| In this investigation, fluid dynamics of a spherical particle in a rotating liquid sphere is studied. Such problems arise during protein crystal growth by the containerless approach in which a drop of protein solution is levitated against gravity, and rotated steadily by a torque from an acoustic field. Viscosity of the solution is assumed to be sufficiently high such that viscous force dominates and the second-order effects in the acoustic field do not penetrate the drop surface. The analysis is carried out at very small Reynolds and Taylor numbers for which the fluid flow is treated by Stokes approximation. With a given geometric configuration, the velocity field is calculated and used to determine the particle velocity at a given time. By integrating the particle velocity, the particle path is obtained and used for optimizing the rotation rate of the drop in an attempt to keep the particle fully contained in the drop.; In addition, the transient dynamics of a rotating levitated liquid drop in unbounded gaseous fluid is investigated. A liquid drop is considered to experience two different fundamental transients, one when the torque is turned off and another when the torque is turned on. The motion of the fluids in the drop interior and surroundings is described by the Stokes equations with the time-derivative term included. The solutions are obtained analytically by the Laplace transform technique. The results show that the transient effects caused by the applied torque are relatively small for the high-viscosity solution considered. Hence, for most applications of containerless protein crystal growth, the liquid drop may be assumed to rotate like a solid body while allowing the solid particle relative motion within that framework. |
