Optical analysis of the spinning drop

Abstract

The accuracy with which the interfacial tension between two immiscible fluid phases can be determined by the spinning drop method is limited by the accuracy with which the spinning drop diameter can be found. Thus it is important to know the factor by which the cylindrical sample tube and its content magnify the on-axis drop or bubble. By the rigorous ray-tracing method of geometric optics, we have analyzed the image formation and magnification factor of the spinning drop. Our analysis shows that when drop, outer wall, and inner wall of the tube are concentric, the ratio of the diameter of the image, as measured by a traveling microscope, to the diameter of the drop is exactly the refractive index of the denser fluid surrounding the drop. Our analysis also reveals that the image, a virtual one, is formed concentric with the drop. We have also analyzed the effect of eccentricity of the walls of the sample tube on the magnification factor.