Numerical investigation of the rheology of a dilute emulsion of drops in an oscillating extensional flow

The rheology of a dilute emulsion of viscous drops in an oscillating extensional flow is investigated. Deforming drop shape is computed using a front tracking finite difference method. Excess stresses due to drops are determined using Bachelor's formula neglecting drop-drop interactions. We present and discuss the relations between the excess stress and the applied strain rate. We explore the linear extensional rheology by computing extensional storage and loss moduli. The effects of frequency and surface tension variations are discussed and compared with analytical models of Oldroyd and Yu and Bousmina. We find that the nature of the excess interfacial stress depends on the relative magnitudes of the time period of oscillation and the relaxation time of the droplet. The excess stress is predominantly elastic (viscous) if the period is much smaller (larger) than the relaxation time. These phenomena are explained using the detail drop dynamics.