Initial conditions to study the temporal behavior of a viscoelastic liquid jet under perturbation

We study the behavior of a viscoelastic liquid jet. To that end, we carry out a temporal stability analysis. The eigenvalue problem has already been solved and is reported in Cottier et al. (2019), but does not provide a complete description of the jet's behavior. In this paper, we propose two different sets of initial conditions to close the corresponding initial-value problem. These conditions are determined by formulating the different quantities that can be imposed over the base flow, and making a correspondence with the expression of these quantities found by solving the eigenvalue problem, evaluated at the initial time. Here the imposed quantities are considered to hold on the jet's surface position, on the axial flow velocity, and on the axial normal extra stress within the flow. After giving a general formulation of the three initial conditions, two different initial configurations are distinguished: the pure deformation and the pure impulse configuration. A linearization of the conditions leads us to the determination of the analytical expressions of the first-order flow quantities in function of control parameters determining the choice of the initial configuration. The reduction of the initial conditions to the Newtonian case is valid and does not induce any physical change at the initial time. An application of the initial conditions is made upon a given liquid jet and the visualization of the flow quantities allows a comparison between the pure deformation and the pure impulse configuration.