Unstable growth of bubbles from a constriction

Marc Grosjean; Elise Lorenceau

Home/Archive/arXiv

arXiv · 2210.08858

Unstable growth of bubbles from a constriction

Marc Grosjean·Elise Lorenceau

View original source ↗Read source document ↗Export metadata ↓

Abstract

Bubbles and droplets are ubiquitous in many areas of engineering, including microfluidics where they can serve as microreactors for screening of chemical reactions. They are often formed out of a constriction (a microfluidic channel or a cylindrical tube) by blowing a given volume of gas into a liquid phase. It is obviously crucial to be able to control their size, which is not always easy due to the coupling between the volume of the bubble and the gas pressure induced by the Laplace law. In this paper, we examine the size and formation dynamics of soap bubbles blown from a cylindrical tube, which is the paradigm geometry for bubble and droplet formation. To do so, one end of the tube is closed by a soap film, while the other end is connected to a large reservoir of variable volume filled with gas. To inflate the gas in the bubble, we reduce the volume of the reservoir, which mimics air inflation through the lung diaphragm or the flow-rate driven bubble formation in microfluidics geometry such as flow-focusing. As the volume of the reservoir decreases, the gas pressure increases, the soap film curves and takes the form of a spherical cap with an increasingly smaller radius of curvature. This quasi-static process continues until a critical pressure is reached for which the bubble is quasi-hemispherical. Beyond this pressure, the film undergoes a rapid topological transformation and swells very rapidly (in less than a hundred ms) until it reaches its final volume. We describe this instability in particular by showing that this unstable regime appears when a dimensionless number - whose expression we specify - reaches a critical value. Using a quasi-static model that we solve analytically, we predict the bubble growth dynamics and the final height of the bubble produced for any reservoir volume and constriction size.

Explore related subjects

physics.flu-dyn cond-mat.soft

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Marc Grosjean, Elise Lorenceau. 2022-10-17. Unstable growth of bubbles from a constriction. https://arxiv.org/abs/2210.08858

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Mathematical modeling on peristaltic flow of a Prandtl fluid with effects of slip conditions and inclined magnetic field

The manuscript provides a description of a theoretical analysis of a non-Newtonian Prandtl fluid subject to peristaltic flow through an inclined asymmetric channel. We explore the effect of an inclined magnetic field on the peristaltic flow. This is relevant for applications involving fluid flow in narrow, inclined (tilted) tubes similar to blood vessels or the digestive system. The model also includes thermodynamic aspects such as heat diffusion (the Soret effect) and viscous dissipation resulting from wall-fluid slip conditions, which may help optimize medical devices such as lab-on-a-chip systems and dialysis machines. In this study, the concentration of a generic chemical, temperature, and fluid velocity are taken into account through mass, heat, and momentum balances, respectively. The solution is approximated using numerical techniques suitable for long wavelengths (low frequency) and low Reynolds numbers. The study also discusses trapping phenomena, which are crucial from a clinical point of view. The developed insights can improve the understanding of physiological flows in the gastrointestinal tract and blood vessels. By understanding how the fluid moves and how particles are trapped, these insights may contribute to the design of improved medical pumps and artificial organs. Graphical visualizations are provided for the fluid velocity profile, temperature distribution, and concentration of a generic chemical. Furthermore, the numerical results are validated through comparison with a closed-form solution from a benchmark problem.

physics.flu-dyn↗

arXiv2026

Discovery of a dispersion model at high Peclet numbers

Peclet number characterises the transition from classical Taylor-Aris dispersion to convection-dominated longitudinal solute transport, with the classical model becoming inadequate at extremely high radial Peclet number $Pe_r$. We develop a novel explicit-closure one-dimensional (1-D) effective dispersion model for this high-$Pe_r$ regime by introducing two closure coefficients, $θ_u$ and $θ_d$, whose functional structures are identified using low-frequency transfer-function matching and a modified Kolmogorov-Arnold network (KAN). The resulting model captures the transition from classical Taylor-Aris dispersion at low $Pe_r$ to convection-dominated dispersion at high $Pe_r$. Analysis reveals that, in the high-$Pe_r$ regime, axial transport is redistributed between the effective convection flux and the dispersive flux, resulting in a reduced macroscopic convection velocity. Numerical validation demonstrates close agreement with the convection-diffusion model over the investigated high-$Pe_r$ conditions, while the classical Taylor-Aris model exhibits substantial deviations. Application of the proposed model to averaged flow velocity inversion further demonstrates improved velocity estimation, particularly in the high-$Pe_r$ regime. These results highlight the importance of accounting for non-classical dispersion for reliable contrast-agent-based arterial blood flow velocimetry and provide new insight into high-$Pe_r$ mass transport.

physics.flu-dyn↗

arXiv2026

Optimization of fluid mixing by reinforcement learning using limit cycles of a dynamical system

We propose a method to overcome the difficulties encountered when applying reinforcement learning to fluid mixing processes. The proposed method has two main features: (i) it does not require detailed measurements of the flow state, and (ii) by effectively exploiting a stable limit cycle of a two-dimensional dynamical system (the Li'enard system), it can stably perform optimization without imposing explicit constraints on the control parameters. As an illustrative example, we optimize a process in which a fluid contained in a cylindrical vessel is mixed by periodically rotating the vessel. The resulting optimal vessel motion is physically reasonable: it reverses its direction of rotation before a solid-body rotation state is established. Furthermore, even when the fluid viscosity increases with time during the mixing process, the method can continuously adapt the control parameters to the changing viscosity.

physics.flu-dyn↗