Transient and steady state three-dimensional drop shapes and dimensions under planar extensional flow

Drop shapes and dimensions in transient and steady states have been studied using a four-roll mill flow apparatus with three-dimensional imaging and real-time derivative edge detection. The deformed drops are approximately ellipsoidal for viscosity ratios of lambda > 0.1 with about 4% maximum deviation of actual drop volume from ellipsoidal volume. For lambda < 0.1, drops retain their ellipsoidal shape up to deformation of similar to 0.5, above which they show progressive deviation from the ellipsoidal shape. The measured length, breadth, and width of deformed drops were compared to predictions of various drop deformation theories. The limit of deformation within which theories predict drop dimensions with 5% accuracy has been tested for 10(-4) < lambda < 10(2). The ellipsoidal model of Maffettone and Minale (1998) gives the best prediction for lambda < 0.3, while the second order theory of Barthes-Biesel and Acrivos (1973) gives the best overall prediction for X > 0.3. The application of some theories to the determination of interfacial tension and drop viscosity is discussed. (C) 2003 The Society of Rheology.