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From droplets to waves: periodic instability patterns in highly viscous microfluidic flows

Published online by Cambridge University Press:  28 January 2020

Xiaoyi Hu Open the ORCID record for Xiaoyi Hu [Opens in a new window]  and
Thomas Cubaud Open the ORCID record for Thomas Cubaud [Opens in a new window]
Xiaoyi Hu
Affiliation:
Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY11794, USA
Thomas Cubaud*
Affiliation:
Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY11794, USA
*
†Email address for correspondence: [email protected]
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Abstract

We experimentally study the transition from droplet to wave regimes in microfluidic liquid–liquid multiphase flows having large differences in viscosity. A unified approach based on periodic pattern analysis is employed to study relationships between dispersed and separated flow regimes, including dripping, jetting, capillary waves, inertial waves and core–annular flows over a wide range of flow rates and viscosity contrasts. We examine the morphology and dynamics of each flow regime based on wavelength, frequency and velocity of repeating unit cells to elucidate their connections and to develop predictive capabilities based on dimensionless control parameters. We demonstrate in particular that pattern selection is contingent upon the propagation velocity of droplets and waves at the transition. We also investigate microfluidic wave breaking phenomena with the formation of ligaments and droplets from wave crests in both capillary and inertial wave regimes. This work expands conventional multiphase flow regimes observed in microchannels and shows new routes to disperse highly viscous materials using interfacial waves dynamics in confined microsystems.

JFM classification

Drops and Bubbles: Drops Micro-/Nano-fluid dynamics: Microfluidics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 887 , 25 March 2020 , A27
Copyright
© 2020 Cambridge University Press

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References

Al-Wahaibi, T. & Angeli, P. 2011 Experimental study on interfacial waves in stratified horizontal oil–water flow. Intl J. Multiphase Flow 37, 930–940.CrossRefGoogle Scholar
Anna, S. L. 2016 Droplets and bubbles in microfluidic devices. Annu. Rev. Fluid Mech. 48, 285–309.CrossRefGoogle Scholar
Augello, L., Fani, A. & Gallaire, F. 2018 The influence of the entry region on the instability of a coflowing injector device. J. Phys.: Condens. Matter 30, 284003.Google ScholarPubMed
Balestra, G., Zhu, L. & Gallaire, F. 2018 Viscous Taylor droplets in axisymmetric and planar tubes: from Bretherton’s theory to empirical models. Microfluid. Nanofluid. 22, 67.CrossRefGoogle Scholar
Baroud, C. N., Gallaire, F. & Dangla, R. 2010 Dynamics of microfluidic droplets. Lab on a Chip 10, 2032–2045.CrossRefGoogle ScholarPubMed
Barrero, A. & Loscertales, I. G. 2007 Micro- and nanoparticles via capillary flows. Annu. Rev. Fluid Mech. 39, 89–106.CrossRefGoogle Scholar
Berna, C., Escrivá, A., Munoz-Cobo, J. L. & Herranz, L. E. 2015 Review of droplet entrainment in annular flow: characterization of the entrained droplets. Prog. Nucl. Energy 79, 64–86.CrossRefGoogle Scholar
Bird, R. B., Stewart, W. E. & Lightfoot, E. N. 2002 Transport Phenomena. Wiley.Google Scholar
Brennen, C. E. 2005 Fundamentals of Multiphase Flow. Cambridge University Press.CrossRefGoogle Scholar
Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10, 166–188.CrossRefGoogle Scholar
Cao, Q., Ventresca, A. L., Sreenivas, K. R. & Prasad, A. K. 2003 Instability due to viscosity stratification downstream of a centerline injector. Can. J. Chem. Engng 81, 913–922.CrossRefGoogle Scholar
Cheng, L., Ribatski, G. & Thome, J. R. 2008 Two-phase flow patterns and flow-pattern maps: fundamentals and applications. Appl. Mech. Rev. 61, 0508021.CrossRefGoogle Scholar
Crowe, C. T. 2006 Multiphase Flow Handbook. CRC Press.Google Scholar
Cubaud, T. & Mason, T. G. 2008 Capillary threads and viscous droplets in square microchannels. Phys. Fluids 20, 053302.CrossRefGoogle Scholar
Cubaud, T. & Notaro, S. 2014 Regimes of miscible fluid thread formation in microfluidic focusing sections. Phys. Fluids 26, 122005.CrossRefGoogle Scholar
Cubaud, T., Ulmanella, U. & Ho, C.-M. 2006 Two-phase flow in microchannels with surface modifications. Fluid Dyn. Res. 38, 772–786.CrossRefGoogle Scholar
D’olce, M., Martin, J., Rakotomalala, N., Salin, D. & Talon, L. 2008 Pearl and mushroom instability patterns in two miscible fluids’ core annular flows. Phys. Fluids 20, 024104.CrossRefGoogle Scholar
Drazin, P. G. & Reid, W. H. 2004 Hydrodynamic Stability. Cambridge University Press.CrossRefGoogle Scholar
Eggers, J. 1997 Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69, 865–930.CrossRefGoogle Scholar
Evangelio, A., Campos-Cortés, F. & Gordillo, J. M. 2016 Simple and double microemulsions via the capillary breakup of highly stretched liquid jets. J. Fluid Mech. 804, 550–577.CrossRefGoogle Scholar
Gordillo, J. M., Sevilla, A. & Campo-Cortés, M. 2014 Global stability of stretched jets: conditions for the generation of monodisperse micro-emulsions using coflows. J. Fluid Mech. 738, 335–357.CrossRefGoogle Scholar
Govindarajan, R. & Sahu, K. C. 2014 Instabilities in viscosity-stratified flow. Annu. Rev. Fluid Mech. 46, 331–353.CrossRefGoogle Scholar
Guillot, P., Colin, A., Utada, A. S. & Ajdari, A. 2007 Stability of a jet in confined pressure-driven biphasic flows at low Reynolds numbers. Phys. Rev. Lett. 99, 104502.CrossRefGoogle ScholarPubMed
Hinch, E. J. 1984 A note on the mechanism of the instability at the interface between two shearing fluids. J. Fluid Mech. 144, 463–465.CrossRefGoogle Scholar
Hu, X. & Cubaud, T. 2016 Inertial destabilization of highly viscous microfluidic stratifications. Phys. Rev. Fluids 1, 044101.CrossRefGoogle Scholar
Hu, X. & Cubaud, T. 2018 Viscous wave breaking and ligament formation in microfluidic systems. Phys. Rev. Lett. 121, 044502.CrossRefGoogle ScholarPubMed
Huerre, P. & Rossi, M. 2005 Hydrodynamic instabilities in open flows. In Hydrodynamics and Nonlinear Instabilities. Cambridge University Press.Google Scholar
Jakiela, S., Makulska, S., Korczyk, P. M. & Garstecki, P. 2011 Speed of flow of individual droplets in microfluidic channels as a function of the capillary number, volume of droplets and contrast of viscosities. Lab on a Chip 11, 3603–3608.CrossRefGoogle ScholarPubMed
Jose, B. M. & Cubaud, T. 2014 Formation and dynamics of partially wetting droplets in square microchannels. RSC Adv. 4, 14962–14970.CrossRefGoogle Scholar
Joseph, D. & Renardy, Y. 1993 Fundamentals of Two-Fluid Dynamics. Part II. Lubricated Transport, Drops and Miscible Liquids. Springer.Google Scholar
Lac, E. & Sherwood, J. D. 2009 Streaming potential generated by a drop moving along the centreline of a capillary. J. Fluid Mech. 640, 55–77.CrossRefGoogle Scholar
Marmottant, P. & Villermaux, E. 2004 On spray formation. J. Fluid Mech. 498, 73–111.CrossRefGoogle Scholar
Moiré, M., Peysson, Y., Herzhaft, B., Pannacci, N., Gallaire, F., Augello, L., Dalmazzone, C. & Colin, A. 2017 Ultralow interfacial tension measurement through jetting/dripping transition. Langmuir 33, 2531–2540.CrossRefGoogle ScholarPubMed
Mowlavi, S., Shukla, I., Brun, P.-T. & Gallaire, F. 2019 Particle size selection in capillary instability of locally heated coaxial fiber. Phys. Rev. Fluids 4, 064003.CrossRefGoogle Scholar
Nath, B., Biswas, G., Dalal, A. & Sahu, K. C. 2017 Migration of a droplet in a cylindrical tube in the creeping flow regime. Phys. Rev. E 95, 033110.Google Scholar
Nunes, J. K., Tsai, S. S. H., Wan, J. & Stone, H. A. 2013 Dripping and jetting in microfluidic multiphase flows applied to particle and fibre synthesis. J. Phys. D: Appl. Phys. 46, 114002.CrossRefGoogle Scholar
Rivero-Rodriguez, J. & Scheid, B. 2018 Bubble dynamics in microchannels: inertial and capillary migration forces. J. Fluid Mech. 842, 215–247.CrossRefGoogle Scholar
Salin, D. & Talon, L. 2019 Revisiting the linear stability analysis and absolute-convective transition of two fluid core annular flow. J. Fluid Mech. 865, 743–761.CrossRefGoogle Scholar
Sangalli, M., Gallagher, C. T., Leighton, D. T., Chang, H. C. & Mccready, M. J. 1995 Finite-amplitude waves at the interface between fluids with different viscosity: theory and experiments. Phys. Rev. Lett. 75, 77–80.CrossRefGoogle ScholarPubMed
Selvam, B., Merk, S., Govindarajan, R. & Meiburg, E. 2007 Stability of miscible core–annular flows with viscosity stratification. J. Fluid Mech. 592, 23–49.CrossRefGoogle Scholar
Tomotika, S. 1935 On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid. Proc. R. Soc. Lond. A 146, 322–337.Google Scholar
Triplett, K. A., Ghiaasiaan, S. M., Abdel-Khalik, S. I. & Sadowski, D. L. 1999 Gas–liquid two-phase flow in microchannels. Part I. Two-phase flow patterns. Intl J. Multiphase Flow 25, 377–394.CrossRefGoogle Scholar
Utada, A. S., Fernandez-Nieves, A., Gordillo, J. M. & Weitz, D. A. 2008 Absolute instability of a liquid jet in a coflowing stream. Phys. Rev. Lett. 100, 014502.CrossRefGoogle Scholar
Wang, Y. & Bourouiba, L. 2018 Unsteady sheet fragmentation: droplet sizes and speeds. J. Fluid Mech. 848, 946–967.CrossRefGoogle Scholar
Wong, H., Radke, C. J. & Morris, S. 1995 The motion of long bubbles in polygonal capillaries. Part 1. Thin films. J. Fluid Mech. 292, 71–94.CrossRefGoogle Scholar
Yih, C.-S. 1967 Instability due to viscosity stratification. J. Fluid Mech. 27, 337–352.CrossRefGoogle Scholar