Cappello, Jean , RIVERO RODRIGUEZ, JAVIER, Scheid, Benoit
No
Eur. Phys. J.-Spec. Top.
Article
Científica
2
2
01/04/2026
001566224800001
When transported by a pressure-driven flow in a cylindrical capillary, bubbles may exhibit very fast velocities. In this paper, we show that when the bubbles are largely deformable, that is, at large capillary numbers Ca, the velocity of the bubble can be larger than the maximal velocity of the flow that transports them. We call this regime "super-fast". However, the situation changes when inertial effects become significant at higher Reynolds numbers (Re\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {Re}$$\end{document}), leading to a decrease in the bubble's relative velocity for sufficiently large values of the Laplace number, defined as La=Re/Ca\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {La}= \text {Re}/ \text {Ca}$$\end{document}. In this article, we uncover the conditions for which the super-fast regime exists: the deformability of the bubble is crucial, and hence the capillary number needs to be larger than a critical value, yet smaller than a threshold above which the bubble breaks up. The two limiting capillary numbers are presented in a phase diagram as a function of the bubble size and the Laplace number.