Mikhail Tsventoukh2020-09-16 15:57 Dr. Uimanov, thank you very much for the question. I've just now looked your presentation. The used linear dependence (r_0 - vt) being close to that results from your detailed simulation (p 13) and to results of recent hydrodynamics work at PRL 2018
Mikhail Tsventoukh2020-09-16 15:57 Is it someshat 'universal' shape i.e. the angle at the liquid 'needle' tip?
Igor Uimanov2020-09-16 15:57 (For Mikhail)Yes, approximate analytical solutions have been obtained near the separation of the drop from the jet both in the inviscid and in the viscous case (see, for example, the equation in  and Fig. 51). When the neck radii are less than the viscous scale, the solutions coincide and give a certain cone angle. However, then the viscosity begins to prevail, which leads to a stretching of the neck. But for your estimations, i would like to suggest that it is more important to choose the correct speed of reduction of the neck radius. The neck formation process has two stages. In the first stage, the neck radius decreases linearly with time. In the second nonlinear stage, the neck radius decreases much faster. The same fully applies to the development of thermal instability at minimal current density which can lead to an explosion of the neck. A significant neck heating at minimal current density occurs only in the nonlinear stage of its formation. Approximately at this stage, you can use a linear relationship, but with a speed several times higher. This is supported by my results of on-time simulation of heating and droplet pinch-off. The point is that droplet breakup is caused by the development of the Rayleigh-Plateau instability and is controlled by surface tension forces. But when the neck heated, the surface tension coefficient decreases and tends to zero at a critical temperature. This slows down the rate of droplet pinch-off, but does not stop the process due to the inertia of the liquid metal. Therefore, heating slightly “lianirizes” the nonlinear stage. It is also important to take into account the convective heat transfer from the neck to the droplet and take into account the finite radius of the neck due to еhermal ﬂuctuations, that is responsible for the random breakup of the droplet-jet neck.
Igor Uimanov2020-09-16 15:57 (For Mikhail) eq. 203 and Fig. 51 in [J. Eggers and E. Villermaux, “Physics of liquid jets,” Rep. Prog. Phys., vol. 71, p. 036601 (79pp), 2008, doi:10.1088/0034-4885/71/3/0366] .