Cavitation onset in transient pressure fields

TL;DR

This work defines cavitation onset under transient pressure fields through the unstable equilibrium radius $R_{\text{Ue}}(t)$, bridging quasi-static and dynamic regimes. By modeling a single bubble with the Keller–Miksis equation under a canonical tension pulse and leveraging a dimensionless framework, it uncovers self-similar cavitation onset and establishes Blake threshold $p_C$ as the lower bound. Phase maps across liquids reveal a minimum required tension that scales with pulse duration and initial bubble size, with long pulses recovering quasi-static behavior. The approach yields a predictive, physics-based criterion for cavitation onset applicable to diverse liquids and pulse conditions, and the authors provide open-source code to reproduce the results.

Abstract

While it is well known that cavitation occurs in liquids under tension, no universally accepted criterion for its onset in transient pressure fields exists. We propose a precise definition of the critical tension for cavitation in transient pressure fields that bridges the gap between quasi-static and dynamic regimes, identifying cavitation as the transition of the bubble radius to a dynamically unstable state. This threshold depends on the instantaneous state of the gas-liquid system and, when combined with an appropriate set of dimensionless parameters, yields a self-similar description of cavitation onset. Phase maps for different liquids reveal a minimum tension required for the onset of cavitation, determined by the duration of the tension event and the initial bubble size, whereby the well-known Blake threshold is the lower bound for cavitation across all conditions.

Figures (12)

• Figure 1: Schematic illustration of the liquid pressure $p_\text{L}$, as given by Eq. \ref{['eq:pL']}, as a function of the bubble radius $R$, assuming that the evolution of the bubble radius is a quasi-static process, i.e. $\dot R \rightarrow 0$. The minimum of $p_\text{L}$ is the Blake threshold $p_\text{C}$, given by Eq. \ref{['eq:p_C']}, at the corresponding radius $R_\text{C}$, given by Eq. \ref{['eq:R_C']}.
• Figure 2: Schematic illustration of the liquid pressure $p_\text{L}$ as a function of the bubble radius $R$, alongside the definition of the unstable equilibrium radius $R_{\text{Ue}}(t)$ for different pressure conditions. The blue line corresponds to the stable equilibrium radii and the red line corresponds to the unstable equilibrium radii of the bubble. The minimum of the liquid pressure $p_\text{C,e}(t)$ and the corresponding radius $R_\text{C,e}(t)$ are time-dependent, due to the finite wall velocity $\dot{R}(t)$ in Eq. \ref{['eq:pL']}. If the evolution of the bubble radius is a quasi-static process with $\dot R \rightarrow 0$, $R_{\text{C,e}}(t) \rightarrow R_\text{C}$ as given by Eq. \ref{['eq:R_C']} and $p_{\text{C,e}}(t) \rightarrow p_\text{C}$ as given by Eq. \ref{['eq:p_C']}.
• Figure 3:
• Figure 4: Evolution of the normalized radius $R(t)/R_{0}$ (solid lines) and the normalized unstable equilibrium radius $R_{\text{Ue}}(t)/R_{0}$ (dashed lines) for a bubble subjected to a single tension pulse, Eq. \ref{['eq:pulse']}, of duration $\tau = 10 t_{\text{i}}$.
• Figure 5: (a) Maximum normalized radius $\hat{R}_\text{max} = R_\text{max}/R_{0}$ as a function of the applied normalized liquid tension $\hat{p}_{\text{ng}} = p_{\text{ng}}/p_{\text{ng,C}}$, where $p_{\text{ng,C}}$ stands for the critical tension for cavitation onset, for a bubble subjected to a single tension pulse, Eq. \ref{['eq:pulse']}, of duration $\tau = 10 t_{\text{i}}$. (b) Partial derivative of $\hat{R}_\text{max}$ with regards to $\hat{p}_{\text{ng}}$ as a function of $\hat{p}_{\text{ng}}$.