Time-dependent dynamical behavior of surface tension on rotating fluids under microgravity environment

Time dependent evolutions of the profile of free surface (bubble shapes) for a cylindrical container partially filled with a Newtonian fluid of constant density, rotating about its axis of symmetry, have been studied. Numerical computations of the dynamics of bubble shapes have been carried out with the following situations: (1) linear functions of spin-up and spin-down in low and microgravity environments, (2) step functions of spin-up and spin-down in a low gravity environment, and (3) sinusoidal function oscillation of gravity environment in high and low rotating cylinder speeds. The initial condition of bubble profiles was adopted from the steady-state formulations in which the computer algorithms have been developed by Hung and Leslie/1/, and Hung et al./2/