Developing Analytical and Numerical Models for Simulations of Fluid Dynamics [electronic resource].

9780438902503

Ann Arbor : ProQuest Dissertations & Theses, 2018.

1 online resource (92 p.)

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With the development of faster and more powerful computers, highly accurate analytical and numerical models have become more commonplace in the study of fluid dynamics. As such, there is a constant need to refine and develop modeling techniques to allow for the study of more complex fluid systems. In this work, two such models will be discussed: an analytical theory for drop generation in microfluidic devices and an adaptive meshing algorithm for numerical simulations of continuously evolving surfaces. A theory is presented for the transition between the co-flowing and drop-generation regimes observed in multiphase microfluidic channels with rectangular cross-section. This transition is characterized by a critical ratio of the dispersed-to-continuous-phase volume flow rates. At flow-rate ratios greater than this critical value, drop generation is suppressed. The critical ratio corresponds to the fluid cross-section where the dispersed-phase fluid is just tangent to the channel walls. The transition criterion is a function of the ratio of the fluid viscosities, the three-phase contact angle formed between the fluid phases and the channel walls, and the aspect ratio of the channel cross-section; the transition is independent of interfacial tension. Hysteretic behavior of drop generation with respect to the flow-rate ratio is predicted for partially-wetting dispersed-phase fluids. Experimental data are consistent with this theory. A robust adaptive meshing algorithm for triangulated evolving surfaces is presented. The algorithm is based on a mesh energy function and is decoupled from surface evolution, following the work of Cristini et al. (2001). The addition of vertex angle restrictions between adjacent edges prevents the formation of highly distorted or degenerate triangles, leading to a robust algorithm. Angle restriction does not affect the energy of the system, only the pathway to the minimum energy state. The algorithm is illustrated on ellipsoids evolving in linear strain fields. Results indicate that the mesh depends only on the instantaneous surface shape, not shape history. Statistics that describe the perfouuance of the mesh are only weakly dependent on the surface shape.

Dissertations & Theses @ Yale University.

Books / Online / Dissertations & Theses

English

August 21, 2019

Thesis (Ph.D.)--Yale University, 2018.

Yale University.