Characterization of kinetic coarsening in a random-field Ising model

We report a study of nonequilibrium relaxation in a two-dimensional random field Ising model at a nonzero temperature. We attempt to observe the coarsening from a different perspective with a particular focus on three dynamical quantities that characterize the kinetic coarsening. We provide a simple generalized scaling relation of coarsening supported by numerical results. The excellent data collapse of the dynamical quantities justifies our proposition. The scaling relation corroborates the recent observation that the average linear domain size satisfies different scaling behavior in different time regimes.Comment: Double-column, 4 pages, 6 figure

Dynamical Properties of Random Field Ising Model

Extensive Monte Carlo simulations are performed on a two-dimensional random field Ising model. The purpose of the present work is to study the disorder-induced changes in the properties of disordered spin systems. The time evolution of the domain growth, the order parameter and spin-spin correlation functions are studied in the non equilibrium regime. The dynamical evolution of the order parameter and the domain growth shows a power law scaling with disorder-dependent exponents. It is observed that, except for very small random fields, exchange interaction never wins over pinning interaction to establish long range order.Comment: 8 pages, 9 figures, Final and accepted version in Phys. Rev.

Effect of uniform electric field on the deformation of a 2D liquid droplet in confined simple shear flow

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 variation with domain confinement depending on the values of electrical permittivity ratio of the droplet and the surrounding fluid. For a leaky-dielectric system, presence of small conductivity further alters the deformation characteristic and it is happened that, at low electric field strength, the deformation increases with confinement monotonically. On contrary, deformation parameter shows non-monotonic variation with the domain confinement at higher electric field strength. Furthermore, in confined domain, the transient evolution of the deformation parameter is also markedly altered by the electric field strength in terms of steady state value of the deformation parameter and steady state time. Finally, the present analysis shows that the domain confinement significantly augment the deformation parameter in presence of electric field that leads to possible droplet break up phenomenon. From the present study, it is worthy to mention that domain confinement can be used to modulate the droplet morphology that has potential applications in modern-days droplet-based micro-fluidic devices.Comment: 28 pages, 12 figure

Uniform electric field induced lateral migration of a sedimenting drop

We investigate the motion of a sedimenting spherical drop in the presence of an applied uniform electric field in an otherwise arbitrary direction in the limit of low surface charge convection. We analytically solve the electric potential in and around the leaky dielectric drop, and solve for the Stokesian velocity and pressure fields. We obtain the drop velocity through perturbations in powers of the electric Reynolds number which signifies the importance of the charge relaxation time scale as compared to the convective time scale. We show that in the presence of electric field either in the sedimenting direction or orthogonal to it, there is a change in the drop velocity only in the direction of sedimentation due to an asymmetric charge distribution in the same direction. However, in the presence of an electric field applied in both the directions, and depending on the permittivities and conductivities of the two fluids, we obtain a non-intuitive lateral migration of drop in addition to the buoyancy driven sedimentation. These dynamical features can be effectively used for manipulating drops in a controlled electro-fluidic environment.Comment: 30 pages, 5 figure

Effect of Marangoni stress on the bulk rheology of a dilute emulsion of surfactant-laden deformable droplets in linear flows

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 limiting case when the surfactant transport is dominated by the surface diffusion relative to surface convection. As an example, we have used two commonly encountered bulk flows, namely, uniaxial extensional flow and simple shear flow. With the assumption of negligible inertial forces present in either of the phases, we are able to show that both the surfactant concentration on the droplet surface as well as the ratio of viscosity of the droplet phase with respect to the suspending fluid has a significant effect on the droplet deformation as well as the bulk rheology. It is seen that increase in the non-uniformity in surfactant distribution on the droplet surface results in a higher droplet deformation and a higher effective viscosity for either of linear flows considered. For the case of simple shear flow, surfactant distribution is found to have no effect on the inclination angle, however, a higher viscosity ratio predicts the droplet to be more aligned towards the direction of flow

Complex Fluid-Fluid Interface may Non Trivially Dictate Droplet Deformation in an Incipient Flow

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 with bulk flow-induced nonuniform surfactant distribution on the drop surface significantly alters drop dynamics. For the present study an asymptotic approach is used to solve the flow field under the limiting case of diffusion-dominated-surfactant transport. Assuming the surfactants to be bulk-insoluble and negligible inertia to be present in fluid flow, it is shown that presence of interfacial viscosity reduces the deformation of a compound drop and enhances the stability of a dilute double emulsion. At the same time the effective viscosity of the emulsion also increases with rise in interfacial viscosity. For large values of interfacial dilatational viscosity the drop deformation is seen to increase and hence the stability of the double emulsion is questionable

Droplet migration characteristics in confined oscillatory microflows

We analyze the migration characteristics of a droplet in an oscillatory flow field in a parallel plate micro-confinement. Using phase filed formalism, we capture the dynamical evolution of the droplet over a wide range of the frequency of the imposed oscillation in the flow field, drop size relative to the channel gap, and the capillary number. The latter two factors imply the contribution of droplet deformability, commonly considered in the study of droplet migration under steady shear flow conditions. We show that the imposed oscillation brings in additional time complexity in the droplet movement, realized through temporally varying drop-shape, flow direction and the inertial response of the droplet. As a consequence, we observe a spatially complicated pathway of the droplet along the transverse direction, in sharp contrast to the smooth migration under a similar yet steady shear flow condition. Intuitively, the longitudinal component of the droplet movement is in tandem with the flow continuity and evolves with time at the same frequency as that of the imposed oscillation, although, with an amplitude decreasing with the frequency. The time complexity of the transverse component of the movement pattern, however, cannot by rationalized through such intuitive arguments. Towards bringing out the underlying physics, we further endeavor in a reciprocal identity based analysis. Following this approach, we unveil the time complexities of the droplet movement, which appear to be sufficient to rationalize the complex movement patterns observed through the comprehensive simulation studies. These results can be of profound importance in designing droplet based microfluidic systems in an oscillatory flow environment.Comment: 25 pages, 8 figure

Cross-stream migration of a surfactant-laden deformable droplet in a Poiseuille flow

The motion of a viscous deformable droplet suspended in an unbounded Poiseuille flow in the presence of bulk-insoluble surfactants is studied analytically. Assuming the convective transport of fluid and heat to be negligible, we perform a small-deformation perturbation analysis to obtain the droplet migration velocity. The droplet dynamics strongly depends on the distribution of surfactants along the droplet interface, which is governed by the relative strength of convective transport of surfactants as compared with the diffusive transport of surfactants. The present study is focused on the following two limits: (i) when the surfactant transport is dominated by surface diffusion, and (ii) when the surfactant transport is dominated by surface convection. In the first limiting case, it is seen that the axial velocity of the droplet decreases with increase in the advection of the surfactants along the surface. The variation of cross-stream migration velocity, on the other hand, is analyzed over three different regimes based on the ratio of the viscosity of the droplet phase to that of the carrier phase. In the first regime the migration velocity decreases with increase in surface advection of the surfactants although there is no change in direction of droplet migration. For the second regime, the direction of the cross-stream migration of the droplet changes depending on different parameters. In the third regime, the migration velocity is merely affected by any change in the surfactant distribution. For the other limit of higher surface advection in comparison to surface diffusion of the surfactants, the axial velocity of the droplet is found to be independent of the surfactant distribution. However, the cross-stream velocity is found to decrease with increase in non-uniformity in surfactant distribution

Electrohydrodynamic migration of a surfactant-coated deformable drop in Poiseuielle flow

In this study we attempt to explore the consequences of surfactant coating on the electrohydrodynamic manipulation of a drop motion in a plane Poiseuielle flow. In addition we consider bulk insoluble surfactants and a linear dependency of the surface tension on the surfactant concentration. Subsequently a double asymptotic perturbation method is used in terms of small electric Reynolds number and capillary number in the limit of a diffusion-dominated surfactant transport mechanism. Also going beyond the widely employed axisymmetric framework, the coupled system of governing differential equations in three dimensions are then solved by adopting the `generalized Lamb solution technique'. The expressions of key variables suggest that the flow curvature of the external flow, the electric field effects and the surfactant effects are coupled in a non-trivial manner, well beyond a linear superposition. A careful investigation shows that surfactant-induced Marangoni stresses interacts with the electrohydrodynamic stresses in a highly coupled fashion. Owing to this, under different combinations of electrical conductivity and permittivity ratios, the Mason number and the applied electric field direction, the surfactants affect differently on the longitudinal as well as cross-stream migration velocity of the drop. The present results may be of utmost importance in providing a deep insight to the underlying complex physical mechanisms. Most importantly the ability of surfactants in selectively controlling the drop motion in different directions, makes them suitable for achieving a new degree of freedom in the electrical actuation of droplets in the microfluidic devices

Electric field-induced droplet deflection in microconfined flow

The deflection of liquid droplet driven through a liquid medium under the combined action of transverse electric field and pressure driven flow has been studied in the present analysis. The present experimental and numerical analysis identifies the domain confinement as a key parameter for transverse migration of the droplets in the presence of a transverse electric field. Notably, the droplet migrates at a faster rate in highly confined domain. The present analysis also illustrates that the droplet can migrate toward the wall electrode or centerline depending on the physical and electrical properties of the system. The achieved steady state transverse position is found independent of its initial positions.Comment: 10 pages,5 figure