Three-dimensional streaming Flow in confined geometries

Bhargav Rallabandi, Alvaro Marin, Massimiliano Rossi, Christian J. Kähler, Sascha Hilgenfeldt

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)408-429
Number of pages22
JournalJournal of Fluid Mechanics
StatePublished - 2015


  • Bubble dynamics
  • Low-Reynolds-number flows
  • Microfluidics

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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