Shape of a Meniscus in a Rotating Vertical Tube

Abstract

The shape of the meniscus separating two immiscible fluid phases in a rotating vertical, cylindrical tube has been calculated numerically from Laplace's equation of capillarity for the case of complete wetting of the tube wall by the lower fluid. Values of the experimentally most accessible quantity, namely the vertical displacement of the bottom of the meniscus, are presented in a detailed table as a function of speed of rotation and capillary constant. Measured displacements are in good agreement with theoretical predictions. The numerical data can be used to determine surface and interfacial tensions. The method has certain experimental advantages over the well-established method of spinning drops in a horizontal tube. However, an error analysis indicates, and the experiments confirm, that the method becomes clearly inferior for low interfacial tensions, because of the increasingly dominant influence of gravity under these conditions. The influence of incomplete wetting is also briefly considered.