Cavitation in Heavy Water and Other Liquids

Abstract

We report on measurements of the cavitation pressure in several liquids subjected to tension in an acoustic wave and compare the results to classical nucleation theory (CNT). This study is motivated by the sizable discrepancy between the acoustic cavitation threshold measured in water and the value predicted by CNT. We find that the same discrepancy is present for heavy water, whereas the agreement is better for ethanol and heptane and intermediate in the case of dimethyl sulfoxide. It is well-known that water is an anomalous liquid, a consequence of its hydrogen-bonded network. The other liquids studied represent very different molecular interactions. Our results indicate that the cavitation threshold approaches the prediction of CNT as the surface tension gets smaller. Conversely, this raises the question of the validity of a simple theory such as CNT to account for high surface tension liquids and suggests that an appropriate microscopic model of such liquids may be necessary to correctly predict the cavitation threshold.

Effects of Ultrasound Frequency and Tissue Stiffness on the Histotripsy Intrinsic Threshold for Cavitation

“…$$p_{t\_\mathrm{italicCNT}}=\left(\frac{16\pi {\alpha }^3}{3{\kappa }_{b}T\ast ln\frac{{\mathrm{italic\Gamma }}_0{V}_f{\tau }_f}{ln2}}\right)0.5$$ where α is the surface energy, k b is the Boltzmann’s constant, T is temperature in Kelvin, Γ 0 is a prefactor, V f is the focal volume for a given frequency, and τ f is the time the focal volume is above a given pressure (Fisher 1948; Pettersen et al 1994; Herbert et al 2006; Arvengas et al 2011a; Arvengas et al 2011b). Γ 0 was set to Γ 0 =10 33 similar to previous work (Pettersen et al 1994) and T was set to 293K to match experiments.…”

“…This value for surface energy was chosen such that results matched the experimental threshold at 500 kHz. Previous work has suggested that, since the cavitation nucleus has a nanoscopic size, it is not accurate to use the bulk, macroscopic surface tension value for surface energy (Herbert et al 2006; Arvengas et al 2011b). The surface energy value used in this study closely matches the value calculated in a previous study by Herbert et al, and resulted in more reasonable results for p t_CNT than those calculated using the macroscopic values of surface tension (Herbert et al 2006).…”

“…Although it is possible that these nuclei too are related to impurities, it seems unlikely, as several groups using different sample processing methods have measured approximately the same threshold for inertial cavitation associated with these nuclei in the range of 24 to 33 MPa in distilled water (Briggs 1950; Greenspan and Tschiegg 1982; Sankin and Teslenko 2003; Caupin and Herbert 2006; Herbert et al 2006; Maxwell et al 2013). Various theoretical studies suggest that the intrinsic nuclei can be modelled as semi-permanent stabilized gas nuclei caused by impurities in the liquid (Harvey et al 1944; Yount 1979; Sankin and Teslenko 2003; Bunkin et al 2009) or spontaneous nuclei that form bubbles in a medium by energy-density fluctuations described by classical nucleation theory (Fisher 1948; Pettersen et al 1994; Arvengas et al 2011a; Arvengas et al 2011b). In the previous study by Maxwell et al ., a theoretical simulation using a 2.5 nm stabilized nuclei resulted in a cavitation threshold closely matching experiments (Maxwell et al 2013).…”

Effects of Temperature on the Histotripsy Intrinsic Threshold for Cavitation

“…CNT predicts that the cavitation threshold decreases at higher temperatures and the corresponding decrease in the surface energy of the medium [40, 42]. The threshold predicted by CNT, p CNT , was calculated as $$p_{\mathit{\text{CNT}}}={true(\frac{16\pi {\alpha }^3}{3k_{b}T\ast \text{ln}\frac{{\mathrm{\Gamma }}_0{V}_f{\tau }_f}{\text{ln }2}}true)}^{0.5}$$where α is the surface energy, k b is the Boltzmann’s constant, T is temperature in Kelvin, Γ 0 is a prefactor, V f is the focal volume for a given frequency, and τ f is the time the focal volume is above a given pressure [24, 40, 42–44]. Γ 0 was set to Γ 0 = 10 34 and τ f set to one half of the acoustic period, similar to previous work [24, 42].…”

Exploring water and other liquids at negative pressure

“…Because the results of acoustic cavitation in water are found to be so far from the CNT prediction, we decided to investigate other liquids to see if the discrepancy was specific to water [41]. Note that this study was performed with our former method to estimate the pressure, which is expected to give values less negative than the actual ones; see [2] nd [35] for details.…”