Hadamard-Rybczynski equation

In bubble dynamics, the Hadamard-Rybczynski equation gives the terminal velocity of slowly moving spherical bubble through an ambient fluid. It is named after Jacques Hadamard and W. Rybczynski:

:$W\_b\; =\; frac\{2\}\{3\}\; frac\; \{R^2\; g\; (\; ho\_b\; -\; ho\_o)\}\{mu\_o\}\; frac\; \{mu\_o\; +\; mu\_b\}\{2mu\_o\; +\; 3mu\_b\}$where
* $R$ is the radius of the buble.
* $g$ the gravitational acceleration.
* $ho\_b$ the density of the bubble.
* $ho\_o$ the density of the ambient fluid.
* $mu\_b$ the viscosity of the bubble.
* $mu\_o$ the viscosity of the ambient fluid.

The Hadamard-Rybczynski equation can be derived from the Navier-Stokes equation by considering only the buoyancy force and drag force acting on the moving bubble. The surface tension force and inertia force of the bubble are neglected. [cite book |last=Clift, R. C., Grace, B. J., and Weber, M. E.,|first= |title=Bubbles, Drops, and Particles |publisher=Dover Publications |year=2005 |isbn=978-0486445809]

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