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Three-dimensional streaming flow in confined geometries

Published online by Cambridge University Press:  20 July 2015

Bhargav Rallabandi ,
Alvaro Marin ,
Massimiliano Rossi ,
Christian J. Kähler  and
Sascha Hilgenfeldt
Bhargav Rallabandi*
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA
Alvaro Marin
Affiliation:
Institute for Aerodynamics and Fluid Mechanics, Bundeswehr University Munich, 85577 Neubiberg, Germany
Massimiliano Rossi
Affiliation:
Institute for Aerodynamics and Fluid Mechanics, Bundeswehr University Munich, 85577 Neubiberg, Germany
Christian J. Kähler
Affiliation:
Institute for Aerodynamics and Fluid Mechanics, Bundeswehr University Munich, 85577 Neubiberg, Germany
Sascha Hilgenfeldt
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA
*
†Email address for correspondence: rallaba2@illinois.edu
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Abstract

Steady streaming vortex flow from microbubbles has been developed into a versatile tool for microfluidic sample manipulation. For ease of manufacture and quantitative control, set-ups have focused on approximately two-dimensional flow geometries based on semi-cylindrical bubbles. The present work demonstrates how the necessary flow confinement perpendicular to the cylinder axis gives rise to non-trivial three-dimensional flow components. This is an important effect in applications such as sorting and micromixing. Using asymptotic theory and numerical integration of fluid trajectories, it is shown that the two-dimensional flow dynamics is modified in two ways: (i) the vortex motion is punctuated by bursts of strong axial displacement near the bubble, on time scales smaller than the vortex period; and (ii) the vortex trajectories drift over time scales much longer than the vortex period, forcing fluid particles onto three-dimensional paths of toroidal topology. Both effects are verified experimentally by quantitative comparison with astigmatism particle tracking velocimetry (APTV) measurements of streaming flows. It is further shown that the long-time flow patterns obey a Hamiltonian description that is applicable to general confined Stokes flows beyond microstreaming.

JFM classification

Drops and Bubbles: Bubble dynamics Low-Reynolds-number flows: Low-Reynolds-number flows Micro-/Nano-fluid dynamics: Microfluidics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 777 , 25 August 2015 , pp. 408 - 429
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Copyright
© 2015 Cambridge University Press 

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