1. Introduction
Oscillation of a cavitation bubble near a liquid surface is a complex process governed by the coupling of bubble dynamics and free-surface deformation (Holt Reference Holt1977; Zhang et al. Reference Zhang, Cui, Cui and Wang2015; Saade et al. Reference Saade, Jalaal, Prosperetti and Lohse2021). When the bubble is in close proximity to the liquid surface, interfacial instability emerges as a dominant phenomenon, generating perturbations on both the bubble wall and the liquid surface (Zeng et al. Reference Zeng, Gonzalez-Avila, Voorde and Ohl2018; Wang, Wang & Wang Reference Wang, Wang and Wang2024). Ventilation occurs when the growing perturbation penetrates the liquid layer, exposing the bubble interior to the atmosphere and thereby fundamentally altering its subsequent dynamics (Stepišnik Perdih et al. Reference Stepišnik Perdih, Zupanc and Dular2019; Klein et al. Reference Klein, Kurilovich, Lhuissier, Versolato, Lohse, Villermaux and Gelderblom2020; Li et al. Reference Li, Zhao, Zhang and Han2024).
Recent experiments (Gonzalez Avila & Ohl Reference Gonzalez Avila and Ohl2016; Klein et al. Reference Klein, Kurilovich, Lhuissier, Versolato, Lohse, Villermaux and Gelderblom2020; Liang et al. Reference Liang, Jiang, Wen and Liu2020) and simulations (Wang, Duan & Wang 2015; Zeng et al. Reference Zeng, Gonzalez-Avila, Voorde and Ohl2018; Huang et al. Reference Huang, Song, Wang and Wang2024; Zeng et al. Reference Zeng, Zhang, Tan, An and Ohl2024) demonstrated that ventilation patterns may be determined by perturbations penetrating the liquid layer from either the bubble wall or the liquid surface. Zeng et al. (Reference Zeng, Gonzalez-Avila, Voorde and Ohl2018) investigated the development of liquid surface perturbation of a spherical droplet caused by laser-induced bubble oscillation. They proposed that the perturbation is induced by Rayleigh–Taylor (RT) instability and accompanied by an additional liquid jet using a three-dimensional numerical simulation. The viscosity of the liquid affects the development of the perturbation and thus affects the formation of the liquid jet. Rosselló et al. (Reference Rosselló, Reese, Raman and Ohl2023) systematically analysed the specific mechanism of the instability on the liquid surface based on experiments and numerical simulations. A bullet-jet shape of a bubble was formed after ventilation occurred. They proposed that the development of the perturbation and bubble is altered by changing the distance between the bubble and the liquid surface. Kang & Cho (Reference Kang and Cho2019) also observed the bullet-jet shape of a bubble when a spark-induced bubble is very close to the liquid surface. They modelled the motions of a jet-like surface using a scaling argument and conservation of momentum and energy. Wang et al. (Reference Wang, Li, Guo, Wang, Du, Wang, Abe and Huang2021) investigated the liquid surface perturbation of a droplet. They used a two-dimensional cylindrical geometry to provide clearer experimental observations for the perturbation and penetration. Three patterns of the droplet are proposed: splashing, ventilating and stable. They presented a theoretical model based on the bubble dynamic equation and perturbation equation to describe the evolution of the interfacial instability. Similarly, the instabilities of the bubble wall and liquid surface are also observed during the bubble oscillation near a water surface. Saade et al. (Reference Saade, Jalaal, Prosperetti and Lohse2021) proposed that the instability of the bubble wall affects bubble dynamics and leads to the splitting of the bubble. Li et al. (Reference Li, Zhang, Wang, Li and Liu2019) proposed that the instability of the liquid surface is an important factor affecting the development of the water skirt. Wang et al. (Reference Wang, Wang, Chen, Huang, Song, Zeng and Wang2025) experimentally studied the ventilation induced by bubble oscillation near a free surface at various stand-off parameters. They captured the perturbation development and penetration of the interface during the ventilation based on three-dimensional simulations. The study indicates that complete ventilation is triggered by RT instability on the bubble wall, whereas partial ventilation results from instability on the liquid surface (see figure 1). Complete ventilation is recognised by the bullet-jet shape of the bubble and a transparent splash sheet formed on the liquid surface (Rosselló et al. Reference Rosselló, Reese and Ohl2022). The partial ventilation phenomenon is identified by a non-transparent bubble interior and a broken water skirt. These findings significantly enhance our understanding of interfacial instability phenomena induced by the coupling dynamics between a cavitation bubble and a liquid surface.
Schematic diagram of three patterns of bubble dynamics near a water surface. Complete ventilation is marked by a bullet-jet shape of a bubble in (a); partial ventilation by a non-transparent bubble interior in (b); and non-ventilation corresponds to a toroidal collapse in (c).
Variations of the radius and pressure of the bubble. During the accelerated expansion stage (red regime), the higher internal pressure drives the interface outward, generating perturbations on the bubble wall. In contrast, during the decelerated expansion and contraction stages (green regime), the external pressure exceeds the internal pressure, causing inward acceleration of the interface and leading to perturbations on the liquid surface. Parameter
$p^*=\Delta p/p_{\infty }$
represents the dimensionless pressure difference between the inside and outside of the bubble, where
$p_{\infty }$
is the atmospheric pressure. Times
$T_1$
and
$T_2$
are the times when
$p^*=0$
.
According to the aforementioned studies, viscosity is a critical physical parameter that fundamentally influences perturbation growth rate and the transitions between ventilation regimes. To quantitatively elucidate the interfacial coupling-induced instability with the influence of viscosity, we develop a theoretical model that couples the perturbation equation with the bubble oscillation equation. Scaling laws for ventilation regime boundaries and ventilation time across various liquid viscosities are obtained based on the analytical solutions of perturbation development during bubble oscillation. Moreover, a scaling law for the dimensionless ventilation time
$t_v^*$
is established as a function of the dimensionless stand-off parameter
$\gamma$
and viscosity
$\nu _l$
. Here, the dimensionless stand-off parameter
$\gamma$
is defined as the distance
$h$
(from the bubble’s initial position to the liquid surface) divided by the maximum bubble radius
$R_{\textit{max}}$
, i.e.
$\gamma =h/R_{\textit{max}}$
. The theoretical predictions are validated against experimental observations.
2. Theoretical model
The RT instability arises from the acceleration of a lighter fluid into a denser one (Taylor Reference Taylor1950). An oscillating cavitation bubble near a liquid surface provides this acceleration, triggering RT instability on both the bubble wall and the liquid surface. As shown in figure 2, the oscillating bubble generates alternating outward and inward accelerations at both the bubble wall and the liquid surface. These accelerated interfaces become susceptible to instability, leading to the development of perturbations. During the early expansion stage indicated by the red regime, perturbations emerge rapidly on the bubble wall, while the liquid surface remains undisturbed. In the subsequent deceleration and contraction stages indicated by the green regime, perturbations on the liquid surface grow quickly, accompanied by the rapid decay of those on the bubble wall. The perturbations on the bubble wall and the liquid interface develop over different stages, which indicates that their interactions can be neglected. A theoretical model comprising a perturbation equation and bubble oscillation equation is presented to describe the development of perturbation for a bubble oscillating near a liquid surface. The growth rate
$\beta$
is derived from the perturbation equation under an exponential ansatz. Assuming growth at its maximum value yields the peak perturbation amplitude. The comparison of this amplitude with the liquid-layer thickness establishes a physical penetration criterion, enabling the prediction of ventilation regime boundaries and the ventilation time scaling law.
Assuming that the perturbation amplitude is small compared with the bubble scale (Sohn Reference Sohn2009; Mikaelian Reference Mikaelian2019), and that the liquid-layer thickness exceeds one-third of the perturbation wavelength (Taylor Reference Taylor1950), the perturbation equation in a planar geometry, accounting for viscosity and surface tension, is described as
\begin{equation} \frac {{\rm d}^2\eta }{{\rm d}t^2}+2\nu _l k^2 \frac {{\rm d}\eta }{{\rm d}t}-\left(Aka-\frac {\sigma }{\rho _o+\rho _i}k^3\right)\eta =0, \end{equation}
where
$\nu$
represents the viscosity coefficient,
$k$
represents the wavenumber,
$A=(\rho _o-\rho _i)/{}(\rho _o+\rho _i)$
represents the Atwood number,
$\rho$
represents the density and
$\sigma$
represents surface tension coefficient. The subscripts
$o$
and
$i$
represent the outer and inner fluids with the bubble centroid as the origin, respectively. When focusing on the bubble wall, the inner fluid refers to the bubble, while the outer fluid refers to the liquid. The expression of perturbation amplitude
$\eta$
is assumed as
$\eta =\eta _0 {\rm e}^{\beta t}$
(Taylor Reference Taylor1950; Sohn Reference Sohn2009), where
$\eta _0$
represents the initial perturbation amplitude,
$\beta$
represents the growth rate of the perturbation and
$t$
represents time. The growth rate of the perturbation is obtained through the perturbation equation, while the time for perturbation growth is estimated when the pressure difference between the inside and outside of the bubble is zero during the oscillation. According to the characteristic equation (2.1), the growth rate of the perturbation
$\beta$
is written as
\begin{equation} \beta =-k^2 \nu _l+\sqrt {Aka+k^4\nu _l^2-\frac {\sigma }{\rho _o+\rho _i}k^3}. \end{equation}
The perturbations on the interfaces driven by the bubble oscillation near a liquid surface exhibit multi-mode characteristics (Wang et al. Reference Wang, Wang, Chen, Huang, Song, Zeng and Wang2025). To obtain an approximate solution for
$\eta$
, we assume that the perturbation grows at the maximum growth rate at the most unstable wavenumbers expressed as
$k=(Aa/\nu ^2)^{1/3}/2$
(Drake Reference Drake2018; Li, Zhang & Kang 2018). Furthermore, the surface tension term is orders of magnitude smaller than the acceleration term and is thus neglected. The maximum growth rate is written as
\begin{equation} \beta _m=\frac {(Aa)^{2/3}}{2\nu _l^{1/3}}, \end{equation}
where
$a$
is the interface acceleration. The acceleration
$a$
promotes the growth rate, whereas the viscosity
$\nu _l$
inhibits this growth primarily by reducing the rate.
An approximate solution for the maximum perturbation amplitude is obtained as
\begin{equation} \eta _{m_i}=\eta _0 {\rm e}^{\beta _m T_i}=\eta _0 {\rm e}^{(1/2)(Aa)^{2/3} \nu _l^{-1/3}T_i}, \quad i =1\; \text{and}\; 2, \end{equation}
where
$T_i$
denotes the time at which perturbation growth ceases and the acceleration
$a$
is obtained based on the Rayleigh–Plesset (RP) equation. The maximum perturbation amplitude
$\eta _{m_i}$
increases with acceleration
$a$
and growth time
$T_i$
, while decreasing with viscosity
$\nu _l$
. Considering that the instability is driven by the pressure difference
$\Delta p$
inside and outside of the interface, the perturbation growth ceases at
$\Delta p=0$
as shown in figure 2. By combining the bubble dynamic equation and the adiabatic state equation, the maximum development time
$T_1 = 0.07T_c$
and
$T_2 = 0.93T_c$
. Here,
$T_1$
and
$T_2$
denote the maximum perturbation growth times on the bubble wall and the liquid surface, respectively.
The criterion for ventilation during bubble collapse is the penetration of the perturbation through the liquid layer. This is assessed by a comparison between the maximum perturbation amplitude (
$\eta _m$
) and the liquid-layer thickness (
$d$
), as formulated in (2.5):
\begin{equation} \left \{ \begin{aligned} &\textrm {Ventilation:}\quad \eta _m \gt d \\ &\textrm {Non-ventilation:}\quad \eta _m \lt d, \end{aligned} \right . \end{equation}
where the liquid-layer thickness scales as
$d\propto \gamma R_{\textit{max}}$
. The liquid layer is driven by the bubble oscillation and is not subject to significant external forcing from the atmosphere. As a result, we assume its motion is coupled to the bubble and its thickness remains constant, neglecting the liquid compressibility.
The maximum perturbation amplitude is computed from (2.4). Complete ventilation originates from perturbations on the bubble wall, while partial ventilation is driven by perturbations on the liquid surface. The boundaries separating the complete, partial and non-ventilation regimes are defined by two critical stand-off parameters,
$\gamma _{c_1}$
and
$\gamma _{c_2}$
:
\begin{equation} \gamma _{c_i} \propto \frac {\eta _0}{R_{\textit{max}}}{\rm e}^{(1/2)(Aa_{T_i}^*R_{\textit{max}}/T_c)^{2/3} T_i\nu _l^{-1/3}} = \frac {\eta _0}{R_{\textit{max}}} {\rm e}^{B_i \nu _l^{-1/3}}, \quad i =1\; \text{and}\; 2, \end{equation}
where
$B_i=(Aa_{T_i}^*R_{\textit{max}}/T_c)^{2/3} T_i/2$
,
$T_1=0.07T_c$
and
$T_2=0.93T_c$
,
$R_{\textit{max}}$
and
$T_c$
are measured through repeated experiments and
$a_{T_i}^*=a_{T_i} T_c^2/R_{\textit{max}}$
is the dimensionless acceleration. The dimensionless interface acceleration
$a_{T_i}^*$
is approximated by the average acceleration of the bubble wall during each stage (from 0 to
$T_1$
and from
$T_1$
to
$T_2$
), which is estimated by integrating the RP equation to obtain the bubble wall velocity. The derivation and verification of interface acceleration can be found in the supplementary material (§ I) available at https://doi.org/10.1017/jfm.2026.11488. The boundaries
$\gamma _{c_i}$
between different regimes follow the viscous scaling
$\gamma _{c_i} \propto {\rm e}^{B_i \nu _l^{-1/3}}$
. These boundaries exhibit negligible viscous dependence when the perturbation growth time
$T_i$
becomes vanishingly short.
The ventilation time
$t_v$
marks the onset of ventilation, as the perturbation penetrates the liquid layer and thereby exposes the bubble interior. It satisfies the condition
$\eta _m = d$
, which is given by
$\eta _0 {\rm e}^{\beta _m t_v} \propto \gamma R_{\textit{max}}$
. The resulting scaling law for dimensional ventilation time
$t_v^*$
is
\begin{equation} t_v^*=\frac {t_v}{T_c} \propto \frac {2(Aa_{T_2}^*R_{\textit{max}}/T_c)^{-2/3}}{T_c}\ln \! \left(\frac {\gamma R_{\textit{max}}}{\eta _0}\right) \nu _l^{1/3}= C \ln \! \left(\frac {\gamma R_{\textit{max}}}{\eta _0}\right) \nu _l^{1/3}, \end{equation}
where
$C=2(Aa_{T_2}^*R_{\textit{max}}/T_c)^{-2/3}/T_c$
.
3. Experimental verification
A series of experiments on bubble oscillation near a liquid surface was conducted to verify the theoretical model. During the experiment, the bubble was generated by laser beam focusing and optical breakdown in the liquid, as shown in figure 3(a). The laser beam was emitted by a pulsed laser (Nd:YAG,
$\boldsymbol{\nabla }=1064$
nm, with 10 ns pulse width; Spectra-Physics Ltd, USA) and focused through a parabolic mirror. A high-speed camera (V2512, Phantom Co. Ltd, USA) was used to record the bubble dynamics with an LED light source (Supponen et al. Reference Supponen, Kobel, Obreschkow and Farhat2015). The sampling frequency of the high-speed camera was
$10^{5}$
frames per second, and the exposure time was 300 ns. More details can be found in a previous study (Wang et al. Reference Wang, Wang, Chen, Huang, Song, Zeng and Wang2025). In the experiments, the distance
$h$
between the initial position of the bubble and the liquid surface is modified by adjusting the height of the liquid surface. The parameter interval of
$\gamma$
is [0.10–1.00] in the study. Viscosity (
$\nu _l$
) is modified by adding different proportions of glycerol to the water and measured using a rotational viscometer. The parameter interval of
$\nu _l$
is [1–25]
$\nu _w$
in the study. Here,
$\nu _w=10^{-6}$
Pa s is the viscosity coefficient of water. The maximum bubble radius
$R_{\textit{max}}$
varies with the laser pulse energy and the liquid viscosity. During the experiment, the laser energy was set at four values: 190, 142.5, 95 and 47.5 mJ. Parameters
$R_{\textit{max}}$
and
$T_c$
range within [1.33, 2.39] mm and [0.24, 0.44] ms, respectively. The experimental observations with different laser energies can be found in the supplementary material (§ II).
(a) Schematic of experimental set-up. Experimental observations of bubble dynamics near a liquid surface with a laser energy of 190 mJ: (b) non-ventilation at
$\gamma =0.40$
and
$25\nu _w$
, (c) partial ventilation at
$\gamma =0.40$
and
$\nu _w$
and (d) complete ventilation at
$\gamma =0.10$
and
$25\nu _w$
. A laser beam was emitted by a pulsed laser (Nd:YAG,
$\boldsymbol{\nabla }=1064$
nm, with 10 ns pulse width; Spectra-Physics Ltd, USA) and focused through a parabolic mirror. A high-speed camera (V2512, Phantom Co. Ltd, USA) was used to record the bubble dynamics with an LED light source. The sampling frequency of the high-speed camera was
$10^{5}$
frames per second, and the exposure time was 300 ns.
As shown in figure 3(b), the bubble undergoes a classical non-spherical collapse. The bubble wall remains smooth and transparent throughout the oscillation, indicating the absence of external air entering the bubble interior. This pattern is accordingly defined as non-ventilation. In contrast, a decrease in liquid viscosity
$\nu$
leads to partial ventilation, as illustrated in figure 3(c). During the late expansion stage (approximately
$0.30T_c$
), irregular white spots appear on the bubble wall and rapidly cover its entire surface, indicating ingress of external air carrying droplets of various sizes. This phenomenon is identified as the partial ventilation pattern. As the stand-off parameter
$\gamma$
decreases further, the ventilation pattern shifts from non-ventilation to partial ventilation and ultimately to complete ventilation. In the complete ventilation regime (figure 3
d), white spots emerge on the bubble wall during the initial expansion stage, indicating rapid external air ingress. The subsequent bubble evolution produces a bullet-jet morphology, serving as a key characteristic of this ventilation pattern.
4. Results and discussion
A series of experiments is conducted with various dimensionless stand-off parameters
$\gamma$
and viscosities
$\nu_l$
systematically. A regime map for the ventilation pattern is obtained from experimental observations as shown in figure 4. The Reynolds number
$\textit{Re}$
represents the effect of viscosity, which is defined as
$\textit{Re}=R_{\textit{max}}^2/\nu _l T_c$
. In the regime map, blue symbols indicate complete ventilations, orange symbols indicate partial ventilations and green symbols indicate non-ventilations. Different symbol shapes denote different laser energies, shown in the legend. As
$\gamma$
increases, the pattern transits from complete ventilation to partial ventilation and then to non-ventilation. This is because the thickness of the water layer above the bubble increases as
$\gamma$
increases, making it more difficult for the perturbation to penetrate the liquid layer and cause ventilation. As
$\textit{Re}$
increases, some of the non-ventilation pattern transits to partial ventilation. A decrease in viscosity increases the perturbation amplitude and makes it easier to penetrate the water layer. The transition between complete and partial ventilation exhibits negligible dependence on
$\textit{Re}$
. This is because complete ventilation occurs during the accelerated expansion stage (
$t \leq T_1$
), where the vanishingly short growth time
$T_1$
precludes the development of significant viscous effects, rendering the process inertia-dominated. The theoretical model predicts the transition condition between ventilation patterns. The obtained theoretical boundary lines of the scaling law through (2.6) are shown in figure 4. Theoretical boundary line 1 is obtained at
$i=1$
and at
$i=2$
for theoretical boundary line 2. The deviations between theoretical boundary lines and experimental results primarily arise from an assumption in the theoretical model. The model assumes that perturbations develop at the maximum growth rate. This overestimates the actual perturbation amplitude, leading to a predicted
$\gamma _c$
that is larger than the experimental results. Overall, the theoretical model provides a good description of different bubble patterns.
Regime map of the ventilation patterns at dimensionless stand-off parameter
$\gamma$
versus Reynolds number
$\textit{Re}$
. Complete, partial and non-ventilation regimes are denoted by blue, orange and green symbols, respectively. Different symbol shapes denote different laser energies, shown in the legend. The theoretical boundaries are indicated by two lines: line 1 between the complete and partial ventilation regimes, and line 2 between the partial and non-ventilation regimes.
The ventilation time
$t_v$
marks the onset of ventilation, as the perturbation penetrates the liquid layer and thereby exposes the bubble interior. We focus on the effect of the dimensionless stand-off parameter
$\gamma$
and the viscosity
$\nu_l$
on the ventilation time
$t_v$
in the regime of partial ventilation. Figure 5 shows the evolution of the partial ventilation bubble for various values of
$\nu_l$
at
$\gamma =0.30$
. The ventilation time
$t_v$
of the experiment is extracted and represented by the blue dashed line. It is observed that
$t_v$
increases as
$\nu _l$
increases. This is because the increase in viscosity suppresses the development of perturbation, which requires a longer development time to penetrate the liquid layer.
Bubble dynamics near a liquid surface at
$\gamma =0.30$
and different viscosities
$v_l$
: (a) partial ventilation at
$\nu_l=1\nu _w$
, (b) partial ventilation at
$\nu_l=10\nu _w$
and (c) partial ventilation at
$\nu_l=20\nu _w$
. Here, the time when the ventilation occurs (
$t_v$
) is defined as the time just before the occurrence of white spots on the bubble wall.
Dimensionless ventilation time
$t_v^*$
as a function of
$\gamma ^*$
for various
$\gamma$
and viscosity
$\nu _l$
. Here,
$\gamma ^*=C \ln(\gamma R_{\textit{max}}/\eta _0)\nu _l^{1/3}-\gamma _0^*$
. The slope of the function is 20, as indicated at the upper left corner. Different symbols represent the cases at different viscosities.
Furthermore, the ventilation times of experiments at different
$\gamma$
and
$\nu _l$
are extracted and shown in figure 6. Dimensionless ventilation time
$t_v^*$
is shown as a function of
$\gamma ^*$
for various
$\gamma$
and
$\nu_l$
. Here,
$\gamma ^*=C \ln(\gamma R_{\textit{max}}/\eta _0)\nu _l^{1/3}-\gamma _0^*$
, with
$\gamma _0^*=C \ln(\gamma _{c_1} R_{\textit{max}}/\eta _0)\nu _l^{1/3}$
being introduced to ensure a consistent scaling behaviour of the ventilation onset across different viscosities. Different symbols represent the cases at different
$\nu_l$
. The dimensionless ventilation time
$t_v^*$
satisfies a proportional relationship with
$\gamma ^*$
at a slope of 20. For RT instability, a decrease in
$\nu_l$
promotes the development of perturbation, while a decrease in
$\gamma$
makes the liquid layer easier to be penetrated by perturbations. Therefore, a decrease in
$\gamma ^*$
causes the advancement of ventilation time. Overall, the experimental results show good agreement with the theoretical model, confirming that the ventilation time satisfies the scaling law of
$t_v^* \propto C \ln(\gamma R_{\textit{max}}/\eta _0) \nu _l^{1/3}$
, given in (2.7).
5. Conclusions
To quantitatively elucidate the interfacial instability on the bubble wall and the liquid surface, a theoretical model was developed that couples the perturbation equation with the bubble oscillation equation. The growth of perturbations, incorporating viscous and surface tension effects, is described within a small-amplitude framework. Ventilation during bubble oscillation is initiated when the perturbation penetrates the liquid layer: complete ventilation stems from perturbations on the bubble wall, whereas partial ventilation results from perturbations on the liquid surface. A scaling law for ventilation regime boundaries is obtained based on the analytical solutions. The complete, partial and non-ventilation regimes are divided by the parameters
$\gamma _{c_1}$
and
$\gamma _{c_2}$
, both scaling as
$\gamma _{c_i} \propto \eta _0 {\rm e}^{B_i \nu _l^{-1/3}}/R_{\textit{max}}$
with liquid viscosity
$\nu_l$
. The boundary between complete and partial ventilation regimes shows negligible viscous dependence due to the vanishingly short perturbation growth time. Furthermore, the ventilation time
$t_v$
marks the onset of ventilation, as the perturbation penetrates the liquid layer and thereby exposes the bubble interior. We obtained the scaling law of dimensionless ventilation time:
$t_v^* \propto C \ln(\gamma R_{\textit{max}}/\eta _0) \nu _l^{1/3}$
. The scaling laws are verified by the experimental observations. The present study advances further by establishing scaling laws for ventilation regime boundaries and ventilation time across various liquid viscosities, based on the analytical solutions of perturbation development during bubble oscillation.
Supplementary material
Supplementary material is available at https://doi.org/10.1017/jfm.2026.11488.
Funding
This work was supported by the National Natural Science Foundation of China (grant nos. 12272382, 12525210, 12293003, 12293000 and 12293004) and the National Key R&D Plan of China (grant no. 2023YFC2810400).
Declaration of interests
The authors report no conflict of interest.
Data availability statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Author contributions
J.H. and G.W. contributed equally to this work.
