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The Interface Dynamics in the Hele-Shaw Cell

Lanre, Akinyemi B.
http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1520530015535937

Abstract Details

2018, Doctor of Philosophy (PhD), Ohio University, Mathematics (Arts and Sciences).
Hele-Shaw free boundary problems have been attracting attention of engineers, physicists and mathematicians for many decades because of the fact that the number of moving boundary processes such as solidification, electro-deposition, flows in porous media can be reduced to Hele-Shaw problems. There are two classical formulation of Hele-Shaw problems which are the one-phase and two-phase Hele-Shaw problems. The one-phase Hele-Shaw problem has been studied extensively by many researchers and many explicit solutions are known. Regarding the two-phase Hele-Shaw problem (also know as the ``Muskat problem''), much less progress has been made. In this dessertation, we study the evolution of a two-phase Hele-Shaw problem under assumption of a negligible surface tension. Our models involve the sinks and sources to be line distributions with disjoint supports located in the exterior and the interior domains as well as time dependent change in the gap width. We use the tools of complex analysis such as the Schwarz function and the complex potential. We give examples of exact solutions when the interface belongs to a certain family of algebraic curves, defined by the initial shape of the boundary.
Tatiana Savin (Advisor)
Aizicovici Sergiu (Committee Member)
Gulisashvili Archil (Committee Member)
Neiman Alexander (Committee Member)
93 p.
Engineering; Mathematics; Physics
Hele-Shaw Cell

Recommended Citations

Citations

  • Lanre, A. B. (2018). The Interface Dynamics in the Hele-Shaw Cell [Doctoral dissertation, Ohio University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1520530015535937

    APA Style (7th edition)

  • Lanre, Akinyemi. The Interface Dynamics in the Hele-Shaw Cell. 2018. Ohio University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1520530015535937.

    MLA Style (8th edition)

  • Lanre, Akinyemi. "The Interface Dynamics in the Hele-Shaw Cell." Doctoral dissertation, Ohio University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1520530015535937

    Chicago Manual of Style (17th edition)

ohiou1520530015535937
979
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This open access ETD is published by Ohio University and OhioLINK.