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Electric-field-mediated morpho-dynamic evolution in drop–drop coalescence phenomena in the inertio-capillary regime

Published online by Cambridge University Press:  07 February 2023

Nalinikanta Behera Open the ORCID record for Nalinikanta Behera [Opens in a new window]  and
Suman Chakraborty Open the ORCID record for Suman Chakraborty [Opens in a new window]
Nalinikanta Behera
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India
Suman Chakraborty*
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India
*
†Email address for correspondence: suman@mech.iitkgp.ac.in
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Abstract

When two drops collide, they may either exhibit complete coalescence or selectively generate secondary drops, depending on their relative sizes and physical properties, as dictated by a decisive interplay of the viscous, capillary, inertia and gravity effects. Electric field, however, is known to induce distinctive alterations in the topological evolution of the interfaces post-collision, by influencing a two-way nonlinear coupling between electro-mechanics and fluid flow as mediated by a topologically intriguing interfacial deformation. While prior studies primarily focused on the viscous-dominated regime of the resulting electro-coalescence dynamics, several non-intuitive features of the underlying morpho-dynamic evolution over the intertio-capillary regime have thus far remained unaddressed. In this study, we computationally investigate electrically modulated coalescence dynamics along with secondary drop formation mechanisms in the inertio-capillary regime, probing the interactions of two unequal-sized drops subjected to a uniform electric field. Our results bring out an explicit mapping between the observed topological evolution as a function of the respective initial sizes of the parent drops as well as their pertinent electro-physical property ratios. These findings establish electric-field-mediated exclusive controllability of the observed topological features, as well as the critical conditions leading to the transition from partial to complete coalescence phenomena. In a coalescence cascade, an electric field is further shown to orchestrate the numbers of successive stages of coalescence before complete collapse. However, an increase of the numbers of cascade stages with the electric field strength and parent droplet size ratio is non-perpetual, and the same is demonstrated to continue until only a threshold number of cascade stages is reached. These illustrations offer significant insights into leveraging the interplay of electrical, inertial and capillary-driven interactions for controllable drop manipulation via multi-drop interactions for a variety of applications ranging from chemical processing to emulsion technology.

JFM classification

Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 956 , 10 February 2023 , A22
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

Aarts, D.G.A.L., Lekkerkerker, H.N.W., Guo, H., Wegdam, G.H. & Bonn, D. 2005 Hydrodynamics of droplet coalescence. Phys. Rev. Lett. 95, 164503.CrossRefGoogle ScholarPubMed
Abbasi, M.S., Song, R., Kim, H. & Lee, J. 2019 Multimodal breakup of a double emulsion droplet under an electric field. Soft Matt. 15, 2292–2300.CrossRefGoogle ScholarPubMed
Ahn, K., Agresti, J., Chong, H., Marquez, M. & Weitz, D.A. 2006 Electrocoalescence of drops synchronized by size-dependent flow in microfluidic channels. Appl. Phys. Lett. 88, 264105.CrossRefGoogle Scholar
Anand, V., Roy, S., Naik, V.M., Juvekar, V.A. & Thaokar, R.M. 2019 Electrocoalescence of a pair of conducting drops in an insulating oil. J. Fluid Mech. 859, 839–850.CrossRefGoogle Scholar
Anna, S.L. 2016 Droplets and bubbles in microfluidic devices. Annu. Rev. Fluid Mech. 48, 285–309.CrossRefGoogle Scholar
Baygents, J.C., Rivette, N.J. & Stone, H.A. 1998 Electrohydrodynamic deformation and interaction of drop pairs. J. Fluid Mech. 368, 359–375.CrossRefGoogle Scholar
Behera, N. & Chakraborty, S. 2020 Effect of charge convection on gravitational settling of drop in uniform electric field. Phys. Fluids 32, 112013.CrossRefGoogle Scholar
Behera, N. & Chakraborty, S. 2022 Electrically modulated relaxation dynamics of pre-stretched droplets post switched-off uniaxial extensional flow. Soft Matt. 18, 3678–3697.CrossRefGoogle ScholarPubMed
Behera, N., Mandal, S. & Chakraborty, S. 2019 Electrohydrodynamic settling of drop in uniform electric field: beyond Stokes flow regime. J. Fluid Mech. 881, 498–523.CrossRefGoogle Scholar
Bell, J.B., Colella, P. & Glaz, H.M. 1989 A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys. 85, 257–283.CrossRefGoogle Scholar
Bird, J.C., Ristenpart, W.D., Belmonte, A. & Stone, H.A. 2009 Critical angle for electrically driven coalescence of two conical droplets. Phys. Rev. Lett. 103, 164502.CrossRefGoogle ScholarPubMed
Blanchette, F. & Bigioni, T.P. 2006 Partial coalescence of drops at liquid interfaces. Nat. Phys. 2, 254–257.CrossRefGoogle Scholar
Blanchette, F. & Bigioni, T.P. 2009 Dynamics of drop coalescence at fluid interfaces. J. Fluid Mech. 620, 333–352.CrossRefGoogle Scholar
Brown, D.L., Cortez, R. & Minion, M.L. 2001 Accurate projection methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 168, 464–499.CrossRefGoogle Scholar
Casas, P.S., Garzon, M., Gray, L.J. & Sethian, J.A. 2019 Numerical study on electrohydrodynamic multiple droplet interactions. Phys. Rev. E 100, 063111.CrossRefGoogle Scholar
Charin, R.M., Chaves, G.M.T., Kashefi, K., Alves, R.P., Tavares, F.W. & Nele, M. 2017 Crude oil electrical conductivity measurements at high temperatures: introduction of apparatus and methodology. Energy Fuels 31, 3669–3674.CrossRefGoogle Scholar
Chen, X., Mandre, S. & Feng, J.J. 2006 Partial coalescence between a drop and a liquid-liquid interface. Phys. Fluids 18, 051705.CrossRefGoogle Scholar
Chorin, A.J. 1968 Numerical solution of the Navier-Stokes equations. Math. Comput. 22, 745.CrossRefGoogle Scholar
Cong, H., Qian, L., Wang, Y. & Lin, J. 2020 Numerical simulation of the collision behaviors of binary unequal-sized droplets at high Weber number. Phys. Fluids 32, 103307.CrossRefGoogle Scholar
Corach, J., Sorichetti, P.A. & Romano, S.D. 2012 Electrical properties of mixtures of fatty acid methyl esters from different vegetable oils. Intl J. Hydrogen Energy 37, 14735–14739.CrossRefGoogle Scholar
Coronado, D. & Wenske, J. 2018 Monitoring the oil of wind-turbine gearboxes: main degradation indicators and detection methods. Machines 6 (2), 25.CrossRefGoogle Scholar
Das, S.K., Dalal, A. & Tomar, G. 2021 Electrohydrodynamic-induced interactions between droplets. J. Fluid Mech. 915, A88.CrossRefGoogle Scholar
Deka, H., Biswas, G., Chakraborty, S. & Dalal, A. 2019 Coalescence dynamics of unequal sized drops. Phys. Fluids 31, 012105.CrossRefGoogle Scholar
Dhar, J., Mukherjee, S., Raj M, K. & Chakraborty, S. 2019 Universal oscillatory dynamics in capillary filling. Europhys. Lett. 125, 14003.CrossRefGoogle Scholar
Duchemin, L., Eggers, J. & Josserand, C. 2003 Inviscid coalescence of drops. J. Fluid Mech. 487, 167–178.CrossRefGoogle Scholar
Eggers, J., Lister, J.R. & Stone, H.A. 1999 Coalescence of liquid drops. J. Fluid Mech. 401, 293–310.CrossRefGoogle Scholar
Eow, J.S., Ghadiri, M., Sharif, A.O. & Williams, T.J. 2001 Electrostatic enhancement of coalescence of water droplets in oil: a review of the current understanding. Chem. Engng J. 84, 173–192.CrossRefGoogle Scholar
Esmaeeli, A. & Behjatian, A. 2020 Transient electrohydrodynamics of a liquid drop at finite Reynolds numbers. J. Fluid Mech. 893, A26.CrossRefGoogle Scholar
Esmaeeli, A. & Sharifi, P. 2011 Transient electrohydrodynamics of a liquid drop. Phys. Rev. E 84, 036308.CrossRefGoogle ScholarPubMed
Francois, M.M., Cummins, S.J., Dendy, E.D., Kothe, D.B., Sicilian, J.M. & Williams, M.W. 2006 A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework. J. Comput. Phys. 213, 141–173.CrossRefGoogle Scholar
Garzon, M., Gray, L.J. & Sethian, J.A. 2018 Electrohydrodynamic coalescence of droplets using an embedded potential flow model. Phys. Rev. E 97, 033112.CrossRefGoogle ScholarPubMed
Gawande, N., Mayya, Y.S. & Thaokar, R. 2020 Jet and progeny formation in the Rayleigh breakup of a charged viscous drop. J. Fluid Mech. 884, A31.CrossRefGoogle Scholar
Ha, J. & Yang, S. 2000 Deformation and breakup of Newtonian and non-Newtonian conducting drops in an electric field. J. Fluid Mech. 405, 131–156.CrossRefGoogle Scholar
Herrada, M.A., López-Herrera, J.M., Gañán-Calvo, A.M., Vega, E.J., Montanero, J.M. & Popinet, S. 2012 Numerical simulation of electrospray in the cone-jet mode. Phys. Rev. E 86, 026305.CrossRefGoogle ScholarPubMed
Higuera, F.J. 2006 Injection of bubbles in a quiescent inviscid liquid under a uniform electric field. J. Fluid Mech. 568, 203.CrossRefGoogle Scholar
Hua, J., Lim, L.K. & Wang, C.-H. 2008 Numerical simulation of deformation/motion of a drop suspended in viscous liquids under influence of steady electric fields. Phys. Fluids 20, 113302.CrossRefGoogle Scholar
Johnson, R.L. 1968 Effect of an electric field on boiling heat transfer. AIAA J. 6, 1456–1460.CrossRefGoogle Scholar
Kahali, T., Santra, S. & Chakraborty, S. 2022 Electrically modulated cross-stream migration of a compound drop in micro-confined oscillatory flow. Phys. Fluids 34, 122015.CrossRefGoogle Scholar
Kahkeshani, S. & Di Carlo, D. 2016 Drop formation using ferrofluids driven magnetically in a step emulsification device. Lab on a Chip 16, 2474–2480.CrossRefGoogle Scholar
Kamsali, N., Prasad, B.S.N. & Datta, J. 2009 Atmospheric electrical conductivity measurements and modeling for application to air pollution studies. Adv. Space Res. 44, 1067–1078.CrossRefGoogle Scholar
Karyappa, R.B., Deshmukh, S.D. & Thaokar, R.M. 2014 Breakup of a conducting drop in a uniform electric field. J. Fluid Mech. 754, 550–589.CrossRefGoogle Scholar
Karyappa, R.B., Naik, A.V. & Thaokar, R.M. 2016 Electroemulsification in a uniform electric field. Langmuir 32 (1), 46–54.CrossRefGoogle Scholar
Kavehpour, H.P. 2015 Coalescence of drops. Annu. Rev. Fluid Mech. 47, 245–268.CrossRefGoogle Scholar
Lac, E. & Homsy, G.M. 2007 Axisymmetric deformation and stability of a viscous drop in a steady electric field. J. Fluid Mech. 590, 239–264.CrossRefGoogle Scholar
Lanauze, J.A., Walker, L.M. & Khair, A.S. 2015 Nonlinear electrohydrodynamics of slightly deformed oblate drops. J. Fluid Mech. 774, 245–266.CrossRefGoogle Scholar
Li, B., Wang, Z., Vivacqua, V. & Wang, Z. 2020 Drop-interface electrocoalescence mode transition under a direct current electric field. Chem. Engng Sci. 213, 115360.CrossRefGoogle Scholar
López-Herrera, J.M., Popinet, S. & Herrada, M.A. 2011 A charge-conservative approach for simulating electrohydrodynamic two-phase flows using volume-of-fluid. J. Comput. Phys. 230, 1939–1955.CrossRefGoogle Scholar
Lu, X., Xie, S., Zhang, J., Lei, Q. & Fang, W. 2020 Density, viscosity and electrical conductivity of alcohol solutions of 2,2-diethyl-1,1,3,3-tetramethylguanidinium bis(trifluoromethylsulfonyl)imide. J. Chem. Thermodyn. 151, 106241.CrossRefGoogle Scholar
Luo, X., Yin, H., Yan, H., Huang, X., Yang, D. & He, L. 2018 The electrocoalescence behavior of surfactant-laden droplet pairs in oil under a DC electric field. Chem. Engng Sci. 191, 350–357.CrossRefGoogle Scholar
Mählmann, S. & Papageorgiou, D.T. 2009 Numerical study of electric field effects on the deformation of two-dimensional liquid drops in simple shear flow at arbitrary Reynolds number. J. Fluid Mech. 626, 367–393.CrossRefGoogle Scholar
Mandal, S., Bandopadhyay, A. & Chakraborty, S. 2016 a Effect of surface charge convection and shape deformation on the dielectrophoretic motion of a liquid drop. Phys. Rev. E 93, 043127.CrossRefGoogle ScholarPubMed
Mandal, S., Bandopadhyay, A. & Chakraborty, S. 2016 b The effect of uniform electric field on the cross-stream migration of a drop in plane Poiseuille flow. J. Fluid Mech. 809, 726–774.CrossRefGoogle Scholar
Mandal, S., Sinha, S., Bandopadhyay, A. & Chakraborty, S. 2018 Drop deformation and emulsion rheology under the combined influence of uniform electric field and linear flow. J. Fluid Mech. 841, 408–433.CrossRefGoogle Scholar
Melcher, J.R. & Taylor, G.I. 1969 Electrohydrodynamics: a review of the role of interfacial shear stresses. Annu. Rev. Fluid Mech. 1, 111–146.CrossRefGoogle Scholar
Menchaca-Rocha, A., Martínez-Dávalos, A., Núñez, R., Popinet, S. & Zaleski, S. 2001 Coalescence of liquid drops by surface tension. Phys. Rev. E 63, 046309.CrossRefGoogle ScholarPubMed
Mhatre, S., Deshmukh, S. & Thaokar, R.M. 2015 a Electrocoalescence of a drop pair. Phys. Fluids 27, 092106.CrossRefGoogle Scholar
Mhatre, S., Vivacqua, V., Ghadiri, M. & Kermani, B. 2015 b Electrostatic phase separation: a review. Chem. Engng Res. Des. 96, 177–195.CrossRefGoogle Scholar
Mousavi, S.H., Ghadiri, M. & Buckley, M. 2014 Electro-coalescence of water drops in oils under pulsatile electric fields. Chem. Engng Sci. 120, 130–142.CrossRefGoogle Scholar
Mousavichoubeh, M., Ghadiri, M. & Shariaty-Niassar, M. 2011 Electro-coalescence of an aqueous droplet at an oil–water interface. Chem. Engng Process. Process Intensif. 50, 338–344.CrossRefGoogle Scholar
Nie, Q., Ma, Q., Yang, W. & Yin, Z. 2021 Designing working diagrams for electrohydrodynamic printing. Chem. Engng Sci. 240, 116661.CrossRefGoogle Scholar
Panigrahi, D.P., Santra, S., Banuprasad, T.N., Das, S. & Chakraborty, S. 2021 Interfacial viscosity-induced suppression of lateral migration of a surfactant laden droplet in a nonisothermal Poiseuille flow. Phys. Rev. Fluids 6, 053603.CrossRefGoogle Scholar
Peng, L., Luo, Z., Zuo, Y.Y., Yan, G. & Bai, B. 2018 Pinch-off of liquid bridge during droplet coalescence under constrained condition. Chem. Engng Sci. 177, 471–480.CrossRefGoogle Scholar
Poddar, A., Mandal, S., Bandopadhyay, A. & Chakraborty, S. 2018 Sedimentation of a surfactant-laden drop under the influence of an electric field. J. Fluid Mech. 849, 277–311.CrossRefGoogle Scholar
Poddar, A., Mandal, S., Bandopadhyay, A. & Chakraborty, S. 2019 Electrical switching of a surfactant coated drop in Poiseuille flow. J. Fluid Mech. 870, 27–66.CrossRefGoogle Scholar
Popinet, S. 2003 Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys. 190, 572–600.CrossRefGoogle Scholar
Popinet, S. 2009 An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228, 5838–5866.CrossRefGoogle Scholar
Qian, J. & Law, C.K. 1997 Regimes of coalescence and separation in droplet collision. J. Fluid Mech. 331, 59–80.CrossRefGoogle Scholar
Ray, B., Biswas, G. & Sharma, A. 2010 Generation of secondary droplets in coalescence of a drop at a liquid-liquid interface. J. Fluid Mech. 655, 72–104.CrossRefGoogle Scholar
Rein, M. 1993 Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn. Res. 12, 61–93.CrossRefGoogle Scholar
Ricci, E., Sangiorgi, R. & Passerone, A. 1986 Density and surface tension of dioctylphthalate, silicone oil and their solutions. Surf. Coatings Technol. 28, 215–223.CrossRefGoogle Scholar
Ristenpart, W.D., Bird, J.C., Belmonte, A., Dollar, F. & Stone, H.A. 2009 Non-coalescence of oppositely charged drops. Nature 461, 377–380.CrossRefGoogle ScholarPubMed
Rowghanian, P., Meinhart, C.D. & Campàs, O. 2016 Dynamics of ferrofluid drop deformations under spatially uniform magnetic fields. J. Fluid Mech. 802, 245–262.CrossRefGoogle Scholar
Salipante, P.F. & Vlahovska, P.M. 2010 Electrohydrodynamics of drops in strong uniform dc electric fields. Phys. Fluids 22, 112110.CrossRefGoogle Scholar
Sánchez Barea, J., Lee, J. & Kang, D.-K. 2019 Recent advances in droplet-based microfluidic technologies for biochemistry and molecular biology. Micromachines 10 (6), 412.CrossRefGoogle ScholarPubMed
Santra, S. & Chakraborty, S. 2021 Steady axial electric field may lead to controllable cross-stream migration of droplets in confined oscillatory microflows. J. Fluid Mech. 907, A8.CrossRefGoogle Scholar
Santra, S., Mandal, S. & Chakraborty, S. 2018 Electrohydrodynamics of confined two-dimensional liquid droplets in uniform electric field. Phys. Fluids 30, 062003.CrossRefGoogle Scholar
Santra, S., Sen, D., Das, S. & Chakraborty, S. 2019 Electrohydrodynamic interaction between droplet pairs in a confined shear flow. Phys. Fluids 31, 032005.CrossRefGoogle Scholar
Saville, D.A. 1997 Electrohydrodynamics: the Taylor-Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29, 27–64.CrossRefGoogle Scholar
Simon, J.C., Sapozhnikov, O.A., Khokhlova, V.A., Crum, L.A. & Bailey, M.R. 2015 Ultrasonic atomization of liquids in drop-chain acoustic fountains. J. Fluid Mech. 766, 129–146.CrossRefGoogle ScholarPubMed
Su, Z.-G., Zhang, Y.-M., Luo, K. & Yi, H.-L. 2020 Instability of electroconvection in viscoelastic fluids subjected to unipolar injection. Phys. Fluids 32, 104102.CrossRefGoogle Scholar
Tang, C., Zhang, P. & Law, C.K. 2012 Bouncing, coalescence, and separation in head-on collision of unequal-size droplets. Phys. Fluids 24, 022101.CrossRefGoogle Scholar
Taylor, G. 1966 Studies in electrohydrodynamics. I. The circulation produced in a drop by electrical field. Proc. R. Soc. Lond. A 291, 159–166.Google Scholar
Thoroddsen, S.T. & Takehara, K. 2000 The coalescence cascade of a drop. Phys. Fluids 12, 1265–1267.CrossRefGoogle Scholar
Thoroddsen, S.T., Takehara, K. & Etoh, T.G. 2005 The coalescence speed of a pendent and a sessile drop. J. Fluid Mech. 527, 85–114.CrossRefGoogle Scholar
Tripathi, M.K., Sahu, K.C. & Govindarajan, R. 2015 Dynamics of an initially spherical bubble rising in quiescent liquid. Nat. Commun. 6, 6268.CrossRefGoogle ScholarPubMed
Valantina, S.R., Susan, D., Bavasri, S., Priyadarshini, V., Saraswathi, R.R. & Suriya, M. 2016 Experimental investigation of electro-rheological properties of modeled vegetable oils. J. Food Sci. Technol. 53, 1328–1337.CrossRefGoogle ScholarPubMed
Varma, S.C., Saha, A., Mukherjee, S., Bandopadhyay, A., Kumar, A. & Chakraborty, S. 2020 Universality in coalescence of polymeric fluids. Soft Matt. 16, 10921–10927.CrossRefGoogle ScholarPubMed
Vlahovska, P.M. 2019 Electrohydrodynamics of drops and vesicles. Annu. Rev. Fluid Mech. 51, 305–330.CrossRefGoogle Scholar
Welch, S.W.J. & Biswas, G. 2007 Direct simulation of film boiling including electrohydrodynamic forces. Phys. Fluids 19, 012106.CrossRefGoogle Scholar
Wu, M., Cubaud, T. & Ho, C.-M. 2004 Scaling law in liquid drop coalescence driven by surface tension. Phys. Fluids 16, L51–L54.CrossRefGoogle Scholar
Yin, J.B. & Zhao, X.P. 2002 Preparation and electrorheological activity of mesoporous rare-earth-doped TiO 2. Chem. Mater. 14, 4633–4640.CrossRefGoogle Scholar
Zhang, F.H., Li, E.Q. & Thoroddsen, S.T. 2009 Satellite formation during coalescence of unequal size drops. Phys. Rev. Lett. 102, 104502.CrossRefGoogle ScholarPubMed
Zhang, F.H. & Thoroddsen, S.T. 2008 Satellite generation during bubble coalescence. Phys. Fluids 20, 022104.CrossRefGoogle Scholar

Behara et al. Supplementary Movie

Seven stage coalescence for $(R, S)$=(10, 2.3), $Ca_{E}$=0.1, $Oh_{i}$=0.005, $Oh_{e}$=0.0002, $Bo$=0.32 and $A$=0.998$.

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