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Magnetofluidic-based controlled droplet breakup: effect of non-uniform force field

Published online by Cambridge University Press:  06 July 2022

Sudip Shyam ,
Bhavesh Dhapola  and
Pranab Kumar Mondal Open the ORCID record for Pranab Kumar Mondal [Opens in a new window]
Sudip Shyam
Affiliation:
Microfluidics and Microscale Transport Processes Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati 781039, India
Bhavesh Dhapola
Affiliation:
Microfluidics and Microscale Transport Processes Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati 781039, India
Pranab Kumar Mondal*
Affiliation:
Microfluidics and Microscale Transport Processes Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati 781039, India
*
†Email address for correspondence: mail2pranab@gmail.com, pranabm@iitg.ac.in
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Abstract

We report the breakup dynamics of a magnetically active (ferrofluid) droplet in a T-shaped Lab on a Chip (LOC) device under the modulation of a non-uniform magnetic field. We adhere to high-speed imaging modalities for the experimental quantification of the droplet splitting phenomenon, while the underlying phenomenon is supported by the numerical results in a qualitative manner as well. On reaching the T-junction divergence, the droplet engulfs the intersection fully and eventually deforms into the dumbbell-shaped form, making its bulges move towards the branches of the junction. We observe that the asymmetric distribution of the magnetic force lines, acting over the T-junction divergence, induces an accelerating motion to the left of the moving bulge (since the magnet is placed adjacent to the left branch). We show that the non-uniform force field gradient allows the formation of a hump-like structure inside the left moving bulge, which triggers the onset of augmented convection in its flow field. We reveal that this augmented internal convection developed in the left moving volume/bulge, on becoming coupled to the various involved time scales of the flow field, leads to the asymmetric splitting of the droplet into two sister droplets. Our analysis establishes that, at the critical strength of the applied forcing, as realized by the critical magnetic Bond number, the flow time scale becomes minimum at the left branch of the channel, leading to the formation of larger sized sister droplets therein. Inferences of the present analysis, which demonstrates a plausible means of independently controlling the size of the sister droplet by manoeuvring the applied force field gradient, will provide a potential solution for rapid droplet splitting, which typically finds significant importance in point-of-care diagnostics.

JFM classification

Drops and Bubbles: Breakup/coalescence MHD and Electrohydrodynamics: Magnetic fluids Micro-/Nano-fluid dynamics: Microfluidics

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 944 , 10 August 2022 , A51
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© The Author(s), 2022. Published by Cambridge University Press

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References

Aboutalebi, M., Bijarchi, M.A., Shafii, M.B. & Kazemzadeh Hannani, S. 2018 Numerical investigation on splitting of ferrofluid microdroplets in T-junctions using an asymmetric magnetic field with proposed correlation. J. Magn. Magn. Mater. 447, 139–149.CrossRefGoogle Scholar
Adamson, D.N., Mustafi, D., Zhang, J.X.J., Zheng, B. & Ismagilov, R.F. 2006 Production of arrays of chemically distinct nanolitre plugs via repeated splitting in microfluidic devices. Lab on a Chip 6 (9), 1178–1186.CrossRefGoogle ScholarPubMed
Badalassi, V.E., Ceniceros, H.D. & Banerjee, S. 2003 Computation of multiphase systems with phase field models. J. Comput. Phys. 190 (2), 371–397.CrossRefGoogle Scholar
Bai, F., He, X., Yang, X., Zhou, R. & Wang, C. 2017 Three dimensional phase-field investigation of droplet formation in microfluidic flow focusing devices with experimental validation. Intl J. Multiphase Flow 93, 130–141.CrossRefGoogle Scholar
Baroud, C.N., Gallaire, F. & Dangla, R. 2010 Dynamics of microfluidic droplets. Lab on a Chip 10 (16), 2032–2045.CrossRefGoogle ScholarPubMed
Batchelor, G.K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41 (3), 545–570.CrossRefGoogle Scholar
Bijarchi, M.A., Dizani, M., Honarmand, M. & Shafii, M.B. 2021 Splitting dynamics of ferrofluid droplets inside a microfluidic T-junction using a pulse-width modulated magnetic field in micro-magnetofluidics. Soft Matt. 17 (5), 1317–1329.CrossRefGoogle ScholarPubMed
Bijarchi, M.A. & Shafii, M.B. 2020 Experimental investigation on the dynamics of on-demand ferrofluid drop formation under a pulse-width-modulated nonuniform magnetic field. Langmuir 36 (26), 7724–7740.CrossRefGoogle Scholar
Bretherton, F.P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10 (2), 166.CrossRefGoogle Scholar
Cahn, J.W. & Hilliard, J.E. 1958 Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28 (2), 258–267.CrossRefGoogle Scholar
Cahn, J.W. & Hilliard, J.E. 1959 Free energy of a nonuniform system. III. Nucleation in a two-component incompressible fluid. J. Chem. Phys. 31 (3), 688–699.CrossRefGoogle Scholar
Chen, Y. & Deng, Z. 2017 Hydrodynamics of a droplet passing through a microfluidic T-junction. J. Fluid Mech. 819, 401–434.CrossRefGoogle Scholar
Christopher, G.F., Bergstein, J., End, N.B., Poon, M., Nguyen, C. & Anna, S.L. 2009 Coalescence and splitting of confined droplets at microfluidic junctions. Lab on a Chip 9 (8), 1102–1109.CrossRefGoogle ScholarPubMed
Cunha, L.H.P., Siqueira, I.R., Cunha, F.R. & Oliveira, T.F. 2020 Effects of external magnetic fields on the rheology and magnetization of dilute emulsions of ferrofluid droplets in shear flows. Phys. Fluids 32 (7), 073306.CrossRefGoogle Scholar
Dalvi, S., van der Meer, T.H. & Shahi, M. 2022 Numerical evaluation of the ferrofluid behaviour under the influence of three-dimensional non-uniform magnetic field. Intl J. Heat Fluid Flow 94, 108901.CrossRefGoogle Scholar
DasGupta, D., Mondal, P.K. & Chakraborty, S. 2014 Thermocapillary-actuated contact-line motion of immiscible binary fluids over substrates with patterned wettability in narrow confinement. Phys. Rev. E 90 (2), 023011.CrossRefGoogle ScholarPubMed
Gorthi, S.R., Mondal, P.K. & Biswas, G. 2017 Magnetic-field-driven alteration in capillary filling dynamics in a narrow fluidic channel. Phys. Rev. E 96 (1), 013113.CrossRefGoogle Scholar
Griffiths, D.J. 2017 Introduction to Electrodynamics. Introduction to Electrodynamics. Cambridge University Press.CrossRefGoogle Scholar
Hejazian, M., Li, W. & Nguyen, N.-T. 2015 Lab on a chip for continuous-flow magnetic cell separation. Lab on a Chip 15 (4), 959–970.CrossRefGoogle ScholarPubMed
Hoang, D.A., Portela, L.M., Kleijn, C.R., Kreutzer, M.T. & Van Steijn, V. 2013 Dynamics of droplet breakup in a T-junction. J. Fluid Mech. 717, R4.CrossRefGoogle Scholar
Ilg, P., Kröger, M. & Hess, S. 2005 Magnetoviscosity of semidilute ferrofluids and the role of dipolar interactions: comparison of molecular simulations and dynamical mean-field theory. Phys. Rev. E 71 (3), 031205.CrossRefGoogle ScholarPubMed
Jacqmin, D. 1999 Calculation of two-phase Navier-Stokes flows using phase-field modeling. J. Comput. Phys. 155 (1), 96–127.CrossRefGoogle Scholar
Jacqmin, D. 2000 Contact-line dynamics of a diffuse fluid interface. J. Fluid Mech. 402, 57–88.CrossRefGoogle Scholar
Jansons, K.M. 1983 Determination of the constitutive equations for a magnetic fluid. J. Fluid Mech. 137, 187–216.CrossRefGoogle Scholar
Jullien, M.C., Tsang Mui Ching, M.J., Cohen, C., Menetrier, L. & Tabeling, P. 2009 Droplet breakup in microfluidic T-junctions at small capillary numbers. Phys. Fluids 21 (7), 072001.CrossRefGoogle Scholar
Kitenbergs, G., Tatulcenkovs, A., Erglis, K., Petrichenko, O., Perzynski, R. & Cebers, A. 2015 Magnetic field driven micro-convection in the Hele-Shaw cell: the Brinkman model and its comparison with experiment. J. Fluid Mech. 774, 170–191.CrossRefGoogle Scholar
Kunti, G., Mondal, P.K., Bhattacharya, A. & Chakraborty, S. 2018 Electrothermally modulated contact line dynamics of a binary fluid in a patterned fluidic environment. Phys. Fluids 30 (9), 092005.CrossRefGoogle Scholar
Leshansky, A.M., Afkhami, S., Jullien, M.C. & Tabeling, P. 2012 Obstructed breakup of slender drops in a microfluidic T junction. Phys. Rev. Lett. 108 (26), 264502.CrossRefGoogle Scholar
Leshansky, M.A. & Pismen, M.L. 2009 Breakup of drops in a microfluidic T junction. Phys. Fluids 21 (2), 023303.CrossRefGoogle Scholar
Li, H., Wu, Y., Wang, X., Zhu, C., Fu, T. & Ma, Y. 2016 Magnetofluidic control of the breakup of ferrofluid droplets in a microfluidic Y-junction. RSC Adv. 6, 778–785.CrossRefGoogle Scholar
Link, D.R., Anna, S.L., Weitz, D.A. & Stone, H.A. 2004 Geometrically mediated breakup of drops in microfluidic devices. Phys. Rev. Lett. 92 (5), 4.CrossRefGoogle ScholarPubMed
Ma, R., Fu, T., Zhang, Q., Zhu, C., Ma, Y. & Li, H.Z. 2017 Breakup dynamics of ferrofluid droplet in a microfluidic T-junction. J. Ind. Engng Chem. 54, 408–420.CrossRefGoogle Scholar
Madadelahi, M., Ghazimirsaeed, E. & Shamloo, A. 2019 Design and fabrication of a two-phase diamond nanoparticle aided fast PCR device. Anal. Chim. Acta 1068, 28–40.CrossRefGoogle ScholarPubMed
Manga, M. 1996 Dynamics of drops in branched tubes. J. Fluid Mech. 315, 105–117.CrossRefGoogle Scholar
Mao, L., Elborai, S., He, X., Zahn, M. & Koser, H. 2011 Direct observation of closed-loop ferrohydrodynamic pumping under traveling magnetic fields. Phys. Rev. B – Condens. Matter Mater. Phys. 84 (10), 104431.CrossRefGoogle Scholar
Marchand, A., Das, S., Snoeijer, J.H. & Andreotti, B. 2012 Contact angles on a soft solid: from Young's law to Neumann's law. Phys. Rev. Lett. 109 (23), 236101.CrossRefGoogle ScholarPubMed
Mondal, P.K. & Chaudhry, S. 2018 Effects of gravity on the thermo-hydrodynamics of moving contact lines. Phys. Fluids 30 (4), 042109.CrossRefGoogle Scholar
Mondal, P.K., DasGupta, D., Bandopadhyay, A., Ghosh, U. & Chakraborty, S. 2015 Contact line dynamics of electroosmotic flows of incompressible binary fluid system with density and viscosity contrasts. Phys. Fluids 27 (3), 032109.CrossRefGoogle Scholar
Mondal, P.K., Ghosh, U., Bandopadhyay, A., Dasgupta, D. & Chakraborty, S. 2013 Electric-field-driven contact-line dynamics of two immiscible fluids over chemically patterned surfaces in narrow confinements. Phys. Rev. E – Stat. Nonlinear Soft Matter Phys. 88 (2), 023022.CrossRefGoogle ScholarPubMed
Moon, S., et al. 2010 Layer by layer three-dimensional tissue epitaxy by cell-laden hydrogel droplets. Tissue Engng C: Methods 16 (1), 157–166.CrossRefGoogle ScholarPubMed
Nozaki, Y., Yoon, D.H., Furuya, M., Fujita, H., Sekiguchi, T. & Shoji, S. 2021 Validation of droplet-generation performance of a newly developed microfluidic device with a three-dimensional structure. Sensors Actuators A: Phys. 331, 112917.CrossRefGoogle Scholar
Odenbach, S. (Ed.) 2002 Ferrofluids, vol. 594. Springer.CrossRefGoogle ScholarPubMed
Rinaldi, C., Chaves, A., Elborai, S., He, X. & Zahn, M. 2005 Magnetic fluid rheology and flows. Curr. Opin. Colloid Interface Sci. 10 (3–4), 141–157.CrossRefGoogle Scholar
Roodan, V.A., Gómez-Pastora, V., Karampelas, H.I., González-Fernández, C., Bringas, E., Ortiz, I., Chalmers, J.J., Furlani, E.P. & Swihart, M.T. 2020 Formation and manipulation of ferrofluid droplets with magnetic fields in a microdevice: a numerical parametric study. Soft Matt. 16 (41), 9506–9518.CrossRefGoogle Scholar
Rosensweig, R.E. 1984 Ferrohydrodynamics, vol. 279. Cambridge University Press.Google Scholar
Rosensweig, R.E. 1987 Magnetic fluids. Annu. Rev. Fluid Mech. 19 (1), 437–461.CrossRefGoogle Scholar
Santos, J., Trujillo-Cayado, L.A., Calero, N., Alfaro, M.C. & Muñoz, J. 2016 Development of eco-friendly emulsions produced by microfluidization technique. J. Ind. Engng Chem. 36, 90–95.CrossRefGoogle Scholar
Schmid, L. & Franke, T. 2013 SAW-controlled drop size for flow focusing. Lab on a Chip 13 (9), 1691–1694.CrossRefGoogle ScholarPubMed
Shamloo, A. & Hassani-Gangaraj, M. 2020 Investigating the effect of reagent parameters on the efficiency of cell lysis within droplets. Phys. Fluids 32 (6), 062002.CrossRefGoogle Scholar
Shyam, S., Asfer, M., Mehta, B., Mondal, P.K. & Almutairi, Z.A. 2020 a Magnetic field driven actuation of sessile ferrofluid droplets in the presence of a time dependent magnetic field. Colloids Surf. A: Physicochem. Engng Aspects 586, 124116.CrossRefGoogle Scholar
Shyam, S., Mehta, B., Mondal, P.K. & Wongwises, S. 2019 Investigation into the thermo-hydrodynamics of ferrofluid flow under the influence of constant and alternating magnetic field by InfraRed thermography. Intl J. Heat Mass Transfer 135, 1233–1247.CrossRefGoogle Scholar
Shyam, S., Mondal, P.K. & Mehta, B. 2020 b Field driven evaporation kinetics of a sessile ferrofluid droplet on a soft substrate. Soft Matt. 16 (28), 6619–6632.CrossRefGoogle ScholarPubMed
Shyam, S., Mondal, P.K. & Mehta, B. 2021 Magnetofluidic mixing of a ferrofluid droplet under the influence of a time-dependent external field. J. Fluid Mech. 917, A15.CrossRefGoogle Scholar
Shyam, S., Yadav, A., Gawade, Y., Mehta, B., Mondal, P.K. & Asfer, M. 2020 c Dynamics of a single isolated ferrofluid plug inside a micro-capillary in the presence of externally applied magnetic field. Exp. Fluids 61 (10), 210.CrossRefGoogle Scholar
Strek, T. 2008 Finite element simulation of heat transfer in ferrofluid. In Modelling and Simulation. I-Tech Education and Publishing.CrossRefGoogle Scholar
Tan, S.H. & Nguyen, N.-T.T. 2011 Generation and manipulation of monodispersed ferrofluid emulsions: the effect of a uniform magnetic field in flow-focusing and T-junction configurations. Phys. Rev. E – Stat. Nonlinear Soft Matter Phys. 84 (3), 036317.CrossRefGoogle ScholarPubMed
Tan, S.-H., Nguyen, N.-T., Yobas, L. & Kang, T.G. 2010 Formation and manipulation of ferrofluid droplets at a microfluidic T -junction. J. Micromech. Microengng 20 (4), 045004.CrossRefGoogle Scholar
Vladisavljević, G.T., Khalid, N., Neves, M.A., Kuroiwa, T., Nakajima, M., Uemura, K., Ichikawa, S. & Kobayashi, I. 2013 Industrial lab-on-a-chip: design, applications and scale-up for drug discovery and delivery. Adv. Drug Deliv. Rev. 65 (11–12), 1626–1663.CrossRefGoogle ScholarPubMed
Whitesides, G.M. & Stroock, A.D. 2001 Flexible methods for microfluidics. Phys. Today 54 (6), 42.CrossRefGoogle Scholar
Wu, Y., Fu, T., Ma, Y. & Li, H.Z. 2013 Ferrofluid droplet formation and breakup dynamics in a microfluidic flow-focusing device. Soft Matt. 9 (41), 9792–9798.CrossRefGoogle Scholar
Wu, Y., Fu, T., Ma, Y. & Li, H.Z. 2014 Active control of ferrofluid droplet breakup dynamics in a microfluidic T-junction. Microfluid Nanofluid 18 (1), 19–27.CrossRefGoogle Scholar
Xi, H.D., Guo, W., Leniart, M., Chong, Z.Z. & Tan, S.H. 2016 AC electric field induced droplet deformation in a microfluidic T-junction. Lab on a Chip 16 (16), 2982–2986.CrossRefGoogle Scholar
Xu, R. 2002 Particle Characterization: Light Scattering Methods (ed. B. Scarlett), vol. 13. Kluwer Academic Publishers.Google Scholar
Yesiloz, G., Boybay, M.S. & Ren, C.L. 2017 Effective thermo-capillary mixing in droplet microfluidics integrated with a microwave heater. Analyt. Chem. 89 (3), 1978–1984.CrossRefGoogle ScholarPubMed
Yue, K., You, Y., Yang, C., Niu, Y. & Zhang, X. 2020 Numerical simulation of transport and adhesion of thermogenic nano-carriers in microvessels. Soft Matt. 16 (45), 10345–10357.CrossRefGoogle ScholarPubMed
Yue, P., Zhou, C. & Feng, J.J. 2010 Sharp-interface limit of the Cahn-Hilliard model for moving contact lines. J. Fluid Mech. 645, 279–294.CrossRefGoogle Scholar
Zheng, B. & Ismagilov, R.F. 2005 A microfluidic approach for screening submicroliter volumes against multiple reagents by using preformed arrays of nanoliter plugs in a three-phase liquid/liquid/gas flow. Angew. Chem. Intl Ed. 44 (17), 2520–2523.CrossRefGoogle Scholar
Zhu, G.-P. & Nguyen, N.-T. 2012 Rapid magnetofluidic mixing in a uniform magnetic field. Lab on a Chip 12 (22), 4772.CrossRefGoogle Scholar

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