Two Fluid Flow in a Capillary Tube

  • Melissa Strait
  • Michael Shearer
  • Rachel Levy
  • Luis Cueto-Felgueroso
  • Ruben Juanes
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 109)


A phase field model for two-phase flow in a capillary tube, developed by Cueto-Felgueroso and Juanes, results in a PDE with higher-order terms. We find traveling wave solutions of the PDE and determine a bound on parameters to obtain physically relevant solutions. We observe that the traveling wave height decreases monotonically with capillary number. Finite difference simulations of the injection of a gas finger into water 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 Taylor in his famous 1961 paper. We find agreement between the traveling wave heights and the plateaus seen in the PDE simulations, and the results also compare favorably with the residual fluid thickness observed in the experiments.


Travel Wave Solution Capillary Number Phase Field Model Fourth Order Partial Differential Equation Bulk Free Energy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Research of the first two authors was funded by NSF grant DMS 0968258. Research of the third author was funded by NSF grant 0968154. Research of the last two authors was funded by a DOE CAREER Award, DE-SC0003907, and a DOE Mathematical Multifaceted Integrated Capability Center, DE-SC0009286.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Melissa Strait
    • 1
  • Michael Shearer
    • 1
  • Rachel Levy
    • 2
  • Luis Cueto-Felgueroso
    • 3
  • Ruben Juanes
    • 3
  1. 1.Department of MathematicsNorth Carolina State UniversityRaleighUSA
  2. 2.Department of MathematicsHarvey Mudd CollegeClaremontUSA
  3. 3.Department of Civil and Environmental EngineeringMassachusetts Institute of TechnologyCambridgeUSA

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