Circulating flows inside a drop under time-periodic nonuniform electric fields

The circulating flows formed inside a spherical drop under time-periodic nonuniform electric fields are considered. For simplicity, it is assumed that there are axisymmetric electric fields and that the flow fields are in the Stokes flow regime. An analytical solution of the streamfunction distribution inside and outside the drop is obtained. The flow field is found to be dependent on the frequency of the time-periodic electric field and the ratios of the material properties such as the viscosity, the electrical conductivity, and the electrical permittivity. As part of the solution, an analytical expression of the dielectrophoretic migration velocity of a drop under a time-periodic electric field is also obtained. The result shows an interesting physics-that dielectrophoretic migration is possible in a time-periodic electric field even in the situation where dielectrophoresis would be impossible in a static electric field. By using the analytical solution of the streamfunction, fluid mixing inside a drop is analyzed based on the Poincare maps. The mass transfer enhancement factor due to fluid mixing has also been computed by solving the unsteady mass transfer equation numerically. The existence of an optimal frequency has been confirmed as in other mass transfer enhancement processes by time-periodic forcing. (C) 2000 American Institute of Physics. [S1070-6631(00)01108-9].