Weakly nonlinear instability of a Newtonian liquid jet

International audience; We investigate the weakly nonlinear instability of an axisymmetric Newtonian liquid jet. First nonlinear studies of the capillary instability of liquid jets revealed the importance of higher-order contributions to the jet deformation in order that the nonlinear process of satellite droplet formation can be described. A recent study on the weakly nonlinear instability of planar Newtonian sheets revealed the role of viscosity in the sheet stability behavior and showed a complicated influence [1]. We study the instability of a liquid jet as the axisymmetric counterpart of the sheet in search for corresponding insight into the role of the liquid viscosity in the jet instability mechanism. Our present analysis is restricted to second order and to Newtonian liquids. Ultimately the aim of our work is to look at liquid jet breakup for viscoelastic liquid. Insofar the present contribution is to be seen as a state-of-progress report.