Three-dimensional soft streaming

Songyuan Cui, Yashraj Bhosale, Mattia Gazzola

Research output: Contribution to journalArticlepeer-review


Viscous streaming is an efficient rectification mechanism to exploit flow inertia at small scales for fluid and particle manipulation. It typically entails a fluid vibrating around an immersed solid feature that, by concentrating stresses, modulates the emergence of steady flows of useful topology. Motivated by its relevance in biological and artificial settings characterized by soft materials, recent studies have theoretically elucidated, in two dimensions, the impact of body elasticity on streaming flows. Here, we generalize those findings to three dimensions, via the minimal case of an immersed soft sphere. We first improve existing solutions for the rigid-sphere limit, by considering previously unaccounted terms. We then enable body compliance, exposing a three-dimensional, elastic streaming process available even in Stokes flows. Such effect, consistent with two-dimensional analyses but analytically distinct, is validated against direct numerical simulations and shown to translate to bodies of complex geometry and topology, paving the way for advanced forms of flow control.

Original languageEnglish (US)
Article numberA7
JournalJournal of Fluid Mechanics
StatePublished - Jan 25 2024


  • general fluid mechanics
  • microfluidics

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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