Dynamics of spheroidal bubbles close to a solid boundary

Abstract

Deviations from spherical symmetry lead to the formation of liquid jets during the collapse of cavitation bubbles. The asymmetry can be introduced into the problem e.g. by nearby boundaries, but also by an initial non-spherical shape of an (over-expanded) bubble.

In this talk we revisit the problem of collapsing bubbles with initially spheroidal shape. To this end, over-expanded (sub-)millimeter sized bubbles of spheroidal shape are placed in a still liquid at some normalized distance D* from a flat solid boundary. We present numerical results from a finite volume method. Previous work, as e.g. [1,2], is extended by following the dynamics beyond the first instant of liquid-liquid impact and by considering also cases, where the initial spheroid would be cut by the solid. The collapse of spheroidal bubbles in a free liquid already is a highly complex process. Depending on the parameters (aspect ratio) of the intial bubble shape different types of jets (axial and annular) can develop. In the course of jet evolution simply connected or toroidal bubbles can be split-off the main bubble. For initially oblate spheroids, cylindrically converging flow impacts at the axis of symmetry, thereby ejecting very fast, axial liquid jets into the bubble. High pressures with subsequent emission of shock waves are generated at the impact events and the final collapse of the torus bubble(s). Adding a solid wall further adds to the complexity of the dynamics. Our primary interest are those configurations of bubbles close to/right at the solid, where the collapse dynamics involves the formation of very fast and thin jets directed towards the solid, as described in [3,4] for bubbles expanding and collapsing very close to the solid. Experimental confirmation for these fast jets with laser-generated bubbles has been given in [5,6] and in [7].

[1] Voinov, O.V. and Voinov, V. V.: On the process of collapse of a cavitation bubble near a wall and the formation of a cumulative jet. Sov. Phys. Dokl. 21 (1976), 133

[2] Aganin, A.A., Ilgamov, M. A., Kosolapova, L. A. and Malakhov, V. G.: Dynamics of a cavitation bubble near a solid wall. Thermophys. Aeromech. 23 (2016), 211

[3] Lechner, C., W. Lauterborn, W., Koch, M. and Mettin, R.: Fast, thin jets from bubbles expanding and col- lapsing in extreme vicinity to a solid boundary: A numerical study. Phys. Rev. Fluids 4 (2019), 021601

[4] Lechner, C., Lauterborn, W., Koch, M. and Mettin, R.: Jet formation from bubbles near a solid boundary in a compressible liquid: Numerical study of distance dependence. Phys. Rev. Fluids 5 (2020), 093604

[5] Koch, M.: Laser cavitation bubbles at objects: Merging numerical and experimental methods. PhD thesis, Georg-August-Universität Göttingen, Third Physical Institute (2020).

[6] Koch, M., Rosselló, J. M., Lechner, C., Lauterborn, W., Eisener, J. and Mettin, R.: Theory-assisted op- tical ray tracing to extract cavitation-bubble shapes from experiment. Exp. Fluids 62 (2021), 60

[7] Reuter, F. and Ohl, C.-D.: Supersonic needle-jet generation with single cavitation bubbles. Appl. Phys. Letters 118 (2021), 134103