Geodesic
Well-posedness of an evaporation model for a spherical droplet exposed to an air flow
Eberhard Bänsch1 ; Martin Doß1 orcid ; Carsten Gräser1 orcid ; Nadja Ray2 orcid
1Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany
2Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany; Catholic University Eichstätt–Ingolstadt, Ingolstadt, Germany
Interfaces and free boundaries, Tome 27 (2025) no. 1, pp. 91-121

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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.
DOI : 10.4171/ifb/524
Classification : 35Q79, 35A01, 35K55, 80A19, 80M10
Mots-clés : single droplet evaporation, Hertz–Knudsen equation, nonlinear boundary condition, coupled ODE–PDE system, direct numerical simulation

Eberhard Bänsch  1   ; Martin Doß  1   ; Carsten Gräser  1   ; Nadja Ray  2

1 Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany
2 Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany; Catholic University Eichstätt–Ingolstadt, Ingolstadt, Germany 
Eberhard Bänsch; Martin Doß; Carsten Gräser; Nadja Ray. Well-posedness of an evaporation model for a spherical droplet exposed to an air flow. Interfaces and free boundaries, Tome 27 (2025) no. 1, pp. 91-121. doi: 10.4171/ifb/524
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