Evolution of a Liquid Drop in a Spinning Drop Tensiometer

Abstract

To obtain desired material properties, a blend of two mostly incompatible polymers is often used. The blend morphology developed during the mixing process of molten polymers is strongly influenced by interfacial tension between the polymers. A spinning drop tensiometer is commonly used to measure the interfacial tension between two polymeric liquids. In this study a numerical method is developed which simulates the evolution of a liquid drop in a spinning drop apparatus. The Navier-Stokes equations are solved with a finite element formulation. A mixed Lagrangian and Eulerian technique is used to deal with the moving interface. The computation domain is remeshed and the flow field is interpolated to avoid mesh entanglement as drop deforms. The simulation generates relaxation curves for the radius and the length of the drop. The numerical results show that the shear stress on the drop surface is quite important. A simple theory of relaxation is then formulated which takes account of the shear stress on the surface of the cylindrical drop. It is found that the exponent for the relaxation of the drop depends on the interfacial tension, the equilibrium radius of the drop, the viscosities of both fluids, and the geometric ratios of the length to the radius of the drop and of the radius of the container to the radius of the drop.