PERSPECTIVE Cavitation in soft matter PERSPECTIVE Christopher W. Barneya,1, Carey E. Douganb,1, Kelly R. McLeoda, Amir Kazemi-Moridanic, Yue Zhengd, Ziyu Yee, Sacchita Tiwaric, Ipek Sacligila, Robert A. Rigglemanf,2, Shengqiang Caid,2, Jae-Hwang Leec,2, Shelly R. Peytonb,2, Gregory N. Tewa,2, and Alfred J. Crosbya,2 Edited by John A. Rogers, Northwestern University, Evanston, IL, and approved March 10, 2020 (received for review December 11, 2019) 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. soft solids | traumatic brain injury | TBI | rheology | bubble Cavitation is the sudden, unstable expansion of a void collapses a cavity, pressure near the cavity wall becomes or bubble within a liquid or solid subjected to a large. In fact, some measurements have suggested that negative hydrostatic stress. While predominantly stud- collapsing pressures can exceed 6 GPa for water or ied in fluids, cavitation is also an origin of damage in nearly the pressure needed to form diamond (10) Al- soft materials, including biological tissues. Examples though direct measurements are challenging, evidence of cavitation in fluids and soft solids are shown in Fig. 1 for the impact of cavitation-related forces, including A–C. As one key example, strong evidence suggests damage and wear on engineered components and that cavitation occurs in the brain during sudden impacts, biological structures, is well documented (11). leading to traumatic brain injury (TBI) (3). Research on this In solids, cavitation can occur in the solid itself or in life-impacting injury and its relation to cavitation has liquid phases within a solid, such as water within a accelerated in recent years (4–8). A broader and deeper swollen hydrogel or tissue. Whereas cavitation in understanding of cavitation within soft matter is neces- liquids leads to damage on nearby solids on col- sary to navigate the complex paths that lead to damage lapse, cavitation within solids can cause damage to in the brain and other soft materials. the material and surroundings during both the ex- Cavitation in fluids has been studied extensively pansion and collapse. Cavitation in solids has been since Rayleigh’s (9) formulation in 1917, which pre- documented since at least the 1930s; however, this dicted that the maximum pressure in a cavitating liq- process and related pathways to damage have re- uid is proportional to the far-field pressure and inversely ceived considerably less attention than cavitation in proportional to the cavity size. As surface energy liquids (12, 13). aPolymer Science & Engineering Department, University of Massachusetts, Amherst, MA 01003; bDepartment of Chemical Engineering, University of Massachusetts, Amherst, MA 01003; cDepartment of Mechanical & Industrial Engineering, University of Massachusetts, Amherst, MA 01003; dDepartment of Mechanical & Aerospace Engineering, University of California San Diego, La Jolla, CA 92093; eDepartment of Chemistry, University of Pennsylvania, Philadelphia, PA 19104; and fDepartment of Chemical & Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104 Author contributions: C.W.B., C.E.D., K.R.M., A.K.-M., Y.Z., Z.Y., S.T., I.S., R.A.R., S.C., J.-H.L., S.R.P., G.N.T., and A.J.C. wrote the paper. The authors declare no competing interest. This article is a PNAS Direct Submission. This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND). 1C.W.B. and C.E.D. contributed equally to this work. 2To whom correspondence may be addressed. Email: [email protected], [email protected], [email protected], [email protected], tew@ mail.pse.umass.edu, or [email protected]. www.pnas.org/cgi/doi/10.1073/pnas.1920168117 PNAS Latest Articles | 1of9 Downloaded by guest on September 27, 2021 A B C 100 μm 10 EFP/E = 5/6 E=10 kPa D γ/Er = 0 150 8 γ/Er = 0.1 γ/Er = 1 r=λr (kPa) o 6 γ/Er = 10 100 E P / P 4 50 2 al Pressure tic 0 Snap 0 Cri 12 4 6 8 10 10-6 10-5 10-4 10-3 Expansion Ratio Initial Void Radius (m) Fig. 1. (A) Example of cavitation in the wake of an artificial heart valve. Reprinted by permission from ref. 1 (Copyright 1999, Springer Nature: Annals of Biomedical Engineering,). (B) Example of cavitation in knuckles as they crack. Reprinted from ref. 2, which is licensed under CC BY 4.0. (C) Example of cavitation in a synthetic silicone on laser ablation. (D) Schematic of a spherical void of initial radius r in a gel that experiences an unstable snap from a low stretch state to a high stretch state at a critical pressure. (E) Pressure–expansion curves for voids with varying ratios of interfacial energy to elastic modulus. (F) Critical pressure against size scale for a hydrogel with a modulus similar to those reported for biological tissues. The pathways to damage induced by cavitation in tissues and unbounded after a critical pressure is reached. This critical other soft materials are expected to be related. A quantitative pressure approaches E for larger voids. Fig. 1F shows the understanding of how damage depends on the rate of cavity critical expansion pressure for a hydrogel where E = 10 kPa, expansion and collapse and on the molecular and mesoscale a modulus of the same order observed in biological tissues structure will lead to improved predictions for injury detection (16, 18, 19), against r, showing that the Laplace pressure and prevention in tissues. This understanding will also lead to becomes important below 100 μm. the design of more sustainable materials that mitigate or prevent Ball (20) made several contributions to the understanding of damage and new technologies that take advantage of the fast, cavitation in the 1980s, including eliminating the need to assume expansive motions that can be associated with soft material an initial void and extending cavitation theory to compressible cavitation. In this perspective, we provide a concise review of the elastic solids. In addition, cavitation in solids with different defect mechanics and dynamics associated with cavitation in soft solids, shapes, stress states, and materials constitutive relationships has describe current experimental methods to measure the effects of been investigated (21–25). This includes materials with complex cavitation deformations on soft materials and tissues, highlight plasticity, such as metals (26–28). More recently, cavitation driven opportunities for new measurements using cavitation, and by humidity (29, 30) or electric fields (31) has also been studied. A discuss unmet needs and challenges with regard to understand- discussion of the unmet needs in modeling cavitation is contained ing cavitation in soft solids and tissues. in Limits of Current Models. Cavitation Mechanics and Dynamics Dynamics. Dynamic effects in cavitation are often significant (for Elasticity and Surface Energy Formulation for Cavitation. example, in TBI-related cavitation, where strain rates can reach as Failure in soft solids was linked to cavitation-like phenomena as high as 103 s−1 during impact events) (7, 32). The dynamics of early as the 1930s, while the relationship between the critical inertial cavitation were first considered by Rayleigh (9) in de- pressure for cavity expansion and the materials properties was not scribing the pressure–size relationship for a spherical gas bubble developed until the 1950s (12–15). Gent and coworkers (14, 15) in an infinite liquid medium: related the pressure P within a spherical void in an infinitely thick, "# 2 2 neo-Hookean material [e.g., rubber, hydrogels, liver (16), etc.] as d R 3 dR P = ρ R + , [2] sketched in Fig. 1D to its expansion, λ, and elastic modulus, E (14). dt2 2 dt A later modification added the resistance provided by the void’s interfacial energy. Thus, the pressure equation is the superposi- where ρ is the liquid density, t is time, and R is the bubble tion of the elastic component and the Laplace pressure: radius. Eq. 2 can be extended to soft solids by adding the !elasticity and surface tension terms, which are given in Eq. 1 5 2 1 2γ P = P + P = E − − + [1] in Elasticity and Surface Energy Formulation for Cavitation. elastic surface λλ 4 λ 6 3 eq 6ðλλeqÞ r , In addition to inertial effects, viscoelasticity can play an im- portant role at both high and low strain rates. Most soft solids where γ is the interfacial energy, r is the undeformed radius of exhibit viscoelastic behavior, and cavitation rheology techniques −4 −1 the cavity, and λeq is a factor that accounts for the balance (see Fig. 3) span strain rates from the quasistatic regime (10 s ) between interfacial energy and elasticity at no applied exter- to the ultrahigh strain rate regime (108 s−1) (33–36). Furthermore, nal pressure (15, 17). This equation is plotted in Fig.