Cavitation is the sudden, unstable expansion of a void or bubble within a liquid or solid subjected to a negative hydrostatic stress. Cavitation rheology is a field emerging from the development of a suite of materials characterization, damage quantification, and therapeutic techniques that exploit the physical principles of cavitation. Cavitation rheology is inherently complex and broad in scope with wide-ranging applications in the biology, chemistry, materials, and mechanics communities. This perspective aims to drive collaboration among these communities and guide discussion by defining a common core of high-priority goals while highlighting emerging opportunities in the field of cavitation rheology. A brief overview of the mechanics and dynamics of cavitation in soft matter is presented. This overview is followed by a discussion of the overarching goals of cavitation rheology and an overview of common experimental techniques. The larger unmet needs and challenges of cavitation in soft matter are then presented alongside specific opportunities for researchers from different disciplines to contribute to the field.
Cavitation is the sudden, unstable expansion of a void or bubble within a liquid or solid subjected to a negative hydrostatic stress. While predominantly studied in fluids, cavitation is also an origin of damage in soft materials, including biological tissues. Examples of cavitation in fluids and soft solids are shown in Fig. 1 A–C. As one key example, strong evidence suggests that cavitation occurs in the brain during sudden impacts, leading to traumatic brain injury (TBI) (3). Research on this life-impacting injury and its relation to cavitation has accelerated in recent years (4567–8). A broader and deeper understanding of cavitation within soft matter is necessary to navigate the complex paths that lead to damage in the brain and other soft materials.
Cavitation in fluids has been studied extensively since Rayleigh’s (9) formulation in 1917, which predicted that the maximum pressure in a cavitating liquid is proportional to the far-field pressure and inversely proportional to the cavity size. As surface energy collapses a cavity, pressure near the cavity wall becomes large. In fact, some measurements have suggested that collapsing pressures can exceed 6 GPa for water or nearly the pressure needed to form diamond (10) Although direct measurements are challenging, evidence for the impact of cavitation-related forces, including damage and wear on engineered components and biological structures, is well documented (11).
In solids, cavitation can occur in the solid itself or in liquid phases within a solid, such as water within a swollen hydrogel or tissue. Whereas cavitation in liquids leads to damage on nearby solids on collapse, cavitation within solids can cause damage to the material and surroundings during both the expansion and collapse. Cavitation in solids has been documented since at least the 1930s; however, this process and related pathways to damage have received considerably less attention than cavitation in liquids (12, 13).
The pathways to damage induced by cavitation in tissues and other soft materials are expected to be related. A quantitative understanding of how damage depends on the rate of cavity expansion and collapse and on the molecular and mesoscale structure will lead to improved predictions for injury detection and prevention in tissues. This understanding will also lead to the design of more sustainable materials that mitigate or prevent damage and new technologies that take advantage of the fast, expansive motions that can be associated with soft material cavitation. In this perspective, we provide a concise review of the mechanics and dynamics associated with cavitation in soft solids, describe current experimental methods to measure the effects of cavitation deformations on soft materials and tissues, highlight opportunities for new measurements using cavitation, and discuss unmet needs and challenges with regard to understanding cavitation in soft solids and tissues.
Failure in soft solids was linked to cavitation-like phenomena as early as the 1930s, while the relationship between the critical pressure for cavity expansion and the materials properties was not developed until the 1950s (121314–15). Gent and coworkers (14, 15) related the pressure within a spherical void in an infinitely thick, neo-Hookean material [e.g., rubber, hydrogels, liver (16), etc.] as sketched in Fig. 1D to its expansion, , and elastic modulus, (14). A later modification added the resistance provided by the void’s interfacial energy. Thus, the pressure equation is the superposition of the elastic component and the Laplace pressure:
Ball (20) made several contributions to the understanding of cavitation in the 1980s, including eliminating the need to assume an initial void and extending cavitation theory to compressible elastic solids. In addition, cavitation in solids with different defect shapes, stress states, and materials constitutive relationships has been investigated (21222324–25). This includes materials with complex plasticity, such as metals (2627–28). More recently, cavitation driven by humidity (29, 30) or electric fields (31) has also been studied. A discussion of the unmet needs in modeling cavitation is contained in Limits of Current Models.
Dynamic effects in cavitation are often significant (for example, in TBI-related cavitation, where strain rates can reach as high as during impact events) (7, 32). The dynamics of inertial cavitation were first considered by Rayleigh (9) in describing the pressure–size relationship for a spherical gas bubble in an infinite liquid medium:
In addition to inertial effects, viscoelasticity can play an important role at both high and low strain rates. Most soft solids exhibit viscoelastic behavior, and cavitation rheology techniques (see Fig. 3) span strain rates from the quasistatic regime () to the ultrahigh strain rate regime () (333435–36). Furthermore, both the strain and strain rate inside a cavitating soft solid can vary dramatically, leading to spatially dependent viscoelastic contributions to cavity dynamics (3738–39). A discussion of the unmet needs in the dynamics of cavitation is contained in Experimental Characterization Challenges and Needs in Materials Synthesis.
While cavitation in soft solids can be elastic, reversible deformation, voids, or defects in a soft solid can also directly or transitionally expand through fracture (14, 40, 41). Fracture is an inelastic, irreversible process involving the rupture of bonds (42). Although cavitation and fracture are different physical processes, differentiating them and understanding their interrelationship have been challenging (40, 434445–46). For soft solids, the question of whether critical deformations are associated with cavitation or fracture is highly relevant for many applications, such as materials characterization (17, 47, 48), design of pressure-sensitive adhesives (42, 49, 50), and understanding damage of biological tissues (3).
The term cavitation rheology was introduced in 2007 by Zimberlin et al. (51) to refer to the characterization technique where a pressurized fluid, either gas or liquid, is injected at the tip of a needle embedded in a gel (i.e., needle-induced cavitation [NIC]), and it has since been widely adopted (17, 18, 35, 36, 47, 5152535455565758596061626364–65). As a diverse set of independently developed cavitation-based characterization techniques has emerged, cavitation rheology has grown to encompass a broad set of characterization methods in addition to NIC (Fig. 2) that rely on the rich dynamics, size scales, and positional sensitivities of cavitation to assess materials properties and behavior. Table 1 contains further information on the dynamic range, spatial sensitivity, and comparison between cavitation rheology and traditional characterization techniques (18, 47, 51, 62, 67).
|Technique||Strain rate* (s-1)||Size scale (μm)||Pressure (Pa)||Single cavity|
|Dynamic uniaxial extension||N/A||N/A|
An overarching goal of cavitation rheology is to exploit the underlying physical principles of cavitation to characterize materials. The ranges of size scales and strain rates over which cavitation rheology operates, summarized in Table 1, make it particularly attractive. Many of these techniques are focused toward soft materials and biological tissues, where standard techniques have issues with clamping, slip, and slump. The inherent complexity of biological tissues makes characterizing them the most demanding application of cavitation rheology (18, 55, 68); however, the unique capability of characterizing properties in the body offers significant promise (53, 69).
Also, cavitation rheology is also used to identify, quantify, and potentially control damage due to cavitation events. Cavitation has long been indicated as a damage mechanism in traumatic tissue injury, but exactly how to quantify the amount of short- and long-term damage caused by cavitation remains an open question (70). Controlling cavitation could lead to strategies to mitigate damage from traumatic cavitation-inducing events, such as high impact and blast situations, or to new therapeutic treatments, similar to breaking up kidney stones.
Below, we introduce three broad categories of cavitation rheology methods.
NIC, as illustrated in Fig. 2A, consists of two distinct processes: 1) puncture of a sample with a needle (71) and 2) pressurization of a fluid at the tip of the embedded needle until rapid deformation of the sample occurs at a critical pressure value (51, 67). The small volume of the measurement, , along with the maneuverability of a needle makes NIC a local measurement with strong position control. When deformation is driven by elasticity, a simplified version of Eq. 1 is used to relate the critical pressure to the elastic modulus of the sample (17, 18, 35, 36, 47, 5152535455565758–59, 62):
The relationships between critical pressure and materials properties that are often used for NIC assume that the samples are well described by a neo-Hookean constitutive relationship. For elastic materials, this assumption has limited influence at the onset of the instability, which often occurs at strains of 30 to 50% (17, 57). As discussed by Pavlovsky et al. (35), viscoelastic effects are also capable of influencing the observed critical pressure. While NIC is typically treated as a quasielastic measurement because the average strain rate on loading is typically of the order , the pressurization rate can be varied to characterize viscoelastic and poroelastic properties (36).
A significant advantage of NIC is the ability to measure mechanical properties across a broad range of size scales (Table 1). However, this ability complicates measurements when probing size scales similar to that of defects or heterogeneous features in the material. Zhu et al. (72) demonstrated the importance of loading conditions by altering the initial stiffness of the instrument to be either compliant (i.e., fixed pressure conditions) or stiff (i.e., fixed volume) loading conditions. Raayai-Ardakani et al. (48, 62) have recently exploited fixed volume conditions to characterize materials properties before and after the critical event to develop a method well suited for characterizing materials stiffer than those typically tested with pressure-controlled systems.
Laser-induced cavitation (LIC) (73), as shown in Fig. 2B, takes advantage of focused optical energy absorption to cause a dielectric breakdown in a transparent medium (74), giving rise to a rapid cavity expansion. In the conventional approach, a high-intensity optical field, typically achieved using a focused laser pulse, ionizes molecules in a transparent (or dielectric) specimen. As ionization substantially increases optical absorption, an avalanche process driven by positive feedback between ionization and optical absorption leads to an abrupt temperature rise and subsequent cavitation at nanosecond timescales and with high expansion speeds (100 to 3,000 m/s). Due to the sensitivity of the initiation and avalanche processes to local variation of material properties, conventional LIC can be less predictable and difficult to quantify with regard to energetics, especially for heterogeneous media, such as biological tissues.
An alternative approach introduces laser-absorbing particles into the specimen to allow for optical energy absorption without the need for nonlinear dielectric breakdown of the medium (75). In this seeded laser-induced cavitation (SLIC), cavitation is significantly less dependent on the optical properties of the test specimens, and the analysis can be more quantitative.
LIC and SLIC have both been broadly applied for tissue imaging and therapy (76), cell lysis (77), drug delivery (78), microfluidic actuation (79), and dynamic mechanical characterization (39). In Estrada et al. (39), a bubble in a gel first rapidly expands to its maximum size and then, oscillates. By fitting theoretical predictions for the oscillations, the viscoelastic responses were quantified through a generalized Kelvin–Voigt model (39). In the case of biological specimens since optical heterogeneity hinders the propagation of optical waves, an optical fiber can be advantageous for LIC within a thick tissue specimen (80, 81). Due to the typical timescale of the cavitation dynamics, which ranges from milliseconds to microseconds, the real-time observation of LIC process is usually achieved by high-frame rate cameras (39). As demonstrated in Fig. 2, fast-repetition rate illumination sources, such as a femtosecond oscillator with a pulse picking system, can be employed in a complementary manner for ultrafast stroboscopic imaging of LIC or SLIC.
Acoustic-induced cavitation (AIC), as shown in Fig. 2C, typically occurs when rapid cycles of large positive and negative pressure are created by high-frequency (kilohertz to megahertz) mechanical vibration. The intense mechanical vibration is achieved either through a direct contact with an ultrasonic transducer or through focused acoustic waves transmitted through a testing medium. AIC using electric transducers has been widely applied to various processes for food (82), energy (83), and nanomaterials (84). Moreover, AIC has long been used in diagnostic and therapeutic applications. For example, focused acoustic energy can alter tissue permeability in cancer treatment, enhancing drug performance and gene delivery (85). In these medical applications, AIC plays a significant role since oscillating and collapsing cavities enhance cellular gene delivery and extravasation. High-intensity focused ultrasound has been applied for destructive applications, such as surgery of premetastatic cancers and lithotripsy, where controlled cavitation can improve the speed and efficacy of the treatments.
Despite the extensive applications of AIC, the rheological applications of AIC are relatively unexplored. In contrast to NIC and LIC, AIC produces a cavitation cloud consisting of microbubbles; thus, collective characteristics of AIC, such as a threshold of the cloud cavitation (86), are preferentially introduced instead of the cavity dynamics of a single bubble.
The techniques discussed in this section are other common examples of cavitation; however, they lack the dynamic and positional control often sought for controlled studies.
The direct dynamic effect of shockwaves on interfaces (i.e., cavitation) can be observed in certain media, such as water and tissues on occasion. Cavitation bubbles occur after the pressure/tension alternating load of a shockwave passes the medium (e.g., heart valve cavitation in Fig. 1C) (1). Many bubbles grow and then, violently collapse while emitting secondary spherical shockwaves. As the shockwave scatters from the proximal cloud surface, a new section of the cloud is generated with each cycle. Shockwave-induced cavitation (SIC), a broad subsection that includes AIC, techniques include drop tower (41), Split–Hopkinson or Kolsky bar (4, 8), and controlled blast (87) setups.
Controlled cavitation events can also occur in specimen geometries where material incompressibility and confining boundaries lead to large hydrostatic pressures in response to a far-field mechanical stress (e.g., knuckle cracking in Fig. 1B) (2). The most common method for controlling such confinement-induced cavitation (CIC) events is uniaxially loading a short cylindrical disc rigidly bonded between two plates (14, 8889–90). This geometry provided the first evidence of cavitation in soft solids (1213–14).
While significant progress has been made in developing cavitation techniques as characterization methods, challenges remain in modeling observed experimental phenomena. Postinstability modeling of cavitation is still limited in both NIC and LIC. In NIC, current experimental protocols exploit the onset of the instability to characterize the mechanical properties (17, 47, 51), which are associated with low strain rates. However, primary damage is most likely incurred during the large-strain, high-strain rate expansion stage. While some work has determined the stabilizing stretch of a cavitation event, addressing damage accumulation during expansion is nontrivial due to the complex large-strain properties of gels and biological tissues (17, 19, 57, 72). In LIC, expansion dynamics have been largely untreated, and the postexpansion modeling has been on inertial effects and viscoelastic dissipation (39). Fracture processes in LIC have been untreated and unexplored.
Modeling cavitation in both solids and fluids is often based on continuum mechanics. However, continuum-level models probe size scales much larger than molecular size scales, and continuum models of cavitation growth assume an initial seeded void site with a specified size. Whether this defect in real materials is an impurity in the sample or a local region of the network where the modulus varies significantly from the bulk remains insufficiently understood. In addition, it is challenging to obtain insights into the transition from cavity expansion to crack initiation and propagation using continuum mechanics models. Recent efforts in glasses, another class of disordered solids, have shown that the response and failure of the material are heavily dictated by the local packing (91) and that certain regions in the sample are more prone to failure than others (92, 93). A similar question can be posed for disordered soft materials, such as polymer networks: is the local network structure important in determining the initial formation and growth of cavity sites, and what must the size of the cavity be before continuum mechanics results can be accurately applied? Is the mesh size of the network the characteristic length that must be exceeded, or is the elastocapillary length the appropriate scale? Molecular dynamics (MD) simulations are expected to play an important role in addressing these issues and connecting to continuum mechanics model length scales, but given the noisy nature of stress data calculated from MD, large-scale simulations with explicit solvent will likely be required to bridge these length scales.
Cavitation rheology techniques span a large range of strain rates and moduli. A summary plot of strain rate against shear moduli measured with different cavitation rheology techniques taken from literature is shown in Fig. 3 with bands representing strain rates during common impact loadings. Considering the data in Fig. 3, one can see that there are still gaps in the current capabilities of cavitation rheology. Comparing the NIC and LIC envelopes, one can see that these characterization techniques operate in distinct regimes, with LIC being a high-strain rate technique and NIC occupying the low-strain regime. Importantly, there are at least two decades separating the properties extracted from each technique. Expanding the capabilities of either technique to bridge this gap is a subject of future interest. Decreasing the pressurization time of NIC to increase strain rate seems to be a viable experimental protocol to accomplish this goal (105).
Experimentally distinguishing cavitation and fracture mechanisms is a significant challenge in cavitation rheology. Gent and Wang (43) first considered this challenge to a limited degree. However, interest in this transition between cavitation and fracture was renewed when Kundu and Crosby (47) experimentally demonstrated that softer solids exhibit a transition from fracture to cavitation at smaller size scales. Following this work, Hutchens et al. (17) used existing theory to generate phase maps of the cavitation and fracture regimes (44, 72).The transition between the two mechanisms was complicated by the fracture criterion often being met during the cavitation expansion. Raayai-Ardakani et al. (48) recently suggested that expansion is not driven solely by fracture and is simultaneously driven by both cavitation and fracture. However, they seem to broadly define cavitation as including any elastic stretching that occurs during the fracture process, whereas cavitation does not occur unless the threshold cavitation pressure is realized.
Observing the void morphology after expansion is insufficient for determining whether or not the deformation was initiated by a fracture process (17). Visualization of the void during the early expansion stage could resolve this ambiguity in the extremes where purely elastic cavitation forms a smooth, spherical bubble and simple crack propagation forms a rough, planar surface. However, soft solids have been found to be particularly susceptible to elastic crack blunting, which could make a fracture process look like a cavitation process in the early stages of expansion (106). Blunting may present itself in NIC, where pressures approach , but should be dynamically present in LIC, where the sample is subjected to pressures well above over a nanosecond timescale. Another solution for NIC is to vary the radius of the needle and observe the size-scale dependence of the critical pressure. As shown in Eqs. 3 and 4, cavitation should have a linear dependence on , while fracture should scale with (47). This solution is limited in that it requires multiple measurements and may not be applicable to small-volume biological samples.
One of the main challenges associated with cavitation is the validation and visualization of a cavitation event, particularly in vivo. Synthetic models are often chosen for transparency, but visualizing a cavitation event is difficult to impossible in opaque tissues. The most common methods of analysis are postdamage MRI and fixing and staining tissue for histopathological analyses. Another method is diffusion tensor imaging, which is sensitive to axonal injury (107). Additionally, there are methods that combine multiple tools (ultrasound, computed tomography scan, and MRI) to analyze cavitation effects for the purpose of developing two-dimensional and three-dimensional (3D) finite difference time domain simulations (108). Thus far, there are no methods that have the capability to detect small-scale cavitation damage on intact tissue in real time. One possibility could be to use NIC or LIC on tissues and image cavitation in real time. Although there have been no successful attempts at visualizing a single bubble cavitation on a fully intact tissue, it is possible to visualize a single bubble cavitation on a thin slice of brain and determine resulting damage to the tissue (8). LIC can be performed on a slice of tissue that is thin enough to be transparent; however, the slicing process alters the 3D integrity of the tissue. To visualize cavitation on a whole intact tissue, one must clarify the tissue. There are two approaches to clearing tissues, solvent-based methods and aqueous methods (109). Although solvent-based methods effectively clear the tissue, the process alters the structure of the tissue by dehydration and lipid removal, making the results inapplicable to real tissue environments. Currently, the best option for visualizing a cavitation event is to fix and stain the tissue immediately after cavitation, allowing for postdamage analysis, similar to the majority of histological analyses performed on animal models undergoing head trauma experiments (110). The ability to visualize a cavitation event in real time is a significant unmet need in the field.
Since the field of cavitation rheology is in its infancy, only a few synthetic systems have been characterized. Gent and coworkers (43, 88) performed many experiments on rubbers. In solvent swollen systems, studies have been performed on physically cross-linked gels, such as agarose and amphiphilic block copolymers (51, 111) and self-assembled organogels (60, 61), and on covalently linked networks, such as polyacrylamide (PAAm) gels (39, 47, 51, 112). However, these systems are “off-the-shelf” materials chosen for convenience rather than specifically designed systems. The development of new materials could drive improved understanding of cavitation in soft materials. The rapid expansion of synthetic chemistry has provided elastic networks with improved connectivity and homogeneity. For example, photo-initiated thiolene chemistry generated bio-inspired networks with excellent resiliency (113).
Cavitation rheology has started to provide a different understanding for some well-studied systems. For example, the mechanical properties of PAAm networks are well established by classical methods in the literature. Although PAAm gels (E =30 kPa) have high resilience at low strains, they are known to be brittle with a strain at break of 40%. More recently, however, high extension values, roughly 300%, in PAAm gels (G = 3 to 10 kPa) were achieved using inertial microcavitation high-strain rate rheometry (39). This discrepancy shows that cavitation phenomenon will provide a different perspective to the field, which classical mechanical testing methods cannot provide.
Another important tool in understanding the stress profile in a cavitation event could be the emergence of so-called “mechanochemistry.” Mechanochromism, a subsection of mechanochemistry, produces color change with mechanical force and is inspired by natural phenomena, such as sonoluminescence (114). In this field, spiropyran-based materials have received significant attention with their ability to turn into a colored merocyanine form in response to applied stress (115, 116).
Biological materials are rich in hydrogen bonds, agarose is gelled with calcium, and titan is known to unfold in multiple steps as the tertiary structure of the protein unravels (117, 118). The continued advancement of highly functionalized, elastic materials is expected to inform cavitation. Beyond improvements in network connectivity and multicomponent systems, the inclusion of dynamic interactions seems to be a rich field ripe for exploration (119120–121). In addition to tailored hydrogen bonding units, metal–ligand interactions that provide tunable interaction strengths and lifetime have been studied (122123–124). The inclusion of folding domains should add new complexity to the cavitation behavior and enable networks to better mimic complex tissues.
The concepts involved in motivating and addressing the needs and challenges in Challenges and Unmet Needs, schematically summarized in Fig. 4, are highly interdisciplinary and vary in scope from applied to deeply fundamental questions that will impact fields beyond cavitation. The versatility in controlling and characterizing complex material response and structure at different size scales and strain rates uniquely qualifies cavitation rheology to address those questions with broader impact. The following subsections summarize open questions discussed fully in Challenges and Unmet Needs, where different communities have the opportunity to contribute to the field of cavitation.
Cavitation rheology is poised to benefit from multiple developments across the mechanics and physics communities. There are currently multiple technical challenges in both the modeling and analysis of cavitation experiments. These challenges lead us to the following open questions.
From applications in tissue characterization to therapeutic and diagnostic medicine, cavitation rheology has immense potential in the field of biology. With regard to injury, specifically TBI, this technique can be utilized to induce cavitation at specific locations within the brain to not only quantify local modulus but also, connect how those variations in moduli correlate with remote tissue and cellular cavitation damage potentially leading to mild TBI. By engaging these questions, biologists will satisfy the overarching goal of establishing cavitation rheology as a foundational tool for characterizing the mechanical response of soft biological tissues.
While the world of cavitation seems to be historically the realm of engineers and physicists, there are growing opportunities for synthetic chemistry to contribute to the field. The chemistry community will significantly aid both the mechanics and biology communities in understanding the physical principles of cavitation as well as using them to advantage in chemical reactions.
Cavitation rheology is a broad field coalescing from the development of characterization, diagnostic, and therapeutic techniques that exploit the underlying physics of cavitation. Cavitation rheology uniquely offers the ability to tune size scales and strain rates from the macro- to microscales and from low to high strain rates, respectively. The larger unmet needs and challenges of cavitation rheology offer opportunities for researchers to contribute toward expanding our knowledge of how soft materials, especially soft tissues, absorb deformation and develop irreversible damage.
This work was funded by Office of Naval Research Grant ONR N00014-17-1-2056. We acknowledge helpful discussions with Prof. Robin C. Young from the Department of Mathematics and Statistics at the University of Massachusetts Amherst.