“…We observed that the truncation limit N needs to be increased with the eccentricity ( e ) and radius ratio ( k ) to retain the same numerical accuracy. A similar observation was reported by Jadhav & Ghosh (2021) in the context of a different physical problem of thermo-capillary migration. We verified that, for k = 0.1, the limit N = 20 can produce accurate results for eccentricities e ≤ 0.5.…”
Section: Theorysupporting
confidence: 87%
“…Notably, the small eccentricity limit for the validity of the semi-analytical solution is pertinent only for the electrostatic problem and not for the hydrodynamic problem. The latter becomes the case since z = 0 does not conform to a hydrodynamic confinement, so that the hydrodynamic aspects remain akin to unbounded flows (Gouz & Sadhal 1989; Mandal, Ghosh & Chakraborty 2016 c ; Jadhav & Ghosh 2021; Boruah et al. 2022).…”
Eccentric compound drops, which are ubiquitous in many naturally inspired and engineering systems, can migrate under the sole presence of a uniform electric field, unlike the case of isolated single drops. Here, we report the migration of eccentric compound drops under a uniform electric field, imposed parallel to the line of centres of the constituting drops, by developing an approximate analytical model that applies to low Reynolds number limits under negligible droplet deformation, following axisymmetric considerations. In contrast to the sole influence of the electrohydrodynamic forces that has thus far been established to be emphatic for the eccentric configuration, here we report the additional effects induced by the dielectrophoretic forces to result in decisive manipulation in the drop migration. We show that the relative velocity between the inner and outer drops, which is a function of the eccentricity itself, dictates the dynamical evolution of the eccentricity variation under the competing electrohydrodynamic and dielectrophoretic interactions. This brings out four distinct regimes of the migration characteristics of the two drops based on their relative electro-physical properties. Our results reveal that an increase in eccentricity and the size ratio of the inner and outer droplets may induce monotonic or non-monotonic variation in the drop velocities, depending on the operating regime. We show how the interplay of various properties holds the control of selectively increasing or suppressing the eccentricity with time. These findings open up various avenues of electrically manipulative motion of encapsulated fluidic phases in various applications encompassing engineering and biology.
“…We observed that the truncation limit N needs to be increased with the eccentricity ( e ) and radius ratio ( k ) to retain the same numerical accuracy. A similar observation was reported by Jadhav & Ghosh (2021) in the context of a different physical problem of thermo-capillary migration. We verified that, for k = 0.1, the limit N = 20 can produce accurate results for eccentricities e ≤ 0.5.…”
Section: Theorysupporting
confidence: 87%
“…Notably, the small eccentricity limit for the validity of the semi-analytical solution is pertinent only for the electrostatic problem and not for the hydrodynamic problem. The latter becomes the case since z = 0 does not conform to a hydrodynamic confinement, so that the hydrodynamic aspects remain akin to unbounded flows (Gouz & Sadhal 1989; Mandal, Ghosh & Chakraborty 2016 c ; Jadhav & Ghosh 2021; Boruah et al. 2022).…”
Eccentric compound drops, which are ubiquitous in many naturally inspired and engineering systems, can migrate under the sole presence of a uniform electric field, unlike the case of isolated single drops. Here, we report the migration of eccentric compound drops under a uniform electric field, imposed parallel to the line of centres of the constituting drops, by developing an approximate analytical model that applies to low Reynolds number limits under negligible droplet deformation, following axisymmetric considerations. In contrast to the sole influence of the electrohydrodynamic forces that has thus far been established to be emphatic for the eccentric configuration, here we report the additional effects induced by the dielectrophoretic forces to result in decisive manipulation in the drop migration. We show that the relative velocity between the inner and outer drops, which is a function of the eccentricity itself, dictates the dynamical evolution of the eccentricity variation under the competing electrohydrodynamic and dielectrophoretic interactions. This brings out four distinct regimes of the migration characteristics of the two drops based on their relative electro-physical properties. Our results reveal that an increase in eccentricity and the size ratio of the inner and outer droplets may induce monotonic or non-monotonic variation in the drop velocities, depending on the operating regime. We show how the interplay of various properties holds the control of selectively increasing or suppressing the eccentricity with time. These findings open up various avenues of electrically manipulative motion of encapsulated fluidic phases in various applications encompassing engineering and biology.
“…Thereafter, they are solved semi-analytically using the procedure outlined in Boruah et al. (2022) and Jadhav & Ghosh (2021 a ), which is not repeated herein for the sake of brevity. This results in unknown coefficients which are then utilized along with force balance conditions to determine the velocities.…”
Section: Problem Formulationmentioning
confidence: 99%
“…From figure 12, we determine that the aforementioned condition is satisfied when the dimensionless time ranges from 450 to 850. Beyond this, the eccentric theory (Jadav & Ghosh 2021 a , b ) needs to be applied. Figure 12.Temporal variation of eccentricity for various K in case of concentric compound drop.…”
Electrohydrodynamic sedimentation of simple drops has been a topic well-studied by researchers. However, electrohydrodynamic sedimentation of a compound drop would be critically influenced by the density of the involved phases and this has hitherto remained unaddressed. Herein, we develop a semi-analytical model for an eccentric compound drop settling under the action of gravity and an electric field using bispherical coordinates. The sedimentation velocity of the two drops (shell and core) is determined, and the same is applied to capture the influence of concomitant physical, hydrodynamic and electric properties on compound droplet sedimentation. The findings indicate that the compound drop may either sediment or de-sediment depending on the amount of eccentricity and its interplay with electrohydrodynamic parameters. Thereafter, the critical limit of eccentricity and time within which similar results are furnished by concentric and eccentric configurations is determined. It is found that, based on the property ratios, the eccentricity remains lower than 0.1 up to a non-dimensional time range of the order of 102–103, within which both the configurations can furnish a similar solution.
“…Tsukada et al 45 investigated how the presence of the core affects shell deformation and compared it to single droplet deformation in a DC electric field due to differences in physical properties within the droplet. Jadhav and Ghosh 46 found that the position of the inner core relative to the outer drop center can cause the inner drop to shift between prolate and oblate shapes. Inner drop deformation increases with eccentricity, while the outer drop remains minimally deformed even at high capillary numbers.…”
In this study of a compound droplet subjected to alternating current (AC) and direct current (DC) superposed (AC/DC) electric fields, both core and shell deformations oscillate, albeit with reduced amplitude compared to solely alternating current electric fields. As surface tension relaxes, periodic cyclic deformation ensues, with mean deformation amplifying alongside electric field amplitude. Concurrently, normal and tangential Maxwell stresses escalate with amplitude, thus augmenting interfacial surface velocities. Manipulating the offset ratio of alternating and direct current superposed electric field modulates mean deformations. Across low frequencies, stable deformation remains constant, yet a delayed onset characterizes higher frequencies. The presence of a core affects the electrohydrodynamics of the compound droplet and shell deformation, thereby mitigating phase differences between cyclic deformations. Contrasting alternating current (AC)—only fields, alternating current and direct current superposed (AC/DC) electric field scenarios exhibit heightened surface charge densities and prompter stable deformation onset. Furthermore, the direct current component magnifies mean deformations while harmonizing phase disparities between core and shell deformations. This study illuminates the intricate interplay between alternating current and direct current fields on compound droplet behavior, offering profound insight with broad implications for applications necessitating precise deformations under electric fields.
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