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Bubble dynamics in microchannels: inertial and capillary migration forces

Published online by Cambridge University Press:  07 March 2018

Javier Rivero-Rodriguez Open the ORCID record for Javier Rivero-Rodriguez [Opens in a new window]  and
Benoit Scheid
Javier Rivero-Rodriguez*
Affiliation:
TIPs, Université Libre de Bruxelles, C.P. 165/67, Avenue F. D. Roosevelt 50, 1050 Bruxelles, Belgium
Benoit Scheid
Affiliation:
TIPs, Université Libre de Bruxelles, C.P. 165/67, Avenue F. D. Roosevelt 50, 1050 Bruxelles, Belgium
*
†Email address for correspondence: jriveror@ulb.ac.be
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Abstract

This work focuses on the dynamics of a train of unconfined bubbles flowing in a microchannel. We investigate the transverse position of the train of bubbles, its velocity and the associated pressure drop when flowing in a microchannel, depending on the internal forces due to viscosity, inertia and capillarity. Despite the small scales of the system, the inertial migration force plays a crucial role in determining the transverse equilibrium position of the bubbles. Besides inertia and viscosity, other effects may also affect the transverse migration of bubbles, such as the Marangoni surface stresses and the surface deformability. We look at the influence of surfactants in the limit of infinite Marangoni effect, which yields a rigid bubble interface. The resulting migration force may balance external body forces, if present, such as buoyancy, centrifugal or magnetic ones. This balance not only determines the transverse position of the bubbles but, consequently, the surrounding flow structure, which can be determinant for any mass/heat transfer process involved. Finally, we look at the influence of the bubble deformation on the equilibrium position and compare it with the inertial migration force at the centred position, explaining the stable or unstable character of this position accordingly. A systematic study of the influence of the parameters, such as the bubble size, uniform body force, Reynolds and capillary numbers, has been carried out using numerical simulations based on the finite element method, solving the full steady Navier–Stokes equations and their asymptotic counterparts for the limits of small Reynolds and/or capillary numbers.

JFM classification

Drops and Bubbles: Bubble dynamics Micro-/Nano-fluid dynamics: Microfluidics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 842 , 10 May 2018 , pp. 215 - 247
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Copyright
© 2018 Cambridge University Press 

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References

Chan, P. C.-H. & Leal, L. G. 1979 The motion of a deformable drop in a second-order fluid. J. Fluid Mech. 92 (01), 131–170.Google Scholar
Chen, X., Xue, C., Zhang, L., Hu, G., Jiang, X. & Sun, J. 2014 Inertial migration of deformable droplets in a microchannel. Phys. Fluids 26 (11), 112003.Google Scholar
Coulliette, C. & Pozrikidis, C. 1998 Motion of an array of drops through a cylindrical tube. J. Fluid Mech. 358, 1–28.Google Scholar
Cox, R. G. & Brenner, H. 1968 The lateral migration of solid particles in Poiseuille flow – I theory. Chem. Engng Sci. 23 (2), 147–173.Google Scholar
Cubaud, T. & Ho, C.-M. 2004 Transport of bubbles in square microchannels. Phys. Fluids 16 (12), 4575–4585.Google Scholar
Di Carlo, D., Edd, J. F., Humphry, K. J., Stone, H. A. & Toner, M. 2009 Particle segregation and dynamics in confined flows. Phys. Rev. Lett. 102 (9), 094503.Google Scholar
Di Carlo, D., Edd, J. F., Irimia, D., Tompkins, R. G. & Toner, M. 2008 Equilibrium separation and filtration of particles using differential inertial focusing. Anal. Chem. 80 (6), 2204–2211.Google Scholar
Donea, J., Giuliani, S. & Halleux, J. P. 1982 An arbitrary Lagrangian–Eulerian finite element method for transient dynamic fluid–structure interactions. Comput. Meth. Appl. Mech. Engng 33 (1), 689–723.Google Scholar
Günther, A., Khan, S. A., Thalmann, M., Trachsel, F. & Jensen, K. F. 2004 Transport and reaction in microscale segmented gas–liquid flow. Lab on a Chip 4 (4), 278–286.Google Scholar
Ho, B. P. & Leal, L. G. 1974 Inertial migration of rigid spheres in two-dimensional unidirectional flows. J. Fluid Mech. 65 (02), 365–400.Google Scholar
Hood, K., Lee, S. & Roper, M. 2015 Inertial migration of a rigid sphere in three-dimensional Poiseuille flow. J. Fluid Mech. 765, 452–479.Google Scholar
Kemna, E. W. M., Schoeman, R. M., Wolbers, F., Vermes, I., Weitz, D. A. & Van Den Berg, A. 2012 High-yield cell ordering and deterministic cell-in-droplet encapsulation using Dean flow in a curved microchannel. Lab on a Chip 12 (16), 2881–2887.Google Scholar
Kennedy, M. R., Pozrikidis, C. & Skalak, R. 1994 Motion and deformation of liquid drops, and the rheology of dilute emulsions in simple shear flow. Comput. Fluids 23 (2), 251–278.Google Scholar
Leshansky, A. M., Bransky, A., Korin, N. & Dinnar, U. 2007 Tunable nonlinear viscoelastic focusing in a microfluidic device. Phys. Rev. Lett. 98 (23), 234501.Google Scholar
Matas, J.-P., Morris, J. F. & Guazzelli, É. 2004 Inertial migration of rigid spherical particles in Poiseuille flow. J. Fluid Mech. 515, 171–195.Google Scholar
McLaughlin, J. B. 1991 Inertial migration of a small sphere in linear shear flows. J. Fluid Mech. 224, 261–274.Google Scholar
Mikaelian, D., Haut, B. & Scheid, B. 2015a Bubbly flow and gas–liquid mass transfer in square and circular microchannels for stress-free and rigid interfaces: CFD analysis. Microfluid. Nanofluid. 19 (3), 523–545.Google Scholar
Mikaelian, D., Haut, B. & Scheid, B. 2015b Bubbly flow and gas–liquid mass transfer in square and circular microchannels for stress-free and rigid interfaces: dissolution model. Microfluid. Nanofluid. 19 (4), 899–911.Google Scholar
Mortazavi, S. & Tryggvason, G. 2000 A numerical study of the motion of drops in Poiseuille flow. Part 1. Lateral migration of one drop. J. Fluid Mech. 411, 325–350.Google Scholar
Oliver, D. R. 1962 Influence of particle rotation on radial migration in the Poiseuille flow of suspensions. Nature 194 (4835), 1269–1271.Google Scholar
Pak, O. S., Feng, J. & Stone, H. A. 2014 Viscous Marangoni migration of a drop in a Poiseuille flow at low surface Peclet numbers. J. Fluid Mech. 753, 535–552.Google Scholar
Pamme, N. 2007 Continuous flow separations in microfluidic devices. Lab on a Chip 7 (12), 1644–1659.Google Scholar
Pereira, A. & Kalliadasis, S. 2008 On the transport equation for an interfacial quantity. Eur. Phys. J. 44 (2), 211–214.Google Scholar
Schonberg, J. A. & Hinch, E. J. 1989 Inertial migration of a sphere in Poiseuille flow. J. Fluid Mech. 203, 517–524.Google Scholar
Segré, G. & Silberberg, A. 1962 Behaviour of macroscopic rigid spheres in Poiseuille flow. Part 2. Experimental results and interpretation. J. Fluid Mech. 14 (01), 136–157.Google Scholar
Shim, S., Wan, J., Hilgenfeldt, S., Panchal, P. D. & Stone, H. A. 2014 Dissolution without disappearing: multicomponent gas exchange for CO2 bubbles in a microfluidic channel. Lab on a Chip 14 (14), 2428–2436.Google Scholar
Singh, R. K., Li, X. & Sarkar, K. 2014 Lateral migration of a capsule in plane shear near a wall. J. Fluid Mech. 739, 421–443.Google Scholar
Stan, C. A., Ellerbee, A. K., Guglielmini, L., Stone, H. A. & Whitesides, G. M. 2013 The magnitude of lift forces acting on drops and bubbles in liquids flowing inside microchannels. Lab on a Chip 13 (3), 365–376.Google Scholar
Stan, C. A., Guglielmini, L., Ellerbee, A. K., Caviezel, D., Stone, H. A. & Whitesides, G. M. 2011 Sheathless hydrodynamic positioning of buoyant drops and bubbles inside microchannels. Phys. Rev. E 84 (3), 036302.Google Scholar
Subramanian, R. S. 1983 Thermocapillary migration of bubbles and droplets. Adv. Space Res. 3 (5), 145–153.Google Scholar
Tachibana, M. 1973 On the behaviour of a sphere in the laminar tube flows. Rheol. Acta 12 (1), 58–69.Google Scholar
Takemura, F., Magnaudet, J. & Dimitrakopoulos, P. 2009 Migration and deformation of bubbles rising in a wall-bounded shear flow at finite Reynolds number. J. Fluid Mech. 634, 463–486.Google Scholar
Vasseur, P. & Cox, R. G. 1976 The lateral migration of a spherical particle in two-dimensional shear flows. J. Fluid Mech. 78 (02), 385–413.Google Scholar
Vasseur, P. & Cox, R. G. 1977 The lateral migration of spherical particles sedimenting in a stagnant bounded fluid. J. Fluid Mech. 80 (3), 561–591.Google Scholar
Yang, B. H., Wang, J., Joseph, D. D., Hu, H. H., Pan, T.-W. & Glowinski, R. 2005 Migration of a sphere in tube flow. J. Fluid Mech. 540, 109–131.Google Scholar
Zhou, H. & Pozrikidis, C. 1993 The flow of suspensions in channels: single files of drops. Phys. Fluids A 5 (2), 311–324.Google Scholar