Equilibrium shapes of two-phase rotating fluid drops with surface tension

Abstract

While rotating single phase fluid drops have been thoroughly investigated, the determination of the shape of a drop consisting of two immiscible liquid phases has not been previously considered. Recently, experiments using rotating micron-scale droplets of liquid helium have been carried out where the liquid can be in a normal or superfluid state depending on the isotope of helium used. Two phases can be present if the helium is a mixture of He3 and He4. Classical results have been very useful in aiding the analysis of single phase liquid helium drops and are similarly needed for two phase drops. In this contribution, the Navier–Stokes equations with surface tension are solved numerically using the finite-element method with surface tension effects on the inner and outer interfaces. The numerical models are time-dependent but are run to a steady state to determine equilibrium shapes. It is found that with an appropriate scaling of the density and surface tension coefficient, the relationships between the angular velocity and the angular momentum and of the outer surface dimensions with angular momentum become very similar to those of a single phase fluid for a broad range of parameters. However, the shapes of the inner drops vary significantly, particularly when the volume of the inner fluid is significantly less than that of the outer fluid. Increasing the relative magnitude of the interfacial surface tension coefficient or decreasing the relative density of the inner region leads to less deformation of the inner drop relative to the outer one.