Shubhadeep Mandal

Uniform electric-field-induced lateral migration of a sedimenting drop

We investigate the motion of a sedimenting drop in the presence of an electric field in an arbitrary direction, otherwise uniform, in the limit of small interface deformation and 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 correction in drop velocity due to shape deformation and surface-charge convection considering small capillary number and small electric Reynolds number which signifies the importance of charge convection at the drop surface. We show that tilt angle, which quantifies the angle of inclination of the applied electric field with respect to the direction of gravity, has a significant effect on the magnitude and direction of the drop velocity. When the electric field is tilted with respect to the direction of gravity, we obtain a non-intuitive lateral motion of the drop in addition to the buoyancy-driven sedimentation. Both the charge convection and shape deformation yield this lateral migration of the drop. Our analysis indicates that depending on the magnitude of the tilt angle, conductivity and permittivity ratios, the direction of the sedimenting drop can be controlled effectively. Our experimental investigation further confirms the presence of lateral migration of the drop in the presence of a tilted electric field, which is in support of the essential findings from the analytical formalism.

Dielectrophoresis of a surfactant-laden viscous drop

The dielectrophoresis of a surfactant-laden viscous drop in the presence of non-uniform DC electric field is investigated analytically and numerically. Considering the presence of bulk-insoluble surfactants at the drop interface, we first perform asymptotic solution for both low and high surface Peclet numbers, where the surface Peclet number signifies the strength of surface convection of surfactants as compared to the diffusion at the drop interface. Neglecting fluid inertia and interfacial charge convection effects, we obtain explicit expression for dielectrophoretic drop velocity for low and high Peclet numbers by assuming small deviation of drop shape from sphericity and small deviation of surfactant concentration from the equilibrium uniform distribution. We then depict a numerical solution, assuming spherical drop, for arbitrary values of Peclet number. Our analyses demonstrate that the asymptotic solution shows excellent agreement with the numerical solution in the limiting conditions of low and h...

Migration of a surfactant-laden droplet in non-isothermal Poiseuille flow

The motion of a surfactant-laden viscous droplet in the presence of non-isothermal Poiseuille flow is studied analytically and numerically. Specifically, the focus of the present study is on the role of interfacial Marangoni stress generated due to imposed temperature gradient and non-uniform distribution of bulk-insoluble surfactants towards dictating the velocity and direction of motion of the droplet when the background flow is Poiseuille. Assuming the thermal convection and fluid inertia to be negligible, we obtain the explicit expression for steady velocity of a non-deformable spherical droplet when the droplet is located at the centerline of the imposed unbounded Poiseuille flow and encountering a linearly varying temperature field. Under these assumptions, the interfacial transport of surfactants is governed by the surface Peclet number which represents the relative strength of the advective transport of surfactant molecules over the diffusive transport. We obtain analytical solution for small and ...

The effect of surface charge convection and shape deformation on the settling velocity of drops in nonuniform electric field

The electrohydrodynamic settling of a leaky dielectric drop suspended in another leaky dielectric medium of unbounded extent in the combined presence of gravity and a nonuniform (combination of uniform and quadrupole) electric field is investigated theoretically in the Stokes flow limit. The present study incorporates both the effects of surface charge convection and shape deformation on the drop settling speed. The drop settling speed in the presence of an electric field is governed by three dimensionless groups: (i) capillary number Ca (the ratio of viscous to capillary stresses), (ii) electric Reynolds number ReE (the ratio of charge relaxation to convection time scales), and (iii) Masson number M (the ratio of electric to viscous stresses). Depending on the material properties of the drop and suspending medium, the strength of the applied electric field, and the drop radius, the following two different kinds of physical systems are identified for which asymptotic solutions for the settling velocity is...

Effect of surface charge convection and shape deformation on the dielectrophoretic motion of a liquid drop

The dielectrophoretic motion and shape deformation of a Newtonian liquid drop in an otherwise quiescent Newtonian liquid medium in the presence of an axisymmetric nonuniform dc electric field consisting of uniform and quadrupole components is investigated. The theory put forward by Feng [J. Q. Feng, Phys. Rev. E 54, 4438 (1996)10.1103/PhysRevE.54.4438] is generalized by incorporating the following two nonlinear effects-surface charge convection and shape deformation-towards determining the drop velocity. This two-way coupled moving boundary problem is solved analytically by considering small values of electric Reynolds number (ratio of charge relaxation time scale to the convection time scale) and electric capillary number (ratio of electrical stress to the surface tension) under the framework of the leaky dielectric model. We focus on investigating the effects of charge convection and shape deformation for different drop-medium combinations. A perfectly conducting drop suspended in a leaky (or perfectly) dielectric medium always deforms to a prolate shape and this kind of shape deformation always augments the dielectrophoretic drop velocity. For a perfectly dielectric drop suspended in a perfectly dielectric medium, the shape deformation leads to either increase (for prolate shape) or decrease (for oblate shape) in the dielectrophoretic drop velocity. Both surface charge convection and shape deformation affect the drop motion for leaky dielectric drops. The combined effect of these can significantly increase or decrease the dielectrophoretic drop velocity depending on the electrohydrodynamic properties of both the liquids and the relative strength of the electric Reynolds number and electric capillary number. Finally, comparison with the existing experiments reveals better agreement with the present theory.

Influence of interfacial viscosity on the dielectrophoresis of drops

The dielectrophoresis of a Newtonian uncharged drop in the presence of an axisymmetric nonuniform DC electric field is studied analytically. The present study is focused on the effects of interfacial viscosities on the dielectrophoretic motion and shape deformation of an isolated suspended drop. The interfacial viscosities generate surface-excess viscous stress which is modeled as a two-dimensional Newtonian fluid which obeys the Boussinesq-Scriven constitutive law with constant values of interfacial tension, interfacial shear, and dilatational viscosities. In the regime of small drop deformation, we have obtained analytical solution for the drop velocity and deformed shape by neglecting surface charge convection and fluid inertia. Our study demonstrates that the drop velocity is independent of the interfacial shear viscosity, while the interfacial dilatational viscosity strongly affects the drop velocity. The interfacial viscous effects always retard the dielectrophoretic motion of a perfectly conducting...

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.

Effect of temperature gradient on the cross-stream migration of a surfactant-laden droplet in Poiseuille flow

The motion of a viscous droplet in unbounded Poiseuille flow under the combined influence of bulk-insoluble surfactant and linearly varying temperature field aligned in the direction of imposed flow is studied analytically. Neglecting fluid inertia, thermal convection and shape deformation, asymptotic analysis is performed to obtain the velocity of a force-free surfactant-laden droplet. The droplet speed and direction of motion are strongly influenced by the interfacial transport of surfactant, which is governed by surface Peclet number. The present study is focused on the following two limiting situations of surfactant transport: (i) surface-diffusion-dominated surfactant transport considering small surface Peclet number, and (ii) surface-convection-dominated surfactant transport considering high surface Peclet number. Thermocapillary-induced Marangoni stress, the strength of which relative to viscous stress is represented by the thermal Marangoni number, has a strong influence on the distribution of surfactant on the droplet surface. The present study shows that the motion of a surfactant-laden droplet in the combined presence of temperature and imposed Poiseuille flow cannot be obtained by a simple superposition of the following two independent results: migration of a surfactant-free droplet in a temperature gradient, and the motion of a surfactant-laden droplet in a Poiseuille flow. The temperature field not only affects the axial velocity of the droplet, but also has a non-trivial effect on the cross-stream velocity of the droplet in spite of the fact that the temperature gradient is aligned with the Poiseuille flow direction. When the imposed temperature increases in the direction of the Poiseuille flow, the droplet migrates towards the flow centreline. The magnitude of both axial and cross-stream velocity components increases with the thermal Marangoni number. However, when the imposed temperature decreases in the direction of the Poiseuille flow, the magnitude of both axial and cross-stream velocity components may increase or decrease with the thermal Marangoni number. Most interestingly, the droplet moves either towards the flow centreline or away from it. The present study shows a critical value of the thermal Marangoni number beyond which the droplet moves away from the flow centreline which is in sharp contrast to the motion of a surfactant-laden droplet in isothermal flow, for which the droplet always moves towards the flow centreline. Interestingly, we show that the above picture may become significantly altered in the case where the droplet is not a neutrally buoyant one. When the droplet is less dense than the suspending medium, the presence of gravity in the direction of the Poiseuille flow can lead to cross-stream motion of the droplet away from the flow centreline even when the temperature increases in the direction of the Poiseuille flow. These results may bear far-reaching consequences in various emulsification techniques in microfluidic devices, as well as in biomolecule synthesis, vesicle dynamics, single-cell analysis and nanoparticle synthesis.

Effect of nonuniform electric field on the electrohydrodynamic motion of a drop in Poiseuille flow

The effect of a nonuniform electric field on the electrohydrodynamic motion of a leaky dielectric suspended drop in the presence of background Poiseuille flow is investigated analytically. Considering the nonuniform electric field to be a linear combination of uniform and quadrupole fields, the velocity of a force-free drop positioned at the flow centerline is obtained. The drop velocity is strongly influenced by the surface charge distribution and drop shape. In the Stokes flow limit, we employ an asymptotic method considering weak surface charge convection and small shape deformation. The present study shows the importance of type of nonuniform electric field (converging or diverging in the direction of the Poiseuille flow), strength of the electric field relative to the Poiseuille flow, and material property ratios on the magnitude and direction of drop motion in the presence of flow curvature. In the presence of a nonuniform electric field, the flow curvature can increase or decrease the drop velocity...

Droplet migration characteristics in confined oscillatory microflows.

We analyze the migration characteristics of a droplet in an oscillatory flow field in a parallel plate microconfinement. Using phase field 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 an 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 be 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.