0
2013
Impact Factor

    Capillary Hydraulic Jump in a Viscous Jet

    Received 29 April 2019; accepted 16 July 2019

    2019, Vol. 15, no. 3, pp.  221-231

    Author(s): Safronov A. A., Koroteev A. A., Filatov N. I., Safronova N. A.

    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.
    Keywords: instability, capillary flows, viscous jet, stationary waves
    Citation: Safronov A. A., Koroteev A. A., Filatov N. I., Safronova N. A., Capillary Hydraulic Jump in a Viscous Jet, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 3, pp.  221-231
    DOI:10.20537/nd190302


    Download File
    PDF, 679.77 Kb

    References

    [1] Koroteev, A. A., Safronov, A. A., and Filatov, N. I., “Influence of the Structure of a Droplet Sheet on the Capacity of Frameless Space Radiators and the Efficiency of the Power Units”, High Temp., 54:5 (2016), 767–770  mathnet  crossref  mathscinet  elib; Teplofizika Vysokikh Temperatur, 54:5 (2016), 817–820 (Russian)  mathscinet
    [2] Safronov, A. A., “Features of Capillary Breakup of a Liquid Jet at Ohnesorge Numbers Larger Than Unity”, J. Eng. Phys. Thermophys., 90:1 (2017), 167–175  crossref  mathscinet  elib; Inzh.-Fiz. Zh., 90:1 (2017), 176–185 (Russian)  mathscinet
    [3] Driessen, T., Jeurissen, R., Wijshoff, H., Toschi, F., and Lohse, D., “Stability of Viscous Long Liquid Filaments”, Phys. Fluids, 25:6 (2013), 062109, 7 pp.  crossref  mathscinet  adsnasa
    [4] Tjahjadi, M., Ottino, J. M., and Stone, H. A., “Satellite and Subsatellite Formation in Capillary Breakup”, J. Fluid Mech., 243 (1992), 297–317  crossref  adsnasa
    [5] Grigoriev, A. L., Koroteev, A. A., Safronov, A. A., and Filatov, N. I., “Self-Similar Patterns of Subsatellites Formation at the Capillary Breakup of Viscous Jets”, Thermophys. Aeromech., 25:4 (2018), 575–585  crossref
    [6] van der Bos, J. A., van der Meulen, M. P., Driessen, T. W., van den Berg, M., Reinten, H., Wijshoff, M. A., and Lohse, D., “Velocity Profile inside Piezoacoustic Inkjet Droplets in Flight: Comparison between Experimental and Numerical Simulation”, Phys. Rev. Appl., 1:1 (2014), 014004, 9 pp.  crossref  adsnasa
    [7] Eggers, J. and Todd, F. D., “Drop Formation in a One-Dimensional Approximation of the Navier – Stokes Equation”, J. Fluid Mech., 262 (1997), 205–221  crossref  mathscinet  adsnasa
    [8] Eggers, J. and Villermaux, E., “Physics of Liquid Jets”, Rep. Prog. Phys., 71:3 (2008), 036601, 79 pp.  crossref  adsnasa  elib
    [9] Eggers, J., “Drop Formation: An Overview”, Z. Angew. Math. Mech., 85:6 (2005), 400–410  crossref  mathscinet  zmath
    [10] Brenner, M. P., Shi, X. D., and Nagel, S. R., “Iterated Instabilities during Droplet Fission”, Phys. Rev. Lett., 73:25 (1994), 3391–3394  crossref  adsnasa
    [11] Brenner, M. P., “Stability of a Viscous Pinching Thread”, Phys. Fluids, 24:7 (2012), 072103, 11 pp.  crossref
    [12] Strutt, J. W. (3rd Baron Rayleigh), The Theory of Sound, v. 2, 2nd ed., Dover, New York, 1945, 504 pp.  mathscinet  zmath
    [13] Nayfeh, A. H., “Nonlinear Stability of a Liquid Jet”, Phys. Fluids, 13:4 (1970), 841–847  crossref  zmath  adsnasa
    [14] Wang, F., Tschukin, O., Marques, G. C., Selzer, M., Aghassi-Hagmann, J., and Nestler, B., Breakup of Liquid Jets and the Formation of Satellite and Subsatellite Droplets, 2018, arXiv: 1805.06818 [physics.flu-dyn]
    [15] Bazilevskii, A. B. and Rozhkov, A. N., “Dynamics of the Capillary Breakup of a Bridge in an Elastic Fluid”, Fluid Dyn., 50:6 (2015), 800–811  crossref  mathscinet  elib
    [16] Argentina, M., Cohen, A., Bouret, Y., Fraysse, N., and Raufaste, C., “One-Dimensional Capillary Jumps”, J. Fluid Mech., 765 (2015), 1–16  crossref  mathscinet  adsnasa  elib
    [17] Bhagat, R. K., Jha, N. K., Linden, P. F., and Wilson, D., I., “On the Origin of the Circular Hydraulic Jump in a Thin Liquid Film”, J. Fluid Mech., 851 (2018), R5, 11  crossref  mathscinet  zmath



    Creative Commons License
    This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License