Analysis of the dripping-jetting transition in compound capillary jets

We examine the behaviour of a compound capillary jet from the spatio-temporal linear stability analysis of the Navier Stokes equations. We map the jetting dripping transition in the parameter space by calculating the Weber numbers for which the convective/absolute instability transition occurs. If the remaining dimensionless parameters are set, there are two critical Weber numbers that verify Brigg's pinch criterion. The region of absolute (convective) instability corresponds to Weber numbers smaller (larger) than the highest value of those two Weber numbers. The stability map is affected significantly by the presence of the outer interface, especially for compound jets with highly viscous cores, in which the outer interface may play an important role even though it is located very far from the core. Full numerical simulations of the Navier Stokes equations confirm the predictions of the stability analysis.