Negative normal stress elasticity of emulsions of viscous drops at finite inertia

The relation between the normal stress and the imposed strain for a Newtonian emulsion in an oscillating extensional flow is computed at finite Reynolds numbers using numerically simulated drop geometry. The interfacial stress was determined using Batchelor's formalism. In the presence of inertia, the phase between the stress and the strain deviates from Stokes's flow, and leads to a negative elastic modulus at small frequencies. The results are explained by a mass-spring-dashpot model.