The motion of a surfactant-laden bubble in a channel or a Hele-Shaw cell

Journal article

We investigate how the addition of surfactant affects the governing equations for a bubble in a two-dimensional channel in the small-capillary-number limit. In the limit where the timescale for absorption of surfactant is much shorter than the timescales for transport of surfactant along the surface of the bubble, we derive a set of idealised free-surface boundary conditions that capture the effects of surfactant in a single dimensionless “elasticity parameter”, and apply them to the front and rear of the bubble separately. At the front of the bubble, there are three regions of interest: the front cap, the thin film region, and a transition region that smoothly connects the other two regions. Through matched asymptotic expansions, we derive predictions for the thin film height and the pressure drop across the front meniscus. We find that the viscous pressure drop across the front meniscus is always larger for a surfactantladen bubble than for a surfactant-free bubble, by an order-one factor of up to 42/3. Using a similar analysis at the rear of the bubble, we find that the viscous pressure drop across the rear meniscus is also always larger in magnitude for a surfactant-laden bubble than for a surfactant-free bubble, again up to a maximum factor of 42/3 . Finally, we use these results to show that, for the same flow conditions, an isolated surfactant-laden bubble in a Hele-Shaw cell will travel more slowly than an isolated surfactant-free bubble.

Authors: Booth, D; Griffiths, IM; Howell, P

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Cambridge University Press
• Journal: Journal of Fluid Mechanics
• Volume: 1025
• Issue: 25
• Article number: A12
• Publication date: 2025-12-12
• Acceptance date: 2025-11-11
• DOI: 10.1017/jfm.2025.10951
• EISSN: 1469-7645
• ISSN: 0022-1120
• Language: English