Numerical simulations of bubble cloud dynamics in tree xylem

Xylem sap transport in trees is driven by a negative pressure gradient [Cochard C. R. Phys. (2006)] generated by transpiration. This mechanism renders the xylem susceptible to embolism formation via cavitation under conditions of reduced ambient pressure. Although cavitation events have been empirically observed in trees [Peters et al. J. Exp. Bot. (2020)], the interaction between cavitation nucleation and the xylem elasticity is poorly understood. We model the internal structure of a tree as a poroelastic material filled with liquid water in which cavitation forms as a dilute population of bubbles (i.e., a bubble cloud). Each bubble in the cloud is concentrically surrounded by liquid water and an elastic material. We use the open-source Multi-component Flow Code (MFC) [Radhakrishnan & Le Berre et al. Comp. Phys. Comm. (2024)] to conduct 3D Euler-Euler sub-grid models of cavitation in a tree-analogous environment. The surrounding material is modeled as a Kelvin-Voigt viscoelastic material with hypoelasticity. We show the wave propagation within the model tree and influence of multiple embolisms. We compare results between polydisperse and monodispersed populations of bubbles for different experimental elastic material stiffnesses.