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Imagine a tiny steam bubble forming inside a fast water flow, like in a Venturi tube. As the water speeds up, pressure drops and the bubble appears. But what happens when the bubble contracts? A recent study introduced a mathematical model that pinpoints the exact moment the bubble "explodes".

The key factor is the bubble's surface temperature. If it exceeds a critical threshold of 647 K (about 374 °C), the bubble becomes unstable and collapses irreversibly, regardless of its size. The model accounts for heat and mass exchange between the bubble and surrounding water, simulating various flow conditions.

Results show that both simulations and real experiments confirm the condition Ts ≥ Tcr predicts collapse with a maximum error of 6 %. This means hydraulic parameters like speed and pressure govern cavitation intensity. Understanding this mechanism is crucial for improving technologies that use cavitation, from industrial cleaning to energy generation.

In short, the critical temperature acts as a "stop signal" for steam bubbles: once crossed, the bubble shatters, releasing energy and creating pressure waves that can be either useful or harmful depending on the application.

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The proposed mathematical model builds upon the Rayleigh‑Plesset equation, augmented with heat and mass transfer terms at the bubble boundary. Surface temperature Ts is computed via an energy balance that includes thermal conduction through the vapor layer, coupled with mass flux due to evaporation/condensation. The critical temperature Tcr = 647 K corresponds to water's critical point, where vapor density and viscosity undergo abrupt changes, promoting surface instability.

Numerical simulations were performed using a finite element method (FEM) in a 2‑D domain representing the velocity profile of a Venturi tube. Reynolds number (Re) and inlet pressure were varied to replicate laminar and turbulent flow conditions. Results show that once Ts exceeds the critical value, internal bubble pressure drops sharply, generating a shock wave that triggers an almost instantaneous collapse.

Comparison with experimental data—obtained via high‑speed imaging and pressure sensors—validated the Ts ≥ Tcr criterion with a maximum discrepancy of 6 %. This error margin stems from uncertainties in surface temperature measurement and micro‑turbulence effects not captured by the model.

Practically, by controlling hydraulic parameters (velocity, pressure, conduit geometry), the intensity of cavitation can be tuned. In applications such as ultrasonic cleaning or micro‑bubble generation for medical therapy, the ability to predict and manage bubble collapse is essential for optimizing efficiency and minimizing component wear.

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Authors:
Hanna KoshlakAnatoliy Pavlenko
Date Published:
Original Article www.mdpi.com
Fact-check verified on 02/03/2026
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Creative Commons License CC BY-NC-SA 4.0

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