A three-phase free boundary problem with melting ice and dissolving gas

  title={A three-phase free boundary problem with melting ice and dissolving gas},
  author={Maurizio Ceseri and John M. Stockie},
  journal={European Journal of Applied Mathematics},
  pages={449 - 480}
  • M. CeseriJ. Stockie
  • Published 3 January 2013
  • Mathematics
  • European Journal of Applied Mathematics
We develop a mathematical model for a three-phase free boundary problem in one dimension that involves interactions between gas, water and ice. The dynamics are driven by melting of the ice layer, while the pressurized gas also dissolves within the meltwater. The model incorporates the Stefan condition at the water–ice interface along with Henry's law for dissolution of gas at the gas–water interface. We employ a quasi-steady approximation for the phase temperatures and then derive a series… 

Numerical modeling of three‐phase dissolution of underground cavities using a diffuse interface model

Natural evaporite dissolution in the subsurface can lead to cavities having critical dimensions in the sense of mechanical stability. Geomechanical effects may be significant for people and

Melting and dripping of a heated material with temperature-dependent viscosity in a thin vertical tube

Abstract We consider the flow of a thermoviscous fluid within a vertical tube which is heated from below, modelling a scenario where a fluid melts, flows and eventually drips due to a

Multiscale model of a freeze–thaw process for tree sap exudation

A multiscale model consisting of a nonlinear system of differential equations governing phase change and transport within wood cells, coupled to a suitably homogenized equation for temperature on the macroscale is derived, providing convincing evidence that a purely physical mechanism is capable of capturing exudation.

Deep learning and American options via free boundary framework

The proposed deep learning method presents an efficient and alternative way of pricing options with early exercise features and establishes equations that approximate the early exercise boundary and its derivative directly from the DNN output based on some linear relationships at the left boundary.

Mathematics For Industry: A Personal Perspective

"I am an industrial mathematician." When asked to identify my profession or academic field of study, this is the most concise answer I can provide. However, this seemingly straightforward statement

A Mathematical Model for Maple Sap Exudation

Sap exudation refers to the process whereby sugar maple trees (Acer saccharum) are capable of generating significant stem pressure in a leafless state, something that occurs to a lesser extent in



Mathematical Models of Gas Hydrates Dissociation in Porous Media

Abstract: In strata hydrates may exist in different forms: as hydrates alone, hydrates in conjunction with free gas, or with gas and water in state of thermodynamic equilibrium, hydrates with excess

Asymptotic results for the Stefan problem with kinetic undercooling

We study the behaviour of the one-phase Stefan problem with kinetic undercooling; moving boundary problems governed by the same formulation also arise in the modelling of silicon oxidation and of

Solutions for the two-phase Stefan problem with the Gibbs–Thomson Law for the melting temperature

  • S. Luckhaus
  • Mathematics
    European Journal of Applied Mathematics
  • 1990
The coupling of the Stefan equation for the heat flow with the Gibbs–Thomson law relating the melting temperature to the mean curvature of the phase interface is considered. Solutions, global in

Free boundary problems in science and technology

854 NOTICES OF THE AMS VOLUME 47, NUMBER 8 F ree boundary problems deal with solving partial differential equations (PDEs) in a domain, a part of whose boundary is unknown in advance; that portion of

Modeling dynamic marine gas hydrate systems

Abstract Dynamically changing marine gas hydrate systems are the subject of this study. The changes may result from varying pressure or temperature at the seafloor, exploration and exploitation

Non-aqueous Phase Liquid Spills in Freezing and Thawing Soils: Critical Analysis of Pore-Scale Processes

The frequent use of non-aqueous phase liquids (NAPLs) in cold regions creates serious risks of soil and groundwater contamination. NAPL contaminants can stay in soil for long times due to their

Existence of Solutions for One-dimensional Wave Equations with Nonlocal Conditions

In this article we study an initial and boundary-value problem with a nonlocal integral condition for a one-dimensional wave equation. We prove existence and uniqueness of classical solution and nd

Free boundary problems in controlled release pharmaceuticals. I: diffusion in glassy polymers

This paper formulates and studies two different problems occurring in the formation and use of pharmaceuticals via controlled release methods. These problems involve a glassy polymer and a penetrant,