Date of Award
1-1-2025
Document Type
Dissertation
Degree Name
Ph.D. in Physics
First Advisor
Likun Zhang
Second Advisor
Nathan Murray
Third Advisor
Cecille Labuda
School
University of Mississippi
Relational Format
dissertation/thesis
Abstract
Capillary–gravity wave scattering is crucial in fluid systems governed by gravitational and surface tension forces, yet classical theories often neglect key boundary and geometric effects. This dissertation examines two influential mechanisms—dynamic contact line conditions and meniscus curvature—that significantly affect wave behavior at smaller scales.
First, a semi-analytical framework is presented to show how dynamic contact lines, modeled by an effective-slip boundary, alter wave reflection and transmission around a fixed, semi-immersed cylindrical barrier. Using linear potential flow theory combined with conformal mapping and integral-equation methods, the study quantifies how barrier geometry, Bond number, and slip parameters shape energy dissipation. It identifies a “dissipation ridge,” where contact line speed resonates with capillary wave speeds, maximizing energy loss through impedance matching.
In a complementary analysis, the second part explores meniscus curvature. Two linearized models are formulated—one measuring wave displacement relative to a static meniscus and another accommodating arbitrary shapes, including overturned surfaces. Numerical comparisons with recent experiments confirm that meniscus geometry can induce sizable deviations from classic flat-surface predictions. Notably, wave transmission rises significantly when the barrier meets the meniscus crest, then falls abruptly as the meniscus overturns.
These findings provide a fuller depiction of small-scale wave–structure interactions, bridging classical scattering theory and new experimental evidence. They reveal how refined boundary conditions and free-surface shapes can strongly influence energy partitioning and dissipation in capillary–gravity flows. Beyond advancing fundamental insights, these results inform practical wave mitigation strategies in coastal and offshore engineering, as well as microfluidic devices that harness capillary effects for flow control.
Recommended Citation
Liu, Guoqin, "Modeling Capillary-Gravity Wave Scattering with Contact Lines and Meniscus" (2025). Electronic Theses and Dissertations. 3320.
https://egrove.olemiss.edu/etd/3320
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