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Updated: May 2, 2026

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System
Published on: May 9, 2021
Multiple steadily translating bubbles in a Hele-Shaw channel
Christopher C Green1, Giovani L Vasconcelos2
1Department of Mathematics , Imperial College London , 180 Queen's Gate, London SW7 2AZ, UK.
Abstract:
Analytical solutions are constructed for an assembly of any finite number of bubbles in steady motion in a Hele-Shaw channel. The solutions are given in the form of a conformal mapping from a bounded multiply connected circular domain to the flow region exterior to the bubbles. The mapping is written as the sum of two analytic functions-corresponding to the complex potentials in the laboratory and co-moving frames-that map the circular domain onto respective degenerate polygonal domains. These functions are obtained using the generalized Schwarz-Christoffel formula for multiply connected domains in terms of the Schottky-Klein prime function. Our solutions are very general in that no symmetry assumption concerning the geometrical disposition of the bubbles is made. Several examples for various bubble configurations are discussed.
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