Viscous Interaction Forces of Two Pulsating Spheres in a Fluid Near their Contact Point
S. V. Sanduleanu1,2
1Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526, Russia
2Moscow Institute of Physics and Technology, Dolgoprudny, 141701, Russia
Keywords: вязкое взаимодействие пузырьков, функция тока Стокса, осевая симметрия, viscous interaction of bubbles, Stokes stream function, axial symmetry
Abstract
We consider the interaction between two spherical bubbles of variable radii during their movement along their centerline in a viscous fluid. A stream function that satisfies the Stokes equation is found in bispherical coordinates as an expansion in Gegenbauer polynomials. Viscous forces that act on the sphere are exactly presented as infinite series. Asymptotic expressions of these forces near the bubble contact zone are derived.
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