Interactions of bubbles in acoustic Lichtenberg figure

Highlights

• •Bubble transportation processes in cavitation field is investigated.
• •A model is proposed to explain the evolution of acoustic Lichtenberg figure.
• •The separation distance and bubble density can affect the stability of ALF.

Abstract

The evolution of acoustic Lichtenberg figure (ALF) in ultrasound fields is studied using high-speed photography. It is observed that bubbles travel along the branch to the aggregation region of an ALF, promoting the possibility of large bubble or small cluster formation. Large bubbles move away from the aggregation region while surrounding bubbles are attracted into this structure, and a bubble transportation cycle arises in the cavitation field. A simplified model consisting of a spherical cluster and a chain of bubbles is developed to explain this phenomenon. The interaction of the two units is analyzed using a modified expression for the secondary Bjerknes force in this system. The model reveals that clusters can attract bubbles on the chain within a distance of 2 mm, leading to a bubble transportation process from the chain to the bubble cluster. Many factors can affect this process, including the acoustic pressure, frequency, bubble density, and separation distance. The larger the bubble in the cluster, the broader the attraction region. Therefore, the presence of large bubbles might enhance the process in this system. Local disturbances in bubble density could destroy the ALF structure. The predictions of the model are in good agreement with the experimental phenomena.

1. Introduction

If an acoustic wave generates a sufficient negative pressure when propagating in a liquid, gas nuclei can grow into cavitation bubbles and experience expansion, compression, and even collapse [1]. Ultrasonic cavitation has widespread application in various fields. Nonlinear oscillations of bubbles can generate significant scattered echoes at harmonic multiples of the incident wave. Thus, bubbles can be used as a contrast agent for ultrasound diagnosis [2], [3], [4], [5]. A contrast agent is especially important in cardiology [3]. Targeted therapy and drug delivery can be achieved by wrapping a specific substance around a bubble [6], [7]. In the chemical engineering [8], [9], materials [10] and water conservancy industries [11], hot spots [12] and high pressures [13] generated by inertial cavitation [14] are used to promote the occurrence or rate of chemical reactions. On the other hand, this effect can also be harmful. For example, the shock waves generated by bubble collapse can damage the surface materials of turbines and propellers, which is dangerous in severe cases [15], [16].

Cavitation effects occur mainly at active bubble locations, while the utilization of ultrasonic cavitation is closely related to the dynamics of each single bubbles and bubble distributions [17]. Bubble dynamic analysis under different conditions has been performed by many literatures, such as bubbles located near an oil-water interface [41], bubbles within a liquid-filled cavity surrounded by an elastic medium [42] and a specific bubble population in unbounded liquids [18], [19], [20]. Bubbles are usually located in a population structure. Cavitation structures with complex evolutionary processes may appear in a cavitation field because of the effects of boundary and acoustic conditions. Bai et al. [21] found that the formation of cavitation structures depended on the acoustic pressure and layer thickness, and “bubble production” and “bubble disappearance” could be the structural stability and transformation mechanisms [22]. Cavitation structures such as chains, spheres [19], and a branched structure called acoustic Lichtenberg figure (ALF) can be observed in three-dimensional liquids [23], [24], [25]. ALF was first described at different acoustic pressures by continuum and particle approaches [23], [24], [25]. The simulation results showed that an ALF could form at a medium amplitude pressure (130 kPa), consistent with experimental observations, and successfully predicted the bubble motion velocity.

However, the ALF simulations only consider the effect of acoustic pressure on the whole structure. The relative motion between bubbles is poorly described, and the secondary Bjerknes force between bubbles is not considered in the continuum model. Secondary Bjerknes forces play an essential role in the self-organization of bubble populations [26], [27], and the movement of bubbles is closely related to the transport of substances in liquids [28]. Therefore, it is crucial to consider the secondary Bjerknes forces between bubbles and to analyze the movement of bubbles in bubble populations. In this paper, the ALF was observed using a high-speed camera, and a physical model is introduced to explore the ALF evolution mechanism.

2. Experimental observation of cavitation field

The experimental setup consisted of an ultrasonic cavitation device, a high-speed imaging system, an illumination system, and a transparent chamber, as shown in Fig. 1. Two ultrasonic transducers generated ultrasonic waves with a radiation surface diameter of 76 mm are mounted at the bottom of an ultrasonic cleaner (Beijing Jingyi Ronghua Jewelry Equipment Co., Ltd. China). A hydrophone (Needle Hydrophone PT – 0800546, Institute of Acoustics, Chinese Academy of Sciences, China) and oscilloscope (UPO2102CS, Uni-Trend Technology Co., Ltd. China) were used to capture acoustic signals in the water. The fundamental frequency of the received signal is about 24 kHz. A high-speed camera (FASTCAM SA-Z type 1000 K-C-32 GB, Photron Ltd., Japan) was used to observed the cavitation structure of tap water in a transparent chamber (200 × 100 × 150 mm³) placed inside the ultrasonic cleaner (230 × 140 × 100 mm³) at 20,000 fps (1024 × 1024 pixels).

Fig. 1.

Schematic diagram of the experimental setup.

An O-xyz coordinate system originates at the lower corner of the ultrasonic cleaner water tank with the sound radiation surface at z = 0. The transparent chamber, having a water depth of 110 mm, was placed into the tank (with an 80 mm water depth), and the bottom of the chamber was at z = 45 mm.

Many filamentary bubble branching structures were observed in the chamber’s water, and the structure formation position and subsequent translational paths were random. Some structures were observed hovering in the camera’s observation area located in the middle region above the two transducers, about 30 mm below the water surface in the chamber. Fig. 2 shows two captured images of the structure’s local distribution, and the time interval is 7.6 ms. As a comparison, it is found that the structures of the bubbles are similar, which presents that the structure might be stable. Therefore, it is essential to analyze the evolution of the structure during these two frames.

Fig. 2.

Two images with a time interval of 7.6 ms.

Many bubbles aggregated within the dashed ellipse region, and bubbles attracted to each other merged into the larger bubbles or small clusters highlighted by the circles. We tracked the bubble motions and found that they traveled sequentially toward the aggregated region along a chain-like trajectory. These trajectories were highly coincident with the stable structure of the bubble chain (Fig. 2, red arrows). Thus, this typical filamentous branching structure (ALF) could be considered as consisting of an aggregated region and many adjacent bubble chains. The position of the bubble chains sometimes changed slightly, but the structure remained essentially stable over the observed time.

The evolution of the internal cavitation structure can be analyzed even though the frame rate of the high-speed camera used is less than the driving frequency. Fig. 3 shows adjacent 5-frame time series photos taken consecutively, with the time axis on the upper side of the photos. T and T' are the sound period and the time interval of two consecutive frames, respectively. Based on experimental observations, the ALF exhibited some degree of stability. Therefore, although the five frames were not captured within a sound cycle, they can still be used to infer the internal evolutionary process by comparing the individual images to the sound cycles on the time axis.

Fig. 3.

Bubble dynamics in cavitation fields.

In the first frame, two small bubble clusters were observed, and in the second frame, captured at a 50 μs interval, the ALF structure appeared when the bubbles were expanding. However, bubbles were no longer observed distal to the branches in region I (Frame 3), and it was difficult to observe the bubbles in region II because their sizes were below the optical resolution (Frame 4). It is noteworthy that the bubbles in region III seem to expand to the maximum at that moment. In the last frame, bubbles collapsed except for the two small bubble clusters in their shrinking phase. It is evident that bubbles collapse in regions I, II, and III, one after another.

According to theoretical predictions [29], the expansion time and maximum radius of the cavitation bubble increase with increasing acoustic pressure, resulting in a delay in the collapse time. Ultrasound radiated from the container bottom into the water and was reflected by the water surface, causing a sound pressure distribution over the water depth. According to the signal received by the hydrophone at the position (115 mm, 40 mm, 130 mm), there are harmonic components in addition to the fundamental components (Fig. 4(a)). On the basis of the amplitude of the fundamental components, we found pressure nodes and antinodes (Fig. 4(b)). In the observation region, the node is located 2λ (wavelength: λ ≈ 62.5 mm) from the radiation surface, close to z = 130.0 mm, where a minimum measured fundamental pressure value exists. A relatively high local pressure occurs in the bubble aggregation region III, which might be why the structure hovers at that location.

Fig. 4.

(a) Frequency spectrum of the signal received by a hydrophone at the position (115 mm, 40 mm, 130 mm). (b) The amplitude of the fundamental components vs. height from the transducer.

Bubbles are subject to the combined effect of the driving acoustic field [30], [31], [32], [33] and secondary radiation [34] from neighboring bubbles. In Fig. 5 (Video 1), the black arrows denote the displacement of large bubbles, and red arrows indicate the translational directions of tiny bubbles. ALF branches play the role of a transportation path for cavitation bubbles. Tiny cavitation bubbles collide at the end of the branches in the aggregation region (high pressure) to generate large bubbles. As shown in the first two frames of Fig. 5, large bubbles move irregularly in the aggregation zone and attract each other, where bubbles marked by orange circles have coalesced in the second frame. The large bubbles tend to move toward the low-pressure area and eventually disappear. The entire process lasts for about 2 ms. This cyclic process balances the number density within the bubble aggregation region, and these behaviors agree well with theoretical prediction and experimental phenomena [30], [31], [32].

Fig. 5.

Movement of bubbles in an ALF.

Bubbles and clusters outside the transportation chains could be attracted by the ALF, as shown in Fig. 6 (Video 2). Several clusters (numbered 1–4) are close to the branches on the right side of the ALF and are arranged in a tail-like formation. The clusters oscillated and attracted neighboring bubbles. The red arrows indicate the translational direction of the clusters. When small clusters are far from the ALF, they have less influence on the bubble transport chain of the ALF structure. However, the clusters would eventually merge into the ALF branches. As the bubble cluster approached the ALF, the distal end of the branches was also affected by the approaching cluster. Slight rotation of bubble branches toward the position of cluster 1 was observed (see Frames 8 and 9). As small bubble clusters enter the branches, the local bubble number density distribution rises, leading to the destruction of the original microstructure and eventually causing the evolution of the branched structure.

Fig. 6.

Interaction of an ALF with small bubble clusters.

Although there were some relatively stable bubble structures, the evolution of the cavitation structures is complex. In a multi-bubble field, the self-organized behavior is modified by bubbles’ translational motion due to the pressure distribution of the primary acoustic field, bubble density, and secondary radiation forces.

3. Theoretical cavitation structure model

From experimental observation, when cavitation bubbles arrive at the aggregation region, large bubbles or small clusters can be formed in the ALF. These bubbles or clusters are spherical or sphere-like in shape. The bubble cluster formation and transport processes in the cavitation field are very complex, and many studies have explored the cavitation evolution process. However, the bubble transportation in the acoustic cavitation field is less well understood theoretically.

Here, a structure model consisting of a spherical cluster and a bubble branch is introduced and shown in Fig. 7 as a simplified model of the ALF. In this analysis, the translational motion and mass exchange at bubble interfaces are neglected, while the predicted motion of the bubbles in the chain is considered. The bubble branch can be approximated as a straight chain in the ALF, and Zhang [35] has confirmed the stability of the bubble chain in the cavitation field. In the following analysis, we research the interaction between the spherical cluster and the straight chain. The equilibrium radii of bubbles in the cluster and chain are assumed to be uniformly distributed with radii R₁₀ and R₂₀, respectively.

Fig. 7.

Model consisting of a spherical bubble cluster and a bubble chain.

Because of the acoustic radiation of bubbles, a secondary pressure can be generated in the cavitation field and expressed as [36].

$$P_{\mathit{rd}}=\rho \frac{\left(2R{\dot{R}}^2+R^2\ddot{R}\right)}{r},$$ (1)

where $\rho$ is the liquid density, r is the distance between the center of the bubble and any point in space, R is the instantaneous radius of the bubble, and the overdots denote time derivatives. For a homogeneous bubble cluster, the bubble oscillations are usually considered to be synchronized [19], [37]. The equation of a bubble in the cluster is given by [19].

$$\begin{array}{c}\left(1-\frac{{\dot{R}}_1}{c}+\frac{3}{2}{M}_0\right)R_1{\ddot{R}}_1+\frac{3}{2}{\dot{R}}_1^2\left(1-\frac{{\dot{R}}_1}{3c}+2M_0\right)\\ =\frac{1}{\rho }\left(1+\frac{{\dot{R}}_1}{c}+\frac{R_1}{c}\frac{d}{\mathit{dt}}\right)P_{B1}-\sum _{k=0}^{N_2-1}\frac{\left(2R_2{\dot{R}}_2^2+R_2^2{\ddot{R}}_2\right)}{D+kd},\end{array}$$ (2)

where$M_0=N_1\frac{R_1}{r_{\mathit{clust}}}\left(1-\frac{r_0^2}{3r_{\mathit{clust}}^2}\right)$, r₀ is the relative position of the bubble in the spherical cluster of a radius r_clust, N₁ is the total number of bubbles in the cluster, and D is the distance between the spherical cluster center and the nearest bubble. N₂ is the total number of bubbles in the chain, and d is the distance separating two adjacent bubbles. The last term on the right-hand side of Eq. (2) is related to the secondary radiation of the bubbles in the chain. When the bubble chain is far enough away from the cluster, the secondary radiation pressure on the nearest bubble can be approximated as

$$\frac{P_{rd21}}{\rho }=\sum _j\frac{\left(2R_j{\dot{R}}_j^2+R_j^2{\ddot{R}}_j\right)}{d_{2j}}\approx \frac{N_1}{D}\left(2R_1{\dot{R}}_1^2+R_1^2{\ddot{R}}_1\right),$$ (3)

where $d_{2j}$ is the bubble separation distance. Therefore, the dynamic equation of the bubble in the chain can be approximated as

$$\begin{array}{c}\left(1-\frac{{\dot{R}}_2}{c}\right)R_2{\ddot{R}}_2+\frac{3}{2}{\dot{R}}_2^2\left(1-\frac{{\dot{R}}_2}{3c}\right)\\ =\frac{1}{\rho }\left(1+\frac{{\dot{R}}_2}{c}+\frac{R_2}{c}\frac{d}{\mathit{dt}}\right)P_{B2}-\sum _{k=1}^{N_2-1}\frac{\left(2R_2{\dot{R}}_2^2+R_2^2{\ddot{R}}_2\right)}{\mathit{kd}}-N_1\frac{\left(2R_1{\dot{R}}_1^2+R_1^2{\ddot{R}}_1\right)}{D},\end{array}$$ (4)

where $P_{\mathit{Bi}}=\left(P_{\infty }+\frac{2\sigma }{R_{i0}}\right){\left(\frac{R_{i0}^3-h_i^3}{R_i^3-h_i^3}\right)}^{\gamma }-\frac{2\sigma }{R_i}-\frac{4\eta {\dot{R}}_i}{R_i}-P_0+P_a\sin \left(2\pi ft\right),(i=1,2)$ is the liquid pressure on the bubble wall, $h_i=R_{i0}/8.54,(i=1,2)$ is the van der Waals hard-core radius [38], $\gamma$ is the polytropic exponent, P₀ is the hydrostatic pressure, and$\sigma$,$\eta$, and c are the liquid surface tension, viscosity, and sound speed, respectively. P_a and f are the pressure amplitude and frequency of the external acoustic field, respectively.

Bubbles are subjected to a primary Bjerknes force due to the driving acoustic field and a secondary Bjerknes force due to the bubble’s secondary acoustic radiation. The primary Bjerknes force influences the translation of the integral structure, while the secondary Bjerknes force affects relative motion of bubbles. The secondary Bjerknes force on a bubble can be expressed as

$${\overrightarrow{F}}_B=-〈V\mathrm{\nabla }{P}_{\mathit{rd}}〉$$ (5)

where $V=4\pi R^3/3$ is a bubble’s volume, $\langle \rangle$ denotes a time average over one acoustic period, and $P_{\mathit{rd}}$ is the total secondary pressure at the position of the given bubble.

The expression for radiation pressure in Eq. (B4) of Ref. [19] indicates that the secondary force on the bubble of the outer layer is approximately.

$${\overrightarrow{F}}_{B1}={\overrightarrow{F}}_{B11}+{\overrightarrow{F}}_{B12}=\frac{N_1\rho }{4\pi r_{\mathit{clust}}^2}〈V_1{\ddot{V}}_1〉{\overrightarrow{e}}_x+\sum _{k=0}^{N_2-1}\frac{\rho }{4\pi {\left(D-r_{\mathit{clust}}+kd\right)}^2}〈{\dot{V}}_1{\dot{V}}_2〉{\overrightarrow{e}}_x$$ (6)

Similarly, the force on the nearest bubble in the chain is approximated by

$${\overrightarrow{F}}_{B2}={\overrightarrow{F}}_{B21}+{\overrightarrow{F}}_{B22}\approx -\frac{N_1\rho }{4\pi D^2}〈{\dot{V}}_1{\dot{V}}_2〉{\overrightarrow{e}}_x+\sum _{k=1}^{N_2-1}\frac{\rho }{4\pi {\left(\mathit{kd}\right)}^2}〈{\dot{V}}_2{\dot{V}}_2〉{\overrightarrow{e}}_x$$ (7)

where ${\overrightarrow{e}}_x$ is the unit vector in the x-direction, and $V_i,(i=1,2)$ are the volumes of bubbles in the cluster and chain, respectively.

4. Numerical analysis

On the basis of Eqs. (2), (4), (6), and (7), the interaction of the bubble cluster and the chain was analyzed numerically to explore the bubble transportation formation mechanism observed in the ALF, as presented in Section 2. Because the secondary Bjerknes force is closely related to the self-organization of bubbles in the cavitation field, various characteristics of this force are presented in this section.

The bubbles in the chain are repelled by the cluster when F_B2 > 0 and are attracted to the cluster when F_B2 < 0. The physical parameters were set at $\eta =0.001\text{kg/(m s)}$, $\rho =998{\text{kg/m}}^{\text{3}}$, $\sigma =0.0725\text{N/m}$, c = 1500 m/s, $\gamma =1.4$, P₀ = 101 kPa, r_clust = 1 mm, N₂ = 5, and d = 0.4 mm [25]. The bubble equilibrium radii considered ranged from 1 μm to 10 μm, which included typical cavitation radii observed medically and experimentally [3], [4], [25], [39].

Fig. 8 presents the secondary Bjerknes force (F_B2) using a grayscale color range in the R₁₀–R₂₀ plane [34] by setting f = 20 kHz, D = 2 mm, N₁ = 10³ [38], and P_a = 1.2 and 1.4 atm. The lighter and darker regions represent positive or negative values of F_B2, respectively. The repulsive region is mainly distributed in the R₁₀ < R₂₀ region, where the cluster repels the bubbles. In the darker regions, bubbles tend to move toward the cluster. Comparing Fig. 8(a) and (b), the attraction region becomes smaller as the pressure increases from 1.2 atm to 1.4 atm, and the dividing lines between the dark and light regions shift to smaller radii. There are attractive (dark) stripes distributed at intervals in the repulsive region in Fig. 8(a), and the strong, attractive forces occur in these separated regions, which may be related to the structure’s resonant response to the acoustic wave. Several isolated, small, white, bar-shaped regions are distributed within the dark region in Fig. 8(b), implying that the interaction may be inverted with size.

Fig. 8.

Secondary Bjerknes force (F_B2) in the R₁₀ - R₂₀ plane. The planes are given for f = 20 kHz and: (a) P_a = 1.2 atm; (b) P_a = 1.4 atm. Repulsive forces (F_B2 > 0) are represented by lighter regions and attractive forces (F_B2 < 0) are coded in gray scales.

The bubble number density increases with the driving acoustic pressure [40], so the probability of bubble aggregation increases, and larger bubbles or clusters are more likely to form in the aggregation region (as shown in Fig. 5). It is found the attraction zone becomes smaller and smaller by parametric analysis when the driving acoustic pressure exceeded 1.5 atm, implying that it is more difficult to form a stable ALF at high acoustic pressures.

The secondary Bjerknes force F_B1 was consistently negative in our calculations, meaning that bubbles in the cluster’s outer layer are less likely to separate from the cluster. Therefore, spherical bubble clusters are stable to some extent [38]. The cavitation structure at 190 kPa in Fig. 10 of Ref. [25] shows that an ALF is difficult to be observed, but some small spherical bubble clusters can be observed, which agrees with our theoretical predictions.

Fig. 10.

Secondary Bjerknes force (F_B2) in the f–P_a plane. The planes are given for R₁₀ = R₂₀ = 5 μm, D = 2 mm, and: (a) N₁ = 10²; (b) N₁ = 10³; (c) N₁ = 10⁴. Repulsive forces (F_B2 > 0) are represented by light regions and attractive forces (F_B2 < 0) are coded in gray scales.

Comparing the three cases shown in Fig. 9(a), the absolute value of the secondary force F_B2 varies with the bubble equilibrium radii distribution in the spherical cluster and the chain. When bubbles have uniform equilibrium radii (5 μm, 5 μm), F_B2 attains a maximum. If the bubble size in the spherical cluster increases to 8 μm, F_B2 decreases (the dashed line), while F_B2 declines sharply when the bubble size on the chain decreases to 3 μm (the dotted line). Bubbles on the chain within a distance of<2 mm from the spherical bubble cluster may be attracted to the spherical bubble cluster; otherwise, bubbles may be ejected. Therefore, the coupled strength in this structure weakens with increasing separation distance D. Similar tendencies can be seen in the curves in Fig. 9(b), where the acoustic frequency is set to 24, 48, and 72 kHz, respectively. Higher frequencies correspond to weaker bubble oscillations and smaller interacting forces. Therefore, the coupling strength of bubbles can be weakened using high-frequency ultrasound.

Fig. 9.

Secondary Bjerknes force (F_B2) vs. separation distance at P_a = 1.3 atm: (a) f = 24 kHz, and solid line: R₁₀ = R₂₀ = 5 μm; dashed line: R₁₀ = 8 μm, R₂₀ = 5 μm; dotted line: R₁₀ = 5 μm, R₂₀ = 3 μm; (b) R₁₀ = R₂₀ = 5 μm, and solid line: f = 24 kHz; dashed line: f = 48 kHz; dotted line: f = 72 kHz.

The secondary Bjerknes force F_B2 varies from negative to positive with increasing separation distance, and the attraction occurs mainly when the distance D is below 2 mm. Therefore, the clusters can only attract bubbles within a finite distance. However, because of the step-by-step transfer of coupling bubbles, a specific bubble migration path can be formed within the cavitation field, which may be the ALF formation mechanism.

It is evident that the acoustic wave frequency and pressure strongly influence the coupling strength, which can be described by the secondary Bjerknes force. If the pressure exceeds the cavitation threshold, cavitation bubbles vibrate violently and collapse, and many daughter bubbles are likely to be generated, possibly affecting the instantaneous bubble number density. Fig. 10 shows that the dark region is enlarged by the high number density of bubbles in the f–P_a plane. A saturation phenomenon exists when N₁ = 10⁴, where attractive (dark gray) stripes exist in the upper region of the plane, implying that the attraction is weak (Fig. 10(c)), and an inverse of the force might be obtained. Therefore, the bubble number density can modify the behavior of a cluster and a chain, and an increase in the number density might destroy the ALF structure, which agrees well with the phenomenon observed in Fig. 6.

5. Conclusion

This paper has experimentally investigated the internal evolution of acoustic Lichtenberg figure (ALF). This structure consists of branched bubble transportation chains and bubble aggregation regions where large bubbles or small clusters arise because of cavitation bubble coalescence. Larger bubbles travel outward, and surrounding bubbles are attracted to the ALF structure; thus, the number of bubbles remains stable in this region. Approaching large bubble clusters can affect ALF stability.

By analyzing ALF morphology, a model was developed that includes a spherical cluster and a bubble chain to explore the ALF evolution mechanism. The interactions between bubbles in cluster and chain were analyzed numerically based on the dynamics equations and an expression for the secondary Bjerknes force (F_B2). It was found that a bubble cluster can attract bubbles from the chain within a distance of 2 mm, and a transportation path might arise in this structure. Moreover, it was theoretically verified that the local bubble number density might destroy the ALF structure’s stability.

This study highlights the self-organization of bubbles in a cavitation field. Many factors modifying the distributing structure of bubbles can be controlled to travel along the transportation paths of the bubble [28]. Therefore, the efficiency of energy utilization can be enhanced by manipulating the cavitation bubbles.

CRediT authorship contribution statement

Fan Li: Investigation, Conceptualization, Formal analysis, Software, Validation, Writing – original draft. Xianmei Zhang: Software, Supervision, Formal analysis, Methodology. Hua Tian: Supervision, Formal analysis. Jing Hu: Formal analysis, Writing – review & editing. Shi Chen: Methodology, Writing – review & editing. Runyang Mo: Methodology, Supervision, Writing – review & editing. Chenghui Wang: Investigation, Conceptualization, Formal analysis, Methodology, Supervision, Writing – review & editing. Jianzhong Guo: Methodology, Writing – review & editing, Resources.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

The following are the Supplementary data to this article: