressure pulse. Here we study the resulting droplet deformation in the regime where the ablation pressure duration is short, i.e. comparable to the time scale on which pressure waves travel through the droplet. To this end an acoustic analytic model for the pressure-, pressure impulse- and velocity fields inside the droplet is developed in the limit of small density fluctuations. This model is used to examine how the droplet deformation depends on the pressure pulse duration while the total momentum to…
In the drop-on-demand (DOD) inkjet system, deformation process and the direct relations between the droplet motions and the liquid properties have been seldom investigated, although they are very critical for the printing accuracy. In this study, experiments and computational simulation regarding deformation of a single droplet driven by a piezoelectric nozzle have been conducted to address the deformation characteristics of droplets. It is found that the droplet deformation is influenced by the pressure wave propagation in the ink channel related to the driven parameters and reflected in the …
The deformation and breakup of droplets in air flows is important in many applications of spray and atomization processes. However, the shear effect of airflow has never been reported. In this study, the deformation and breakup of droplets in the shear flow of air is investigated experimentally using high-speed imaging, digital image processing, and particle image velocimetry. We identify a new breakup mode of droplets, i.e., the butterfly breakup, in which the strong aerodynamic pressure on the lower part of the droplet leads to the deflection of the droplet and then the formation of a butter…
In the present study, we have studied the electro-hydrodynamic of a physical system where a Newtonian dielectric liquid column or droplet suspended in another Newtonian dielectric liquid medium in presence of a simple shear flow. Taking both the phases as leaky dielectric and perfect dielectric in to consideration, we have performed 2D numerical solution for capturing the essential features of droplet deformation in between the parallel plate configuration. For a perfect dielectric system, this study shows that the deformation characteristic follows a monotonic as well as non-monotonic variati…
Condensation is an important aspect of many flow applications due to the universal presence of humidity in the air at ambient conditions. For direct numerical simulations of such flows, simulating the gas phase as a mixture characterized by temperature and humidity coupled by the release and absorption of latent heat has been shown to yield results consistent with multiphase direct numerical simulations at reduced costs. Modeling sessile droplets as quasi-static deformations based on the underlying condensation rates at the surface extends the single-phase approach to include the interaction b…
Here, we trap and control the position of droplets to study their dynamics using hydrodynamic forces alone without an external field. The hydrodynamic trap is adapted from a previously implemented Stokes trap by incorporating a drop-on-demand system to generate droplets at a T-junction geometry on the same microfluidic chip. We then study confined droplet dynamics in response to perturbation by applying a millisecond-pressure pulse to deform trapped droplets. Droplet shape relaxation after cessation of the pressure pulse follows an exponential decay. The characteristic droplet shape relaxation…
The influence of the underlying flow topology on the shape and size of sub-Kolmogorov droplets dispersed in a turbulent flow is of considerable interest in many industrial and scientific applications. In this work we study the deformation and orientation statistics of sub-Kolmogorov droplets dispersed into a turbulent Taylor-Couette flow. Along with Direct Numerical Simulations (DNS) of the carrier phase and Lagrangian tracking of the dispersed droplets, we solve a phenomenological equation proposed by Maffettone and Minale (\emph{J. Fluid Mech.} 78, 227-241 (1998)) to track the shape evolutio…
Two-dimensional numerical simulations with Eulerian-Lagrangian method and detailed chemical mechanism are conducted to study the methane detonation propagation across a water curtain with finite thickness. The critical length of the water curtain with sprayed droplets is determined through parametric simulations with different water mass loadings and droplet sizes. The influence of water curtain length on the methane detonation is examined by the trajectories of peak pressure and time history of average heat release rate. The results indicate that the water curtain not only inhibit the inciden…
The motion and deformation of a droplet suspended in an unbounded fluid with an arbitrary, but Stokesian, imposed flow is investigated when there is a slip at the interface between the two liquids. The boundary condition at the interface is accounted by means of a simple Navier slip condition. Expressions are derived considering the effect of slip on the velocity and the shape deformation of the droplet for any arbitrary imposed flow field, and results are presented for the specific cases of shear flow and Poiseuille flow with the results of Hetsroni and Haber (J. Fluid Mech., 1970, vol. 41(04…
We experimentally investigate the deformation and breakup of droplets interacting with an oblique continuous air stream. A high-speed imaging system is employed to record the trajectories and topological changes of the droplets of different liquids. The droplet size, the orientation of the air nozzle to the horizontal and fluid properties (surface tension and viscosity) are varied to study different breakup modes. We found that droplet possessing initial momentum prior to entering the continuous air stream exhibits a variation in the required Weber number for the vibrational to the bag breakup…
The present study deals with the effect of interfacial slip on the deformation and emulsion rheology of a dilute suspension of droplets in a linear flow. The droplets are laden with surfactants that are bulk-insoluble and get transported only along the interface. An asymptotic approach is adopted for the present analysis in order to tackle the nonlinearity present due to deformation of droplets. The analysis is carried out under two different limiting scenarios namely: surface diffusion-dominated-surfactant transport and surface convection-dominated surfactant transport. For either of the limi…
In the present study we analytically investigate the deformation and bulk rheology of a dilute emulsion of surfactant-laden droplets suspended in a linear flow. We use an asymptotic approach to predict the effect of surfactant distribution on the deformation of a single droplet as well as the effective shear and extensional viscosity for the dilute emulsion. The non-uniform distribution of surfactants due to the bulk flow results in the generation of a Marangoni stress which affects both the deformation as well as the bulk rheology of the suspension. The present analysis is done for the limiti…
In this paper we numerically investigate the breakup dynamics of droplets in an emulsion flowing in a tapered microchannel with a narrow constriction. The mesoscale approach for multicomponent fluids with near contact interactions is shown to capture the deformation and breakup dynamics of droplets interacting within the constriction, in agreement with experimental evidences. In addition, it permits to investigate in detail the hydrodynamic phenomena occurring during the breakup stages. Finally, a suitable deformation parameter is introduced and analyzed to characterize the state of deformatio…
The impact of droplets on a liquid pool is ubiquitous in nature and important in many industrial applications. A droplet impacting on a liquid pool can result in the pinch-off of a regular bubble or entrap a large bubble under certain impact conditions. In this study, the cavity deformation and the bubble entrapment during the impact of droplets on a liquid pool are studied by combined experimental measurements and numerical simulations. The time evolution of the free surface profile obtained in the numerical simulation is in good agreement with the experimental results. The cavity created by …
The propulsion of a liquid indium-tin micro-droplet by nanosecond-pulse laser impact is experimentally investigated. We capture the physics of the droplet propulsion in a scaling law that accurately describes the plasma-imparted momentum transfer, enabling the optimization of the laser-droplet coupling. The subsequent deformation of the droplet is described by an analytical model that accounts for the droplet's propulsion velocity and the liquid properties. Comparing our findings to those from vaporization-accelerated mm-sized water droplets, we demonstrate that the hydrodynamic response of la…
Despite a rigorous analysis of nonlinear electrohydrodynamics of a liquid droplet deformation in air, its influence on the surrounding gas phase has received less attention. We observed, air circulations created due to large deformation oscillations of a pendant water droplet subject to a resonating electric field act like a micro or mini blower in the air around the droplet. This is demonstrated through the deterioration of a strong electrostatic airborne particulate capture onto the droplet, when it is placed in an aerosol. Such strong local aerodynamic influence on the surrounding aerosol p…
The non-linear interaction between air and a water droplet just prior to high-speed impingement on a surface is a phenomenon that has been researched extensively and occurs in a number of industrial settings. The role that surface deformation plays in an air cushioned impact of a liquid droplet is considered here. In a two-dimensional framework, assuming small density and viscosity ratios between the air and the liquid, a reduced system of integro-differential equations is derived governing the liquid droplet free-surface shape, the pressure in the thin air film and the deformation of the surf…
The deformation and breakup of droplets in airflows is important in spray and atomisation processes, but the shear effect in non-uniform airflow is rarely reported. In this study, the deformation and breakup of droplets in a shear flow of air is investigated experimentally using high-speed imaging, digital image processing, and particle image velocimetry. The results show that in airflow with a strong shear effect, the droplet breakup exhibits unique features due to the uplift and stretching produced by the interaction between the deformed droplet and the shear layer. The breakup process can b…
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 …
Droplet-droplet interactions is ubiquitous in various applications ranging from medical diagnostics to enhancing and optimizing liquid jet propulsion. We employ an experimental technique where the laser pulse interacts with a micron-sized droplet and causes optical breakdown. The synergy of a nanosecond laser pulse and an isolated spherical droplet is accurately controlled and manipulated to influence the deformation and fragmentation of an array of droplets. We elucidate how the fluid dynamic response (such as drop-drop and shock-drop interactions) of an arrangement of droplets can be regulat…
We investigate the electrohydrodynamics of an initially spherical droplet under the influence of an external alternating electric field by conducting axisymmetric numerical simulations using a charge-conservative volume-of-fluid based finite volume flow solver. The mean amplitude of shape oscillations of a droplet subjected to an alternating electric field for leaky dielectric fluids is the same as the steady-state deformation under an equivalent root mean squared direct electric field for all possible electrical conductivity ratio $(K_r)$ and permittivity ratio $(S)$ of the droplet to the sur…
Accurate prediction of spray atomization process using an Euler-Lagrange (EL) approach is challenging because of high volume fraction of the liquid phase in dense regimes. This would in reality displace a remarkable portion of the gaseous phase which is commonly ignored in the standard EL approaches. In addition, deformation of droplet due to the interaction of aerodynamic force, surface tension and viscous forces is typically neglected in modeling dense sprays. In this work, to capture the volumetric displacement effects using an EL approach, the spatio-temporal changes in the volume fraction…
We report on the experimental studies of the deformation and fragmentation of liquid metal droplets by picosecond and subpicosecond laser pulses. The experiments were performed with laser irradiance varying in 10E13-10E15 W/cm^2 range. The observed evolution of the droplet shape upon the impact dramatically differs from the previously reported for nanosecond laser pulses. Instead of flattening the droplet undergoes rapid asymmetric expansion and transforms into a complex shape which can be interpreted as two conjunct spheroid shells and finally fragments. We explain the described hydrodynamic …
The deformation of a viscous liquid droplet suspended in another liquid and subject to an applied electric field is a classic multiphase flow problem best described by the Melcher-Taylor leaky dielectric model. The main assumption of the model is that any net charge in the system is concentrated on the interface between the two liquids as a result of the jump in Ohmic currents from the bulk. Upon application of the field, the drop can either attain a steady prolate or oblate shape with toroidal circulating flows both inside and outside arising from tangential stresses on the interface due to a…
A three dimensional small deformation theory is developed to examine the motion of a magnetic droplet in a uniform rotating magnetic field. The equations describing the droplet's shape evolution are derived using two different approaches - a phenomenological equation for the tensor describing the anisotropy of the droplet, and the hydrodynamic solution using perturbation theory. We get a system of ordinary differential equations for the parameters describing the droplet's shape, which we further analyze for the particular case when the droplet's elongation is in the plane of the rotating field…
Droplets bouncing on a vibrated liquid bath open ways to methods of manipulating droplets, creating double emulsion and performing pilot wave model experiments. In this work, we focus on the role of the droplet deformations in the vertical bouncing dynamics by neglecting the deformation of the surface of the bath. To be under this favorable conditions, low viscous oil droplet are dropped over a highly viscous oil bath. These droplets bounce vertically on the surface of the bath and exhibit many periodic trajectories and resonant modes when tuning the forcing parameters, i.e. the oscillation of…
Noneqiuilibrium dynamics of rotating droplets are studied by molecular dynamics simulations. Small deviations from the theoretical prediction are observed when the size of a droplet is small, and the deviations become smaller as the size of the droplet increases. The characteristic timescale of the deformation is observed, and we find (i) the deformation timescale is almost independent of the rotating velocity with for small frequency and (ii) the deformation timescale becomes shorter as temperature increases. A simple model is proposed to explain the deformation dynamics of droplets.
The dynamics of a single elastoviscoplastic (EVP) drop immersed in plane shear flow of a Newtonian fluid is studied by 3D direct numerical simulations using a finite-difference and level-set method combined with the Saramito model for the EVP fluid. This model gives rise to a yield stress behavior, where the unyielded state of the material is described as a Kelvin-Voigt viscoelastic solid and the yielded state as a viscoelastic Oldroyd-B fluid. Yielding of an initially solid drop of Carbopol is simulated under successively increasing shear rates. We proceed to examine the roles of nondimension…
The statistics of the deformation and breakup of neutrally buoyant sub-Kolmogorov ellipsoidal drops is investigated via Lagrangian simulations of homogeneous isotropic turbulence. The mean lifetime of a drop is also studied as a function of the initial drop size and the capillary number. A vector model of drop previously introduced by Olbricht, Rallison and Leal [J. Non-Newtonian Fluid Mech. $\mathbf{10}$, 291 (1982)] is used to predict the behaviour of the above quantities analytically.
The present study deals with the dynamics of a double emulsion confined in a microchannel under the presence of a uniform electric field. Towards investigating the non-trivial electrohydrodynamics of a compound droplet, confined in between two parallel plate electrodes, a phase field approach has been adopted. Under the assumption of negligible fluid inertia and small shape deformation, an asymptotic model is also developed to predict the transient as well as the steady state droplet dynamics in the limiting case of an unbounded suspending medium. The phases involved are either assumed to be p…
The present study theoretically predicts the effect of interfacial viscosity on the deformation of a compound drop as well as on the bulk rheology. The system at hand comprises of a dilute emulsion of concentric compound drops, laden with surfactants and suspended in a linear flow. Two types of linear flows are considered in this study, namely, a uniaxial extensional flow and a simple shear flow. Presence of surfactants along the drop surface leads to the generation of an interfacial viscosity, which is different from the bulk. This interfacial viscosity generates a viscous drag that along wit…
We report on experiments that consist in deforming a collection of monodisperse droplets produced by a microfluidic chip through a flow-focusing device. We show that a proper numerical modelling of the flow is necessary to access the stress applied by the latter on the droplet along its trajectory through the chip. This crucial step enables the full integration of the differential equation governing the dynamical deformation, and consequently the robust measurement of the interfacial tension by fitting the experiments with the calculated deformation. Our study thus demonstrates the feasibility…
We investigate the break-up of Newtonian/viscoelastic droplets in a viscoelastic/Newtonian matrix under the hydrodynamic conditions of a confined shear flow. Our numerical approach is based on a combination of Lattice-Boltzmann models (LBM) and Finite Difference (FD) schemes. LBM are used to model two immiscible fluids with variable viscosity ratio (i.e. the ratio of the droplet to matrix viscosity); FD schemes are used to model viscoelasticity, and the kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbe…
Fluidic interfaces disintegrate under sufficiently strong electric fields, leading to electrohydrodynamic (EHD) tip streaming. Taylor cones, which emit charged droplets from the tip of a conical cusp, are among the most prominent and well-studied examples of EHD instabilities. In liquid-liquid systems, more complex interface deformation modes than simple Taylor cones can be observed, with the interface being pushed away from the electrode, and additional cone structures emerging from the rim of the dimple. In this article, we investigate the mechanisms behind these deformation modes experiment…
While a drop of liquid is placed on another liquid surface, two possible coalescence outcomes are observed. The parent drop bounces several times, floats and then disappears within the liquid pool without producing daughter droplets. This is called complete coalescence. Another outcome is the generation of secondary droplets from the primary drop itself. This is called partial coalescence. Repetitions of such phenomenon as a successive self-similar event is also known as coalescence cascade. In a nutshell, complete coalescence is governed strongly by swallowing mechanism whereas partial coales…
A spherical droplet is given an initial rotation in the streamwise direction and is impulsively accelerated by a uniform free stream. Numerical results for the deformation and dynamics of the droplet are obtained by utilising a finite volume staggered mesh method with a moving mesh interface tracking scheme. The fluid dynamics videos of the droplet are presented in the Gallery of Fluid Motion, 2010. By initially rotating the droplet in the streamwise direction, the droplet deforms differently depending on the non-dimensional rotation rate, $Ω^*$. The families of droplet shape are, in ascending…
