Investigating the effects of surfactants on nanobubble stability in plant xylem using mathematical models

Carpenter, Jared Connor (2026) Investigating the effects of surfactants on nanobubble stability in plant xylem using mathematical models. Doctoral thesis, University of East Anglia.

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Abstract

Water transport in vascular plants occurs under negative pressures, placing xylem sap in a metastable state that is susceptible to cavitation and embolism. Recent experimental observations have revealed the widespread presence of long-lived, surfactant-coated nanobubbles in xylem sap, challenging the traditional view that gas bubbles inevitably lead to hydraulic failure. The mechanisms by which such nanobubbles persist under physiologically relevant conditions, however, remain poorly understood.

In this thesis, a mathematical framework is developed to investigate the dynamics and stability of surfactant-covered nanobubbles in plant xylem. Starting from the Navier–Stokes equations, the Stokes flow regime appropriate for xylem conditions is derived using dimensional analysis, and classical bubble dynamics are reviewed through the Rayleigh–Plesset equation. Linear stability theory and Floquet theory are employed to analyse both steady and time-periodic bubble behaviour.

Axisymmetric models are formulated to describe deformable bubbles with surfactant-coated interfaces, incorporating interfacial stress balances, gas compressibility, and surfactant transport along the bubble surface. Exact expressions for growth rates are obtained for bubbles with constant base-state radius, both in the presence and absence of surfactants, while time-periodically varying bubbles are analysed using a combination of analytical and numerical techniques. Numerical optimisation methods, including genetic algorithms and simulated annealing, are used to explore the high-dimensional parameter space associated with these models.

The analysis is extended to non-axisymmetric perturbations, allowing fully three-dimensional surface deformations to be considered. In addition, inertial effects are incorporated by relaxing the Stokes flow assumption and considering a simplified inertial regime. Across all models investigated, numerical results consistently indicate that surfactant-covered nanobubbles are dynamically stable over a wide range of physiologically relevant parameters. No growing modes are observed for either axisymmetric or non-axisymmetric perturbations, even under periodic forcing of the bubble radius. The inclusion of inertia does not destabilise steady bubbles within the regimes considered.

These findings suggest that surfactants play a stabilising role in nanobubble dynamics and provide a plausible theoretical explanation for the persistence of nanobubbles observed experimentally in plant xylem. The results support the view that surfactant-covered nanobubbles need not inevitably lead to embolism and contribute to a mathematical understanding of water transport under tension in vascular plants.

Item Type:	Thesis (Doctoral)
Faculty \ School:	Faculty of Science > School of Engineering, Mathematics and Physics
Depositing User:	Chris White
Date Deposited:	18 Jun 2026 07:20
Last Modified:	18 Jun 2026 07:20
URI:	https://ueaeprints.uea.ac.uk/id/eprint/103424
DOI:

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