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A Numerical Analysis of the Influence of Korteweg Stresses on the Flow and Mixing of Miscible Fluids

Wilson, Raymond Gary

Abstract Details

2004, Doctor of Philosophy, Case Western Reserve University, Mechanical Engineering.
When two fully miscible fluids initially share a common dividing surface a surface tension between the fluids can not exist since they are fully miscible and yet very often the interface appears to act as if there were an interfacial tension. Possible sources of this behavior are the theoretical Korteweg stresses which, according to Korteweg’s theory occur when there are high concentration gradients. These Korteweg stresses which are in addition to the usual Navier-Stokes stresses may impact the behavior of the interface. When one fluid is displacing another the behavior of the interface is important in how efficiently the fluid being displaced is removed from the medium in which it is contained. For example, if the interface remains flat (stable) and the two fluids do not penetrate one another then the removal process will be efficient. However, if the interface is unstable, and one fluid penetrates the other, the removal process becomes inefficient since the displacing fluid would eventually “break through” ending the removal process. Determining the sources of instability and knowing under what conditions the instability will occur will help in the design of fluids for extracting a second fluid from a porous medium or piping system. To study the impact of the Korteweg stresses a problem was selected so that the mass diffusion and velocity fields would reach steady-state. The problem is analogous to the Graetz heat transfer problem except that concentration at the wall makes a step change and is held constant rather than temperature or heat flux. The concentration field reaches a steady-state and a region of high concentration gradient forms where the step change occurs. In the regions of high concentration gradient the impact of Korteweg stresses is studied as well as the impact of viscosity ratio and Reynolds number. The results of the study show that the viscosity ratio of a more viscous fluid displacing a less viscous fluid has the most influence on the flow field. The Reynolds number and the Korteweg stress Delta coefficient had a minimal impact on the flow field for the range of Reynolds number and Peclet number that was studied.
J. Iwan Alexander (Advisor)
408 p.

Recommended Citations

Citations

  • Wilson, R. G. (2004). A Numerical Analysis of the Influence of Korteweg Stresses on the Flow and Mixing of Miscible Fluids [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1081283678

    APA Style (7th edition)

  • Wilson, Raymond. A Numerical Analysis of the Influence of Korteweg Stresses on the Flow and Mixing of Miscible Fluids. 2004. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1081283678.

    MLA Style (8th edition)

  • Wilson, Raymond. "A Numerical Analysis of the Influence of Korteweg Stresses on the Flow and Mixing of Miscible Fluids." Doctoral dissertation, Case Western Reserve University, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=case1081283678

    Chicago Manual of Style (17th edition)