- Access by Xinjiang University
Dynamics of a compound droplet under the combined influence of electric field and shear flow
Phys. Rev. Fluids 6, 023603 – Published 9 February, 2021
DOI: https://doi.org/10.1103/PhysRevFluids.6.023603
Abstract
We present a numerical investigation on the dynamics of a compound droplet under the combined influence of an applied electric field and shear flow. The paper is carried out by solving the electro-hydrodynamic equations in a two-dimensional framework, and the interface is captured using a volume-of-fluid approach. Both perfect dielectric as well as leaky dielectric fluids are considered. For the case of dielectric fluids, the deformation of both the inner and outer interfaces can be modulated by either variation of the permittivity contrast between the fluids or the applied field strength. The nature of the polarization forces acting at both the interfaces can be either compressive or tensile depending on the magnitude of the permittivity ratio. The investigations for leaky dielectric fluids reveal that the ratio of electrical permittivity and conductivity between the two phases plays a critical role in deciding the magnitude of deformation and orientation of the compound droplet. The variation of charge accumulated at the interfaces modifies the behavior of the Coulombic forces thereby fundamentally altering the droplet deformation and orientation characteristics. Furthermore, it is demonstrated that the electric field can be suitably applied to engender breakup of the compound droplets.
Physics Subject Headings (PhySH)
Article Text
References (42)
- A. Utada, E. Lorenceau, D. Link, P. Kaplan, H. Stone, and D. Weitz, Monodisperse double emulsions generated from a microcapillary device, Science 308, 537 (2005).
- D. Lee and D. A. Weitz, Double emulsion-templated nanoparticle colloidosomes with selective permeability, Adv. Mater. 20, 3498 (2008).
- S.-H. Kim, H. C. Shum, J. W. Kim, J.-C. Cho, and D. A. Weitz, Multiple polymersomes for programmed release of multiple components, J. Am. Chem. Soc. 133, 15165 (2011).
- A. R. Abate, C.-H. Chen, J. J. Agresti, and D. A. Weitz, Beating Poisson encapsulation statistics using close-packed ordering, Lab Chip 9, 2628 (2009).
- A. Abate and D. Weitz, High-order multiple emulsions formed in poly (dimethylsiloxane) microfluidics, Small 5, 2030 (2009).
- M. P. Borthakur, G. Biswas, and D. Bandyopadhyay, Dynamics of drop formation from submerged orifices under the influence of electric field, Phys. Fluids 30, 122104 (2018).
- B. Nath, G. Biswas, A. Dalal, and K. C. Sahu, Cross-stream migration of drops suspended in poiseuille flow in the presence of an electric field, Phys. Rev. E 97, 063106 (2018).
- B. Nath, G. Biswas, and A. Dalal, Influence of electric field on deformation of a drop in shear flow, Phys. Fluids 31, 042102 (2019).
- O. A. Basaran, Small-scale free surface flows with breakup: Drop formation and emerging applications, AIChE J. 48, 1842 (2002).
- Y. Wu and R. L. Clark, Electrohydrodynamic atomization: a versatile process for preparing materials for biomedical applications, J. Biomater. Sci., Polym. Ed. 19, 573 (2008).
- S. Sadhal and H. Oguz, Stokes flow past compound multiphase drops: The case of completely engulfed drops/bubbles, J. Fluid Mech. 160, 511 (1985).
- E. Rushton and G. Davies, Settling of encapsulated droplets at low Reynolds numbers, Int. J. Multiphase Flow 9, 337 (1983).
- S. Kawano, A. Shirai, and S. Nagasaka, Deformations of thin liquid spherical shells in liquid-liquid-gas systems, Phys. Fluids 19, 012105 (2007).
- R. E. Johnson and S. Sadhal, Fluid mechanics of compound multiphase drops and bubbles, Annu. Rev. Fluid Mech. 17, 289 (1985).
- H. Stone and L. Leal, Breakup of concentric double emulsion droplets in linear flows, J. Fluid Mech. 211, 123 (1990).
- P. Stroeve and P. P. Varanasi, An experimental study on double emulsion drop breakup in uniform shear flow, J. Colloid Interface Sci. 99, 360 (1984).
- K. A. Smith, J. M. Ottino, and M. O. Olvera de la Cruz, Encapsulated Drop Breakup in Shear Flow, Phys. Rev. Lett. 93, 204501 (2004).
- S. Mandal, A. Bandopadhyay, and S. Chakraborty, The effect of uniform electric field on the cross-stream migration of a drop in plane poiseuille flow, J. Fluid Mech. 809, 726 (2016).
- S. Sadhal et al., Growth and collapse of translating compound multiphase drops: Analysis of fluid mechanics and heat transfer, J. Fluid Mech. 179, 105 (1987).
- P. Gao and J. J. Feng, Spreading and breakup of a compound drop on a partially wetting substrate, J. Fluid Mech. 682, 415 (2011).
- M. P. Borthakur, G. Biswas, and D. Bandyopadhyay, Dynamics of deformation and pinch-off of a migrating compound droplet in a tube, Phys. Rev. E 97, 043112 (2018).
- Y. Chen, X. Liu, and M. Shi, Hydrodynamics of double emulsion droplet in shear flow, Appl. Phys. Lett. 102, 051609 (2013).
- Y. Chen, X. Liu, and Y. Zhao, Deformation dynamics of double emulsion droplet under shear, Appl. Phys. Lett. 106, 141601 (2015).
- L. Zhu and F. Gallaire, Bifurcation Dynamics of a Particle-Encapsulating Droplet in Shear Flow, Phys. Rev. Lett. 119, 064502 (2017).
- H. Hua, J. Shin, and J. Kim, Dynamics of a compound droplet in shear flow, Int. J. Heat Fluid Flow 50, 63 (2014).
- T. V. Vu, L. V. Vu, B. D. Pham, and Q. H. Luu, Numerical investigation of dynamic behavior of a compound drop in shear flow, J. Mech. Sci. Technol. 32, 2111 (2018).
- J.-W. Ha and S.-M. Yang, Fluid dynamics of a double emulsion droplet in an electric field, Phys. Fluids 11, 1029 (1999).
- A. Behjatian and A. Esmaeeli, Electrohydrodynamics of a compound drop, Phys. Rev. E 88, 033012 (2013).
- A. Behjatian and A. Esmaeeli, Transient electrohydrodynamics of compound drops, Acta Mech. 226, 2581 (2015).
- P. Soni, V. A. Juvekar, and V. M. Naik, Investigation on dynamics of double emulsion droplet in a uniform electric field, J. Electrost. 71, 471 (2013).
- M. S. Abbasi, R. Song, J. Kim, and J. Lee, Electro-hydrodynamic behavior and interface instability of double emulsion droplets under high electric field, J. Electrost. 85, 11 (2017).
- M. P. Borthakur, G. Biswas, and D. Bandyopadhyay, Formation of liquid drops at an orifice and dynamics of pinch-off in liquid jets, Phys. Rev. E 96, 013115 (2017).
- J. Brackbill, D. B. Kothe, and C. Zemach, A continuum method for modeling surface tension, J. Comput. Phys. 100, 335 (1992).
- S. Popinet, A quadtree-adaptive multigrid solver for the Serre-Green-Naghdi equations, J. Comput. Phys. 302, 336 (2015).
- S. Popinet, Gerris: A tree-based adaptive solver for the incompressible Euler equations in complex geometries, J. Comput. Phys. 190, 572 (2003).
- M. Balla, M. K. Tripathi, and K. C. Sahu, A numerical study of a hollow water droplet falling in air, Theor. Comput. Fluid Dyn. 34, 133 (2020).
- G. I. Taylor, Studies in electrohydrodynamics. I. The circulation produced in a drop by an electric field, Proc. R. Soc. A 291, 159 (1966).
- P. H. Rhodes, R. S. Snyder, and G. O. Roberts, Electrohydrodynamic distortion of sample streams in continuous flow electrophoresis, J. Colloid Interface Sci. 129, 78 (1989).
- B. Nath, M. P. Borthakur, and G. Biswas, Electric field induced dynamics of viscoplastic droplets in shear flow, Phys. Fluids 32, 092110 (2020).
- S. Santra, S. Mandal, and S. Chakraborty, Confinement effect on electrically induced dynamics of a droplet in shear flow, Phys. Rev. E 100, 033101 (2019).
- M. P. Borthakur, G. Biswas, D. Bandyopadhyay, and K. C. Sahu, Dynamics of an arched liquid jet under the influence of gravity, Eur. J. Mech. B/Fluids 74, 1 (2019).
- M. S. Abbasi, R. Song, S. Cho, and J. Lee, Electro-hydrodynamics of emulsion droplets: Physical insights to applications, Micromachines 11, 942 (2020).