Abstract
dc:description.abstractWhen a water droplet freezes on a cold plate, a pointy tip forms as the result of volume expansion. In this dissertation, we will introduce a quasi-compressible phase-field model that deals with this non-isothermal three-phase system involving water, ice, and air. The water-ice phase transition and the water-air fluid interface are handled by the Allen-Cahn and the Cahn-Hilliard equations, respectively. The governing equations, including the two phase-field equations, the Navier-Stokes equations, and the energy equation, are designed such that the non-negative entropy production is guaranteed. These equations are then solved by finite-element methods using the open-source deal.ii library. Our model reproduces the Gibbs-Thomson and Clausius-Clapeyron equations, which establish the dependence of the melting temperature on interface curvature and pressure, respectively. Furthermore, the built-in quasi-compressibility accurately accounts for the volume change due to the water-ice density contrast during the phase transition. With proper parameters, our simulation captures the pointy tip of the frozen droplet with good agreement with the experiment.
Degree
thesis:*- Name thesis:degree_name
- Doctor of Philosophy
- Level thesis:degree_level
- doctoral
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 2026
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Li, Yichen
- Chair dc:contributor.committeechair
-
- Yue, Pengtao
- Committee members dc:contributor.committeemember
-
- Liu, Honghu
- Iliescu, Traian
- Borggaard, Jeffrey T.
Subjects
dc:subject × 5Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
- Language dc:language.iso
- en
Identifiers
dc:identifier.*- Dc Identifier Other
- vt_gsexam:45552
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/140809