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Phase Field Models of Two-Fluid Flow...

North Carolina State University.

Phase Field Models of Two-Fluid Flow in a Capillary Tube and Hele-Shaw Cell.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Phase Field Models of Two-Fluid Flow in a Capillary Tube and Hele-Shaw Cell.
作者:	Strait, Melissa Elna.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, 2017
面頁冊數:	124 p.
附註:	Source: Dissertation Abstracts International, Volume: 79-05(E), Section: B.
附註:	Adviser: Michael Shearer.
Contained By:	Dissertation Abstracts International79-05B(E).
標題:	Applied mathematics.
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10708408
ISBN:	9780355458930

Phase Field Models of Two-Fluid Flow in a Capillary Tube and Hele-Shaw Cell.
Strait, Melissa Elna.

Phase Field Models of Two-Fluid Flow in a Capillary Tube and Hele-Shaw Cell. - Ann Arbor : ProQuest Dissertations & Theses, 2017 - 124 p.

Source: Dissertation Abstracts International, Volume: 79-05(E), Section: B.

Thesis (Ph.D.)--North Carolina State University, 2017.

Two recent phase field models, developed by Cueto-Felgueroso and Juanes, describe two-fluid flow in a thin capillary tube and in a Hele-Shaw cell, a configuration in which fluid flows between closely spaced parallel plates. The phase field model for two-fluid ow in a capillary tube [19] results in a degenerate fourth-order partial differential equation (PDE) for the fluid saturation. We find traveling wave solutions of the PDE to capture the injection of a long gas finger into a liquid-filled tube and we determine a bound on parameters to obtain physically relevant solutions. These traveling waves are undercompressive in the sense of shocks and have finite length, ending at the tip of the gas finger, due to the degeneracy of the PDE. We observe that the traveling wave height decreases monotonically with capillary number. Finite difference simulations of the injection of a gas finger into a liquid-filled tube show a traveling wave advancing ahead of a rarefaction, leaving a plateau region of fluid adjacent to the tube wall. The residual thickness of this region was measured in experiments by G.I. Taylor in his famous 1961 paper. We find agreement between the heights of the traveling waves and the plateaus seen in the PDE simulations, and the results also compare favorably with the residual fluid thickness observed in the experiments.

ISBN: 9780355458930Subjects--Topical Terms:

377601
Applied mathematics.

Phase Field Models of Two-Fluid Flow in a Capillary Tube and Hele-Shaw Cell.
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245 1 0 $a Phase Field Models of Two-Fluid Flow in a Capillary Tube and Hele-Shaw Cell.
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500 $a Source: Dissertation Abstracts International, Volume: 79-05(E), Section: B.
500 $a Adviser: Michael Shearer.
502 $a Thesis (Ph.D.)--North Carolina State University, 2017.
520 $a Two recent phase field models, developed by Cueto-Felgueroso and Juanes, describe two-fluid flow in a thin capillary tube and in a Hele-Shaw cell, a configuration in which fluid flows between closely spaced parallel plates. The phase field model for two-fluid ow in a capillary tube [19] results in a degenerate fourth-order partial differential equation (PDE) for the fluid saturation. We find traveling wave solutions of the PDE to capture the injection of a long gas finger into a liquid-filled tube and we determine a bound on parameters to obtain physically relevant solutions. These traveling waves are undercompressive in the sense of shocks and have finite length, ending at the tip of the gas finger, due to the degeneracy of the PDE. We observe that the traveling wave height decreases monotonically with capillary number. Finite difference simulations of the injection of a gas finger into a liquid-filled tube show a traveling wave advancing ahead of a rarefaction, leaving a plateau region of fluid adjacent to the tube wall. The residual thickness of this region was measured in experiments by G.I. Taylor in his famous 1961 paper. We find agreement between the heights of the traveling waves and the plateaus seen in the PDE simulations, and the results also compare favorably with the residual fluid thickness observed in the experiments.
520 $a The phase field Hele-Shaw model [20] is a two-dimensional extension of the capillary tube model and results in a system of two PDEs for the fluid saturation and pressure. We capture the front of a non-wetting fluid when it is injected into a Hele-Shaw cell filled with wetting-fluid by finding one-dimensional traveling wave solutions of the model that connect to zero saturation and have finite length for two different constitutive relations. We determine a bound on parameters so that the saturation remains positive, similar to the bound found in the analysis of the capillary tube model. We also determine that the parameters of the Hele-Shaw model must satisfy an additional restriction in order for the model to admit traveling wave solutions connecting to zero saturation. In the regime in which this requirement is satisfied, we determine that for a given set of parameters, there is a unique traveling wave solution connecting to zero saturation whose height corresponds to a layer of wetting fluid that remains attached to the cell walls during displacement. We find striking behavior when the parameters for the Hele-Shaw model do not satisfy the requirement to have traveling wave solutions connecting to zero saturation. In this regime, numerical simulations show the existence of traveling wave solutions that are expansive in the sense of shocks, and connect to a small positive value.
520 $a We also show that the two-dimensional Hele-Shaw model captures the viscous fingering instability at the interface between the two fluids through a long wave linear stability analysis of a simplified system of equations. This instability occurs when a less viscous fluid displaces a more viscous fluid. Two-dimensional finite-difference simulations confirm this result and we investigate the role of model parameters on the development of this instability through numerical experiments.
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