Well-posedness of an evaporation model for a spherical droplet exposed to an air flow

Bänsch E, Doß M, Gräser C, Ray N (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Interfaces and Free Boundaries European Mathematical Society

Book Volume: 27

Pages Range: 91-121

Journal Issue: 1

DOI: 10.4171/IFB/524

Abstract

In this paper, we address the well-posedness of an evaporation model for a spherical liquid droplet taking into account the convective impact of an air flow in the ambient gas phase. From a mathematical perspective, we are dealing with a coupled ODE–PDE system for the droplet radius, the temperature distribution, and the vapor concentration. The nonlinear coupling arises from the evaporation rate modeled by the Hertz–Knudsen equation. Under physically meaningful assumptions, we prove existence and uniqueness of a weak solution until the droplet has evaporated completely. Numerical simulations are performed to illustrate how different air flows affect the evaporation process.

Authors with CRIS profile

Eberhard Bänsch Lehrstuhl für Angewandte Mathematik (Wissenschaftliches Rechnen) Martin Doß Carsten Gräser Professur für Wissenschaftliches Rechnen Nadja Ray Department Mathematik

How to cite

APA:

Bänsch, E., Doß, M., Gräser, C., & Ray, N. (2025). Well-posedness of an evaporation model for a spherical droplet exposed to an air flow. Interfaces and Free Boundaries, 27(1), 91-121. https://doi.org/10.4171/IFB/524

MLA:

Bänsch, Eberhard, et al. "Well-posedness of an evaporation model for a spherical droplet exposed to an air flow." Interfaces and Free Boundaries 27.1 (2025): 91-121.

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