Studies on Droplet Deformation and Breakup. I. Droplet Deformation in Extensional Flow

Abstract

The extensional deformation of a viscoelastic droplet suspended in a viscoelastic medium was investigated, both theoretically and experimentally. A theoretical analysis was carried out on the deformation of a droplet suspended in a steady extensional flow field, where both fluids may be represented by the second‐order fluid model. The study took into account the effects of the elasticity, viscosity, and interfacial tension of the fluids concerned. The shape of a deformed droplet is determined by solving the equations of motion for both fluids (droplet phase and medium). A perturbation technique was employed and the iteration method was used to determine the shape of the droplet undergoing extensional deformation. Series solutions of stream function inside and outside the droplet, pressure distribution around the droplet, and the deformation of the droplet were obtained. For the experimental study, a transparent flow channel consisting of a conical section and a straight cylindrical tube was constructed. Along its central axis, the conical section provides extensional flow. Droplets of known volume were injected in the conical section at the centerline of the flow channel, through which a viscoelastic fluid was flowing at a constant flow rate. The deformation patterns of droplets were recorded on both movie and still films as they were traveling along the centerline of the conical section. Tracer particles were used to determine the axial velocity profiles. The suspending liquids were aqueous solutions of polyacrylamide at various concentrations (viscoelastic fluids) and corn syrup (Newtonian fluid). For viscoelastic droplets, polyisobutylene dissolved in decalin at various concentrations was used, and for Newtonian droplets, Indopols and benzene were used. It was observed that the droplets, initially spherical, were slightly deformed in the upper section of the cone and greatly elongated at the entrance region of the cylindrical tube. The viscoelastic droplets were less deformable than the Newtonian droplets, and highly viscoelastic media gave rise to large deformations of droplets. The deformability of droplets was analyzed based on the flow conditions and the rheological properties of the fluids concerned. A comparison is made between the theoretically predicted and experimentally observed shapes of droplets in the conical section, only where extension rate is constant.