Capillary Hydraulic Jump in a Viscous Jet

Abstract

Stationary waves in a cylindrical jet of a viscous fluid are considered. It is shown that when the capillary pressure gradient of the term with the third derivative of the jet radius in the axial coordinate is taken into account in the expression, the previously described self-similar solutions of hydrodynamic equations arise. Solutions of the equation of stationary waves propagation are studied analytically. The form of stationary soliton-like solutions is calculated numerically. The results obtained are used to analyze the process of thinning and rupture of jets of viscous liquids.

Investigation of the Structure of Waves Generated by a $\delta$-perturbation of the Surface of a Capillary Jet

“…The liquid jet is unstable with respect to long-wave perturbations of its surface. This phenomenon is used to generate droplet flows in many technical applications, including chemical technology [1,2], heat removal systems [3][4][5][6], inkjet printers [7][8][9], engine nozzles [10][11][12][13], etc. For theoretical modeling of the process of capillary disintegration of jets into drops, approximate quasi-one-dimensional equations are used, obtained by asymptotic expansion of the system of Navier -Stokes equations.…”

“…For a theoretical description of the regularities of the decay of a jet flowing out at a lower velocity, it is necessary to use the theory of convective instability [3]. In this case, it is assumed that perturbations of the jet surface in one way or another (with the help of acoustic or electromagnetic fields, nozzle vibration, periodic change in the fluid outflow rate, etc.)…”