Abstract
The reaction of ensembles of spherical particles (bubbles, drops, balls) embedded in a fluid to residual accelerations is studied. The creeping flow approximation is applied. The Fourier transform of the residual acceleration from the time representation to the frequency representation is used. The response of the particles in the frequency representation is calculated. Eventually the reverse Fourier transformation from the frequency representation to the time representation is applied. If a single particle is subjected to a constant external force, its velocity rises linearly in time and approaches the final Stokes velocity inversely proportional to the square root of time. Two identical particles aligned in the direction of a periodic external force move with equal velocity and phase shift. Pushing of the first particle by the second is as strong as pulling of the second particle by the first. The velocity of two closely spaced bubbles is larger by a factor 1/log2 than that of single bubbles. When several equally spaced particles are subjected to a periodic force, the inner particles assume a higher velocity than the outer particles, such that the condition of equal spacing gets violated and the former particles strike the latter.
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