Abstract
Impinging gas jets can induce depressions in liquid surfaces, a phenomenon familiar to anyone who has observed the cavity produced by blowing air through a straw directly above a cup of juice. A dimple-like stable cavity on a liquid surface forms owing to the balance of forces among the gas jet impingement, gravity and surface tension1,2. With increasing gas jet speed, the cavity becomes unstable and shows oscillatory motion, bubbling (Rayleigh instability) and splashing (Kelvin–Helmholtz instability)3,4. However, despite its scientific and practical importance—particularly in regard to reducing cavity instability growth in certain gas-blown systems—little attention has been given to the hydrodynamic stability of a cavity in such gas–liquid systems so far. Here we demonstrate the stabilization of such instabilities by weakly ionized gas for the case of a gas jet impinging on water, based on shadowgraph experiments and computational two-phase fluid and plasma modelling. We focus on the interfacial dynamics relevant to electrohydrodynamic (EHD) gas flow, so-called electric wind, which is induced by the momentum transfer from accelerated charged particles to neutral gas under an electric field. A weakly ionized gas jet consisting of periodic pulsed ionization waves5, called plasma bullets, exerts more force via electrohydrodynamic flow on the water surface than a neutral gas jet alone, resulting in cavity expansion without destabilization. Furthermore, both the bidirectional electrohydrodynamic gas flow and electric field parallel to the gas–water interface produced by plasma interacting ‘in the cavity’ render the surface more stable. This case study demonstrates the dynamics of liquids subjected to a plasma-induced force, offering insights into physical processes and revealing an interdependence between weakly ionized gases and deformable dielectric matter, including plasma–liquid systems.
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Data availability
The authors declare that the data supporting the findings of this study are available within the paper. All additional raw and derived data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
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Acknowledgements
This work was partially supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (grant number 2020R1C1C1004645). This work was also supported by Slovenian Research Agency (ARRS) and the High-Risk and High-Return Project funded by KAIST. We acknowledge the assistance of J. Olenik and B. Krašovec from the Jožef Stefan Institute in the use of supercomputing facilities. We also thank Hyoungsoo Kim and C. Bae at Department of Mechanical Engineering, KAIST for private communications and asistance with the fast camera.
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S.P. and W.C. conceived the experiments. S.P. conducted all experiments, and S.P. and H.L. performed all numerical simulations. All authors analysed the results. S.P., W.C. and U.C. prepared the manuscript and figures, and all authors contributed to the compilation and review of the manuscript.
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Extended data figures and tables
Extended Data Fig. 1 Modelled plasma–water system.
a, Schematic illustration of the experimental set-up consisting of the gas/plasma jet system and shadowgraph imaging system. The conductive nozzle flowing helium gas was connected to the high-voltage, nanosecond-pulse switching system. The direction of the helium gas jet ejected from the nozzle was normal to the free surface of water poured into a transparent dielectric dish sitting on the grounded metallic plate. b, Simplified schematic of the system with specified dimensions, where din = 0.6 mm, dout = 1 mm, hg = 2.2 mm and hd = 10 mm (not to scale). The distance between the end of the nozzle and the water surface, which strongly affects the plasma characteristics, was maintained throughout the experiments; identical set-ups were used for experiments with and without plasma generation. c, Conductivity of the distilled water used in our experiments. Data in c are shown as mean ± s.d. (n = 3), which were measured by a 4-point electrode (Orion Versa Star Pro with a conductivity cell 013005MD) over different experiment times. Note that some errors are smaller than the size of the symbol.
Extended Data Fig. 2 Shadowgraph images of the water surfaces.
a, Depression of the water surfaces owing to helium gas jets ejected from the nozzle, depending on the gas flow rate. The flow rates are 0.6, 0.7, 0.8, 0.9 and 1.0 slpm from left to right. b, Cavity deformation caused by weakly ionized helium jets. The flow rate of neutral (non-ionized) helium gas was fixed at 0.90 slpm. The widths of the 10-kHz voltage pulse applied to the nozzle were set at 1–50 μs, and the pulse height was fixed at 3.0 kV. A comparison of the cavity shapes is provided in Fig. 2. c, Corresponding voltage waveforms with a constant pulse height and various pulse widths in the range 0.5–50.0 μs. Note that the pulse rise and fall times were in the range 50–60 ns. d, Surface charge accumulated on water surfaces owing to different pulsed plasma jets.
Extended Data Fig. 3 Nanosecond-resolved images of the plasma jets.
Quantification of the plasma jet spatiotemporal dynamics (Extended Data Fig. 3) provides a first step towards understanding why the plasma-forced cavity depends on the pulse duration and, furthermore, how the cavity remains stable. a, b, Time-resolved sequential (left panels) and time-integrated images (right) of the plasma jets driven by a pulse with 1 μs (a) and 50 μs (b) widths. The leftmost frame corresponds to time t = 0. The iCCD camera was operated with a 4-ns gate width (exposure), and the time interval between successive frames is 4 ns. The intensity of all frames was normalized by each frame. The scales on the y axis for each panel are identical, and the gas nozzle with an outer diameter of 1.0 mm is used as a substitute for scale bars. c–f, Spatiotemporal dynamics of positive (cathode-directed) pulsed streamers during the on-pulse phase with pulse widths of 1 μs (c), 5 μs (d), 20 μs (e) and 50 μs (f). Here, t = 0 corresponds to the beginning of the voltage pulse. All profiles were extracted from iCCD images along the jet axis, and the intensity was individually normalized by each profile. The time intervals between adjacent frames are 2 ns (left panels) and 15 ns (right) with 4-ns and 15-ns gate widths (exposure) of the iCCD camera, respectively. Note that a negative (anode-directed) pulsed streamer appears at t > 1 μs in the right panel of c. g, Simplified diagram of the FEHD-induced water cavity along with the relevant circuit model. The plasma–water system can be described by a series circuit consisting of two resistors, Rh>0 and Rh<0, and a capacitor Cw.
Extended Data Fig. 4 Numerical simulation of the flow dynamics in the two-phase fluid system.
a, Schematic diagram of the computational domains and boundaries used in the flow model. This configuration, which is almost identical to the experimental set-up, has a cylindrical symmetric axis at r = 0. The boundary A–B that represents a dish wall includes a Navier-slip wall at |r| = 15 mm and a no-slip wall at h = −5 mm. The boundaries A–C and D–B, which are mathematical open boundaries, implicitly impose a zero normal stress for the flow equations and fixed mass fractions of air molecules for the transport equations to describe exterior boundaries in contact with a tremendous reservoir of air. b, The flow model result with an average gas speed vi of 47.25 m s−1 partly shows the distribution of a helium mole fraction (r < 0, left) and gas flow speed (r > 0, in units of m s−1, right) with a deformed, balanced water surface at t = 2 s. c, Depression of the water surface owing to the helium gas jet, obtained from our numerical result of the flow model with vi = 47.25 m s−1 (r < 0), excellently agrees with the experiment (r > 0) with 0.90-slpm helium gas flow rate.
Extended Data Fig. 5 Changes in the water surface characteristics with increasing gas jet speed.
a–d, Calculated total stress (a, b) and curve angle (c, d) along the distance of the water surface S, depending on vi = 39.75–52.25 m s−1 in steps of 2.5 m s−1. Results imposed on the corresponding gas–water boundaries in cylindrical coordinates (a, c) are replotted (b, d) as one-dimensional profiles. Colour-scaled total stress and curve angle in a and c are in units of mN mm−2 and degrees, respectively. The origin S = 0 corresponds to r = 0. Note that the curves obtained with vi = 47.25 m s−1 are relevant to the experimental result with 0.90 slpm, which is the critical flow rate within the stable regime (Extended Data Fig. 9). e, Computed gas–water boundary with vi = 47.25 m s−1 without ionizing gas. Two arbitrary lines are used to extract one-dimensional profiles of the speed of helium gas flowing parallel to the deformed water surface. f, Solid curves show the speed of outflowing helium gas at each colour-matched line given in e, and corresponding spatial average flow speeds are depicted by the dashed lines. Line distance 0 corresponds to the leftmost edge of each line in e.
Extended Data Fig. 6 Numerical simulation of the pulsed helium plasma jet.
a, Maintaining the overall geometry used in the flow model (Extended Data Fig. 4a), the computational domain was tailored, as depicted by the red box for plasma modelling. In this schematic diagram, the greyscale image of the initial helium mole fraction in the plasma model (Extended Data Fig. 4b) is overlaid. A time-varying potential was applied to the nozzle boundaries, and boundary A′–B′ was grounded. Except for the electrodes and gas–water boundaries, the remaining boundaries are mathematical boundaries, where flux continuity was imposed, to truncate the computational domain. Other boundary conditions are discussed in the text. b, Voltage applied to the nozzle and discharge current obtained from the model. Rising time of the voltage pulse was assumed to be 10 ns.
Extended Data Fig. 7 Computed spatiotemporal characteristics of the pulsed plasma jet.
a–h, Plasma characteristics obtained from the plasma modelling at t = 10 ns (a–d) and t = 500 ns (e–h): logarithmic-scaled ne in units of m−3 (a, e), mean electron temperature in eV (b, f), space charge density in C m−3 (c, g) and FEHD in mN mm−3, with direction and strength given by the grey arrows (d, h). The plasma bullet, of which the front is an ion-dominant regime, appears in the early phase of the voltage pulse (a–d) and eventually reaches the water surface (e–h).
Extended Data Fig. 8 Prediction of water surface deformation in the presence of the plasma jet.
a, b, Partial 2D images of the gas flow speed (a) and the EHD force strength per unit volume (b) with the initial (t = 0; left) and stabilized water surface (t > 2 s; right), corresponding to without and with the plasma jet, respectively. The colour-scaled flow speed in a and the EHD force in b are in units of m s−1 and mN mm−3, respectively. Grey arrows and their lengths in b indicate the direction and strength of FEHD, respectively. The EHD force per unit volume was adjusted during computation to maintain the volume-integrated FEHD constant as the cavity volume expanded with time. Curves in a are streamlines that are instantaneously tangent to the velocity vector of the gas flow.
Extended Data Fig. 9 Stabilizing effect of the plasma-induced electric field on the water cavity.
a, Schematic boundary between the weakly ionized helium gas and water with an infinitesimal perturbation. This magnified configuration shows a part of the side slope with an incline angle β in the water cavity. Coloured arrows show the direction of tangential and normal components of the electric field, Etan and Enor, applied at the interface. As discussed, a sufficiently strong Etan makes the perturbed boundary move towards its origin (a dashed line), resulting in instability suppression. b, Neutral stability curves obtained using equation (1) with Enor = 0 and angle β in the range 0–90°. The critical flow speed on the y axis corresponds to vG − vL. As expressed in equation (1), Enor always produces a destabilizing effect, but its effect is negligible on the stability curve in this case. c, Tangential electric field Etan profiles computed by the plasma model along the water surface at different times. The origin of the profile distance, S = 0, equals r = 0.
Extended Data Fig. 10 Results of particle image velocimetry.
a, Sample PIV image of a subregion of the plasma jet–water system. The scattered white points indicate the probing particles (Nylon 12) with a diameter range 25–30 μm, and the intense white column is due to plasma emission. b, Velocity vector plot overlaid on a shadowgraph image. The white arrows representing the velocity vector of water flow were obtained from the set of particle images, including the image in a. Note that a symmetric pattern of water flow, showing frictional flow in the proximity of the gas cavity, and a rotational flow (vortex) far from the cavity are clearly observed. For imaging, a 10-kHz pulsed plasma jet was operated with a 3-kV pulse height and a 1-μs pulse width. c, Changes in the velocity maps of the water flow induced by pure helium gas jets, showing a linear dependence of the gas flow rate on a vortex. The vortex core linearly drifts from left to right, far from the gas jet. d, Velocity maps of the water flow induced by plasma jets depending on the pulse width, with the other parameters all fixed. Red scattered points (showing cavity areas) represent PIV void areas. The fact that plasma-induced speed increases in the rotational water flow with increasing pulse width is clearly related to the simultaneous increase in the outflow gas speed vout with vi.
Supplementary information
Supplementary Information
This file contains Supplementary Figures 1-4.
Video 1
: Water surface deformation – applying a 0.5 μs-pulsed plasma. A 1 ms-resolved video showing the initial perturbation of the water surface induced by plasma ignition with a 10 kHz voltage pulse with a 0.5 μs pulse width.
Video 2
: Water surface deformation – applying a 5.0 μs-pulsed plasma. A 1 ms-resolved video showing the initial perturbation of the water surface induced by plasma ignition with a 10 kHz voltage pulse with a 5.0 μs pulse width.
Video 3
: Water surface deformation – applying a 50.0 μs-pulsed plasma. A 1 ms-resolved video showing the initial perturbation of the water surface induced by plasma ignition with a 10 kHz voltage pulse with a 50.0 μs pulse width.
Video 4
: Water surface recovery – after removing the 50.0 μs-pulsed plasma. A 1 ms-resolved video showing the fast recovery of the water surface profile after cutting off the 50 μs-pulsed plasma.
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Park, S., Choe, W., Lee, H. et al. Stabilization of liquid instabilities with ionized gas jets. Nature 592, 49–53 (2021). https://doi.org/10.1038/s41586-021-03359-9
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DOI: https://doi.org/10.1038/s41586-021-03359-9
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