How the Texture Density Affect Dynamics of a Single Acoustic Cavitation Bubble Near a Skin-Like Wall in Sonophoresis Applications

For better applications of low-frequency sonophoresis in transdermal interstitial fluid extraction and transdermal drug delivery, the microscopic mechanism of skin permeabilization by low-frequency sonophoresis have drawn much attention. In the present work, influence of skin texture density on a single cavitation bubble in an ultrasonic field is studied. A novel experimental system based on high-speed photography has been designed to investigate the temporary evolution of single bubble near skin-like walls with different texture densities exposed to a 20.51kHz ultrasound in liquids. In addition, the dynamic characteristics of single bubbles near skin-like walls with different texture densities are analyzed. It is found that the influences of the texture density on the bubble dynamics are obvious, which reflect on the changes in the maximum size of the bubble margin during bubble oscillating and the moving speed of the bubble to the wall, as well as the collapse time and the jet speed during collapses, especially for the bubble with an ultra-high texture density. These effects of the texture density on the bubble dynamics can explain the mechanism of skin texture structure for promoting acoustic cavitation in related application fields.


I. INTRODUCTION
Ultrasonic cavitation, as an emerging frontier in the interdisciplinary field of acoustics and microfluidics in recent years, holds significant potential applications in industry and daily life.The complex physical and chemical effects generated during the collapse and rupture of cavitation bubbles, particularly in the medical, petroleum engineering, marine engineering, and chemical manufacturing fields, contribute to The associate editor coordinating the review of this manuscript and approving it for publication was Wen-Sheng Zhao .its broad applicability [1], [2], [3], [4].In these applications, the movement of cavitation bubbles near solid walls (such as ultrasonic lapping [5] and ultrasonic wall cleaning [6]) induces physical or chemical changes on the walls, leading to diverse applications.Therefore, the study of the dynamic processes of cavitation bubbles near different walls is a crucial focus in the field of ultrasonic cavitation [7], [8], [9].Traditionally, due to the limitations of application areas focused on cavitation mechanism research, most researchers have concentrated on studying the collapse mechanisms of cavitation bubbles near rigid walls.However, with the widespread application of ultrasonic cavitation in medicine in recent years, such as transdermal drug delivery based on low-frequency ultrasound technology [10], percutaneous extraction of tissue fluid [11], ultrasonic thrombolysis [12], ultrasonically assisted liposuction [13], ultrasound treatment of soft tissue injuries [14], ultrasonic targeted drug delivery [15], and gene therapy [16], there is an increasing interest among researchers in studying cavitation mechanisms near elastic walls resembling biological tissues [17], [18], [19].
In clinical medical applications based on cavitation effects, such as low-frequency ultrasound transdermal technology, the elastic wall resembling human skin is the primary subject affected by the ultrasonic cavitation effect.Excessive cavitation intensity can cause irreversible damage to skin tissues, impacting human health.On the other hand, low cavitation intensity can significantly reduce the effectiveness of clinical treatment.Therefore, precise control of the intensity of ultrasonic cavitation in clinical medical applications is crucial [20], [21].The dynamic characteristics of cavitation bubbles and their interaction mechanisms with elastic walls play a key role in accurately controlling ultrasonic cavitation, which could contribute to the safety and the efficiency of medical applications of cavitation effects.These contributions are essential factors in advancing clinical medicine.However, the deformation and physical characteristics of elastic walls themselves make the study of their mutual interactions with nearby cavitation bubbles a highly complex problem [22].Currently, research on cavitation bubbles near elastic walls is very limited, and the specific mechanisms of cavitation effects remain unclear.This lack of clarity leads to certain issues and potential threats in practical medical applications [23].
Low-frequency ultrasound skin permeation technology (LUSPT) is a crucial medical application of ultrasonic cavitation, holding significant importance in elevating the standards of modern medicine and improving the current conditions of patients.In comparison to other skin permeation technologies such as chemical enhancers, iontophoresis, or electroporation, LUSPT possesses several key advantages.Firstly, among various methods to enhance skin permeability, LUSPT stands out as a technique with a large molecular transdermal transport capacity and high efficiency.Moreover, its application in transdermal drug delivery does not compromise the biological activity of drug molecules.Secondly, following low-frequency ultrasound pretreatment, the skin's high permeability can be maintained for several hours, with a painless and infection-free recovery within 24-48 hours.Thirdly, low-frequency ultrasound skin permeation technology can be combined with various other methods to enhance skin permeability, such as chemical permeation enhancers, iontophoresis, and microneedle arrays [24], [25].In-depth research into the mechanisms of LUSPT will facilitate more efficient transdermal delivery of a variety of drugs.This advancement will lay the foundation for achieving quantitative extraction of tissue fluid and precise dosage injection of drugs, thereby promoting the clinical application of LUSPT.
Tezel et al. [26] discovered, through the analysis of the acoustic spectra during the low-frequency ultrasound skin permeation process, that transient cavitation plays a crucial role in the effect of LUSPT.In the field of low-frequency ultrasound, the size distribution of cavitation bubbles ranges from 10 to 150 µm, while the thickness of the stratum corneum is approximately 15 µm.Therefore, Tezel et al. suggested that transient cavitation primarily occurs in the coupling agent between the ultrasound probe and the skin.Tezel and Mitragotri [27] proposed three mechanisms for the interaction between bubbles and the stratum corneum during transient cavitation.Mitragotri conducted a theoretical analysis of these mechanisms, establishing relationships between the number of cavitation events, collapse pressure, and skin permeability coefficient.They pointed out that only the collapse process of bubbles very close to the surface of the stratum corneum (within approximately 50 µm) could positively contribute to the low-frequency ultrasound skin permeation effect.Building upon this, Azagury et al. [28] proposed interaction mechanisms between cavitation bubbles and the stratum corneum, including shock wave emission near the surface of the stratum corneum and the microjet effect produced when cavitation bubbles collapse on the stratum corneum, disrupting the ''brick'' structure formed by necrotic corneocytes.Alvarez-Román et al. [29] found, in the process of low-frequency ultrasound skin permeation, that the lipid bilayer structure of the stratum corneum's lipid bilayer structure reduced by approximately 30%, and this reduction played a role in the permeation effect.Fong et al. [30] and Ohl et al. [31] employed numerical simulation methods to study the dynamics of bubbles on different biological surfaces, including the skin.Wolloch and Kost [32] evaluated the impact of microjets and shock waves on the low-frequency ultrasound skin permeation effect through molecular transdermal import experiments, finding that the effect of microjets was significantly higher than that of shock waves.Additionally, Wu et al. [33] experimentally studied the influence of skin properties such as elasticity and sebum on cavitation microbubbles near the skin wall, discovering the dynamic impact of skin-related characteristics on single acoustic cavitation microbubbles near the skin wall.However, the specific impact mechanisms of characteristics such as skin texture density on the cavitation effect in low-frequency ultrasound skin permeation technology have not been thoroughly investigated.As the texture density varies depending on different people (as shown in FIGURE 1), which might play a vital role in LUSPT.
In present work, a single bubble near skin-like walls exposed to a low-frequency ultrasound, which is the basic model unit in applications of LUSPT, was observed and analyzed in liquids.Important results about the differences of bubble's dynamics near skin-like walls with different texture densities were recorded and analyzed.This will help to determine or understand the main effect mechanisms of the skin's texture density on acoustic cavitation and how to improve the application efficiency of LUSPT for different skin walls.

A. EXPERIMENTAL SETUP
This study utilized an experimental system based on TTL signal synchronized control for photographic imaging.The design objective of this experimental system is to investigate the transient dynamic processes of cavitation bubbles near an elastic wall with texture structures.As depicted in FIGURE 2(a), the experiments on the dynamics of ultrasonic cavitation bubbles were conducted in a transparent rectangular acrylic water tank, which has been introduced in previously work [33].The dimensions of the water tank were 100×100×40 mm 3 .Prior to the experiments, a vacuum pump was used to remove any residual gases in the deionized water.Subsequently, deionized water was introduced into the acrylic water tank, with the height of deionize water approximately 35 mm.In present work, the temporal evolution of the bubble dynamics was recorded at 480,000 frames per second from the bottom view of the water tank with a resolution of 2.0 µm/pixel.The bubble was generated near the elastic wall, and the detail information about the relative position between the bubble and the wall is shown in FIGURE 2(b).The normalized standoff distance between a bubble and the rigid wall (the initial distance parameter) can be calculated by the for2mulas γ 0 = L/R 0 , where L is the distance from the bubble center to the external surface at inception and R 0 is the initial radius of the generated bubble.In addition, the width and the heigh of the texture structure are respectively represented as w and h.In the present work, w=50 µm and h=40 µm, and the Young's modulus of the elastic walls is 0.12 MPa which is within the elastic range of the most human skin.

B. MATERIALS
The skin-like walls with various texture structures were fabricated with Polydimethylsiloxane (PDMS) following three main steps: 1) Pre-treat the silicon mold with a mold release agent.Immerse the silicon mold in the release agent for 10 minutes, then remove it and blow-dry any remaining release agent on the mold surface.Place the mold in a vacuum drying oven at 120 • C for 10 minutes, then take it out and let it cool to room temperature.2) Prepare PDMS by mixing polydimethylsiloxane prepolymer and curing agent in a ratio of 30:1.Cure the PDMS by heating it continuously at 65 • C for 4 hours.3) After cooling the PDMS to room temperature, cut it with the channel as the center to obtain PDMS membranes with dimensions of 4 × 25×45 (width × width × length, in millimeters).Pictures of skin-like walls with different texture densities are shown in FIGURE 3, the texture density increases from FIGURE 3(a) to FIGURE 3(d).The size and texture density of the skin-like walls made with PDMS used in the present work are listed in Table 1.The texture density (D t ) is defined as: In equation ( 1), the number of channels per unit area is denoted by N , and S represents the unit area.

C. DATA ANALYSIS
All image analysis was conducted using Fiji (a distribution of the ImageJ software, US National Institutes of Health, Bethesda, Maryland, USA).Data graphing utilized Origin (OriginLab, USA), and statistical analysis was performed with SPSS (IBM, USA).Image sequences capturing individual bubbles generating and oscillating within the field of view were employed for extracting bubble outlines for further analysis.These images underwent cropping and contrast enhancement to improve visibility.Background interference was minimized by eliminating objects smaller than 4 pixels using the Analysis Particles plugin.Subsequently, the bubble's outline was created using the 'Outline' function in the Binary menu of Fiji.These steps were repeated for all time points during a bubble's generation and movement.The x-y coordinates of the binary bubble outline were established to record the bubble's localization during exposure to ultrasound.The origin coordinate was defined at the center of the bubble at time zero (t=0), corresponding to the moment when the ultrasonic generator was triggered to operate.In this study, the velocity (v) of the bubble margin was determined by calculating the displacement between two consecutive frames and their corresponding time interval.The direction pointing towards the wall was defined as the positive direction for v.The definitions of time zero (t=0), time of bubble collapse (t c ), and the velocities of the microjets (v 1 , v 2 , v 3 ) have been previously detailed in our earlier work [34], [35].

III. RESULTS
As the fundamental unit of acoustic cavitation in LUSPT applications, single acoustic cavitation bubble near a skin-like walls play a vital role.To assess the effect mechanism of the texture density on acoustic cavitation efficiency, single bubbles exposed to ultrasound were investigated near skin-like walls with different texture densities.

A. TIME EVOLUTION OF BUBBLE SHAPE
As shown in FIGURE 4, typical dynamics of single bubble near skin-like walls with different texture densities are compared.It was found that there is no significant difference in the radial movement process of bubble morphology near skin-like walls with different texture densities under ultrasound.However, due to the increased texture density, the acoustic field distribution and flow field around the bubble become more complex.As a result, the translational movement speed of the bubble toward the wall under ultrasound significantly decreases, as shown in frames 0 and 1 in FIGURE 4(a-d), directly leading to a delay in the collapse time of the bubble (frames 2-4 of FIGURE 4(a-d)).
It is worth noting that after the first collapse of the bubble, the entire bubble enters the interior of the texture structure.Due to the smaller width between channels on the skin-like wall with a higher texture density, it is easier for the grooves to deform.Therefore, the expansion process of the bubble in the groove before the subsequent collapse is less restricted.The deformation situation of grooves on skin-like walls with different texture densities under the impact of bubble collapse is shown in FIGURE 5.During the second and third collapse of the bubble, the deformation of the groove walls and the position of the bubble at the crossroads of the channels lead to less restriction on the bubble.For channels with a density of 400, the typical  ''mushroom'' shape of the channel wall bubble during the second and the third collapses do not appear (frames 5 and 8 of FIGURE 4(d)), which was evident with texture densities of 1, 25, and 100 (frames 5 and 8 of FIGURE 4(a-c)).This indicates that with the increasing texture density of the skinlike wall, the gradual reduction in the constraining effect of the sidewalls of the groove on the internal bubble directly affects the severity of the subsequent collapse of the bubble.Apart from these, with the increasing texture density, there is no apparent trend in the morphological changes of the bubbles.Additionally, we have observed that the time interval for each bubble collapse is consistently around 50 microseconds, corresponding to one ultrasound cycle.

B. CHARACTERISTICS OF BUBBLE COLLAPSE
For a more detailed analysis of the impact of the texture density on the dynamic characteristics of single cavitation bubbles, we further analyzed the characteristics of bubble collapse time and collapse velocity near skin-like walls with different texture densities.FIGURE 6(a) shows the time of bubble collapse (t c ) with the texture density of skin-like walls.The value of t c , which directly affects the efficiency of acoustic cavitation, is approximately 120 µs when the texture density is 1.As the texture density increases, the collapse time of the bubble continues to increase.For a texture density of 25, the collapse time of the bubble is 126 µs; for a texture density of 100, the bubble collapse time is 144 µs; and for a texture density of 400, the bubble collapse time reaches around 171 µs.Compared to the conditions with a density of 1, the bubble collapse time is delayed by approximately 52 µs under the density of 400 channels.The flow field inside and around the channels is much complex as the presence of texture structure and the ultrasound.With the continuous increase in the number of grooves per unit area, the flow field near the wall becomes more complex.This significantly affects the dynamic process of the bubble.The pressure difference at both sides of the bubble decreases, resulting in a slower translational speed of the bubble to the wall and a longer duration of the translational stage, thus delaying the bubble collapse time.
FIGURE 6(b) illustrates the velocities of the three microjets generated during the collapse of single cavitation bubbles near skin-like walls with different texture densities.The results reveal the following observations: First, there is no significant difference in the values of microjet velocities when cavitation bubbles near skin-like walls with different texture densities undergo the first collapse.This may be attributed to the limitations in the time resolution of the high-speed camera, affecting the accurate capture of the instantaneous process of bubble collapse and preventing precise measurement of microjet velocities.
Second, when the texture density is 1, 25, and 100 (indicated by black, red, and blue colors, respectively), the velocity values of the microjets generated during the three collapses show a trend of initial increase followed by a decrease.This trend is similar to the typical behavior of bubbles near skin-like walls with single groove.
Third, when the texture density is 1, 25, and 100, the values of the microjet velocities during the second and third collapses exhibit a slight increase with the increasing density.This may be attributed to the irregular flow field around the bubble, which increases the total energy during the bubble collapse, leading to larger microjet velocities.
Fourth, when the texture density is 400, the microjet velocities of the bubble undergo significant changes, especially during the third microjet, where the velocity not only does not decrease but also experiences a considerable increase.This may be due to the excessively high texture density, resulting in extremely thin groove side walls.When the bubble collapses, significant deformation of the side walls occurs, affecting the dynamic process of the bubble.Thus, the side walls of the groove cannot restrict the bubble and the collapse velocity keeps increasing.
At last, as the tiny size of the bubble and the ultrafast process of the bubble collapse, the speed of the micro-jet in the present work is actually the average speed during the time interval between two adjacent frames, so the speed of the micro-jet is much slowed in our experiments compared to previous research works.

IV. CONCLUSION
The effects of the skin-like wall's texture density on the dynamics of the single cavitation bubble in an ultrasonic field are investigated in the present work.Synchronous high-speed microscopic imaging is used to record the bubble evolution for investigating the bubble outline.For fabricating skinlike wall, the soft contact lithography is used with PDMS.Four different skin-like walls with various texture density are used in this work.Cavitation bubbles' typical dynamic characteristics are analyzed, and the related findings are as follows: 1) The radial movement time, translational movement time, and collapse time of bubbles increase with the increase in texture density.
2) When the texture density is relatively low (D t =1, 25 or 100), values of the microjet velocities during the second and third collapses show a trend of initial increase followed by a decrease with the increasing texture density.
3) When the texture density is 400, the microjet velocities of the bubble undergo significant changes, especially during the third microjet, where the velocity not only does not decrease but also experiences a considerable increase.
In summary, the difference in the texture density of the skin-like wall significantly changes the bubble dynamics near the skin-like wall in an ultrasonic field.The higher texture density of the skin-like wall's texture density is, the more complex the flow filed near the wall is, the later the bubble collapse firstly, and the more intense dynamics of the bubble later are, such as the increasing speed of the micro-jets.In addition, the bubble near a skin-like wall with a high texture density (D t =400 in this work) shows a trend to more intense dynamics as time goes.These results give an insight in the influence mechanism of the texture density on the single acoustic cavitation bubble and would provide more information in the applications of LUSPT to facilitate their optimizations.According to the conclusions of this work, if a patient's skin has a high texture density, then the intensity of ultrasound should be properly reduced for with a prolonged treatment time in low-frequency ultrasound-assisted drug delivery preventing skin damage.

FIGURE 1 .
FIGURE 1.(a) An example of the skin with a high texture density and (b) skin with a low texture density.

FIGURE 2 .
FIGURE 2. (a) The Schematic diagram of the experimental set-up.(b) the detailed information about the relative position between the bubble and the elastic wall.

FIGURE 3 .
FIGURE 3. Pictures of skin-like walls with different texture densities.

FIGURE 4 .
FIGURE 4. Comparison of the bubble dynamic behaviors near various elastic walls with different densities of the texture (D t ): (a) D t = 1 mm −2 , (b) D t = 25 mm −2 , (c) D t = 100 mm −2 , (d) D t = 400 mm −2 in an ultrasonic field with a frequency of 20.51 kHz.The initial radius of the bubble is R 0 =24 µm, and the initial distance parameter is γ 0 = 2.00.

FIGURE 5 .
FIGURE 5. Deformation of the sidewalls of the texture structure during the initial collapse of the bubble near skin-like walls with various texture densities: (a) D t = 1 mm −2 , (b) D t = 25 mm −2 , (c) D t = 100 mm −2 , (d) D t = 400 mm −2 .
YAN YANG is currently pursuing the B.S. degree in pharmaceutical engineering with Shandong University of Traditional Chinese Medicine, Shandong, China.His research interests include drug delivering systems and medical ultrasound device.HUI CHEN was born in Huangpi, Wuhan, Hubei, China, in 1962.He received the B.S., M.S., and Ph.D. degrees in clinical medicine from Wuhan University, Hubei, in 1985, 1988, and 1999, respectively.From 1999 to 2001, he was a Postdoctoral Researcher with the Western Medical Institute, University of Toronto, Canada.He became a Lecturer in 2001, an Assistant Professor in 2005, and an Associate Professor in 2011 with Downstate College of Medicine, State University, USA.Since 2013, he has been a Professor with the Biomedical Engineering Department, Tianjin Medical University, China.Since 2018, he has been a Distinguished Professor with the Innovative Institute of Chinese Medicine and Pharmacy, Shandong University of Traditional Chinese Medicine, China.He is the author of more than 40 articles.His research interests include neuroscience, brain research, and psychiatry.YUANYUAN LI received the B.S. degree in anesthesiology form Xinxiang Medical University, Henan, China, in 2014, and the Ph.D. degree in biomedical engineering from Tianjin Medical University, Tianjin, China, in 2020.Since 2020, she has been a Lecturer with the Innovative Institute of Chinese Medicine and Pharmacy, Shandong University of Traditional Chinese Medicine, China.Her research interests include neuroscience, brain research, and the applications of medical ultrasound.HAO WU received the B.S. degree in measuring and controlling technology form Sichuan University, Sichuan, China, in 2013, and the M.S. degree in biomedical engineering and the Ph.D. degree in instrument science and technology from Tianjin University, Tianjin, China, in 2016 and 2020, respectively.Since 2020, he has been a Lecturer with the Innovative Institute of Chinese Medicine and Pharmacy, Shandong University of Traditional Chinese Medicine, China.He is the author of one book, more than 20 articles, and five inventions.His research interests include acoustic cavitation, medical instruments, and the applications of medical ultrasound.

TABLE 1 .
Physical characteristics of elastic walls with different texture densities.