Year: 2026
Type: preprint
Abstract: Epithelial tissues play a fundamental role in morphogenesis. Mechanically they can be viewed as thin soft materials exhibiting a solid-fluid duality. The Surface Navier-Stokes-Helfrich model accounts for these properties by combining bending and surface hydrodynamics. In order to account for varying cell thickness we incorporate a thickness field in the spirit of a shallow-water equation, but defined on the (self-)evolving surface. This replaces the inextensibility constraint of the two-dimensional fluid and with it the conservation of surface area by an incompressibility constraint of the thin film fluid allowing for changes in surface area. We develop a numerical scheme based on surface finite elements, perform convergence tests, demonstrate the impact on shape evolution of closed surfaces with a constant enclosed volume and discuss implications on modeling morphogenesis.
Source: arXiv (Cornell University)
Authors: Sischka, Jan Magnus, Voigt, Axel
Institution: Technische Universität Dresden
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Awards: G1438622245, G1575401848
OpenAlex ID: W7221197388