SPIN-UP FROM REST OF A MIXTURE

A cylindrical container, filled with a homogeneous suspension of heavy particles in a fluid, is instantaneously set into rapid rotation around its axis of symmetry. The subsequent mixture motion is investigated within the framework of an averaged continuum approach, by asymptotic and numerical solutions of the "mixture" and "two-fluid" models, respectively. The resulting velocity field is similar to that of a homogeneous fluid [J. Fluid Mech. 20, 383 (1964)], where three regions can be distinguished: a nonrotating, shrinking, core (I); the embedding, spinning but still undeveloped domain (III); and the Ekman layers (II), which transport fluid from region I into region III. This flow field induces a novel and peculiar solution for the volume fraction α, whose details are governed by λ (=ratio of separation to spin-up time intervals). The results indicate that the initial α(0) prevails in regions I and II, but considerable separation takes place in domain III - provided that λ is not large. Therefore, during the spin-up process, [α/α(0)] decays substantially not only with time, but also with the axial distance from the endplates (Ekman layers) and with radial distance from region I. Moreover, if λ≪1, [α/α(0)]≪1 is expected in region III. © 1990 American Institute of Physics.