Faraday Wave Singularities Trigger Microbubble Jetting

Abstract

Wall-attached bubbles can produce repeated jets under gentle ultrasound stimulation through the Faraday instability. We identify three distinct jetting regimes defined by the jetting frequency and the bubble surface topology. We demonstrate that these jets form via flow-focusing singularities following two distinct collapse modes of the bubble interface: conical, producing a jet towards the substrate, or parabolic, generating a pair of oppositely directed jets. Scaling laws governing these collapse events are derived, revealing a universal self-similar structure governed by inertia and capillarity. Furthermore, we establish the dependence of the interface acceleration for jetting on driving frequency and characterise the jet speed as a function of Faraday wave height and bubble size. These findings may inform the design of low-power biofilm removal ultrasound systems and contribute to improved safety in targeted drug delivery.

Figures (5)

• Figure 1: Experimental setup. (A) Air, (B) Bubble, (BG) Bubble generator, (C) Camera, (CO) Condenser, (DW) Deionised water, (GC) Glass capillary, (LI) Laser illuminator, (OL) Objective lens, (SF) Sheath flow, (SR) Sound reflector, (TL) Tube lens, (US) Ultrasound transducer, (W) Water.
• Figure 2: (a) Map of jetting regimes of wall-attached bubbles driven by ultrasound for a range of bubble equilibrium radii and driving pressures. (0) Spherical oscillations without jetting. (I) Half-harmonic jets directed towards the substrate. (II) Half-harmonic bubble splitting with Worthington-like jet pairs formation. (III) Harmonic jets directed against the wall. The coloured area represents the experimentally-determined parameter space for bubble jetting. The red line indicates the resonant bubble size (for details, see Ref. Cattaneo2025ShapeBubblesb). The dashed line marks the theoretical transition between bubble sizes exhibiting shape modes of degree $l=1$ and those with higher-degree modes (for details, see Ref. Cattaneo2025ShapeBubblesb). (b) Image sequences of the three jetting regimes. Red arrows highlight jets or bubble splitting.
• Figure 3: (a) Image sequence illustrating the conical collapse of the bottom lobe of the shape mode, culminating in a singularity from which a single jet emerges. (b) Image sequence illustrating the conical collapse of the shape mode bottom bowl, culminating in a singularity from which a jet pair emerges. (c),(d) Collapsing cavity profiles at ten time instants preceding the singularity, spaced 0.1µs apart, extracted from (a),(b). Darker curves occur later in time. $r$ and $z$ are physical coordinates; $\mathcal{R}$ and $\mathcal{Z}$ are the rescaled ones. Dashed lines indicate conical and parabolic profiles.
• Figure 4: Bottom lobe acceleration for visually identified jetting events across bubble equilibrium radii at two ultrasound frequencies: 30kHz (from our previous study Cattaneo2025ShapeBubblesb) and 100kHz. The dimensionless acceleration $\mathcal{A}$ is rescaled by $\mathcal{W}_{\mathrm{d}}^{4/3}$, with $\mathcal{W}_{\mathrm{d}}$ as the dimensionless driving angular frequency. The red line indicates the frequency-independent, acceleration threshold for jetting.
• Figure 5: (a) Jet speed from conical collapse as a function of bottom lobe height. (b) Jet pair speed from parabolic collapse as a function of bubble equilibrium radius at constant ultrasound pressure $p_{\rm a} = 26.67kPa$. Dashed lines indicate the minimum threshold for jet formation. Red lines mark critical or resonant conditions.