Mathematical models for fluids with pressure-dependent viscosity flowing in porous media. (February 2015)

• Record Type: Journal Article
• Authors: Fusi, Lorenzo; Farina, Angiolo; Rosso, Fabio
• Is Part Of: International journal of engineering science. Volume 87(2015:Feb.)
• Page Start: 110
• Page End: 118
• Publication Date: 2015-02
• Subjects: Filtration -- Darcy's Law -- Pressure dependent viscosity -- Exact solutions; Engineering -- Periodicals; Ingénierie -- Périodiques; Engineering; Periodicals; 620
• DOI: 10.1016/j.ijengsci.2014.11.007
• Languages: English
• ISSNs: 0020-7225

Abstract

Abstract: In this paper we study three filtration problems through porous media, assuming that the viscosity of the fluid depends on pressure. After showing that in this case Darcy's law is "formally" preserved (meaning that the formal relation remains unchanged except for viscosity that now depends on pressure), we focus on the following problems: Green–Ampt infiltration through a dry porous medium; the Dam problem; the Muskat problem. For each model (free boundary problems) we obtain explicit solutions that allow to quantify the detachment from the classical case, where with the word "classical" we mean that viscosity is taken constant.