Keywords
Rayleigh-Plesset equation, bubbles, fluid dynamics
Abstract
This thesis explores bubble dynamics described by the Rayleigh-Plesset equation. The primary focus is on bubble growth. A theoretical discussion of bubble growth is given using the Rayleigh-Plesset equation. This work considers bubble growth in four different cases: a polytropic case without the consideration of surface tension, an isothermal case without surface tension, a polytropic case with surface tension, and an isothermal case with surface tension. Based on these cases, this work develops asymptotic solutions for the evolution of radial bubble growth over time. This thesis provides numerical solutions to these cases through the use of the Runge-Kutta method. These numerical solutions are graphed, showing the evolution of radial growth of bubbles over time. The numerical calculations and analytical asymptotic solutions agree with and, thus, validate one another. By comparison of bubble growth in these four cases, the effects of the polytropic and isothermal states, and of surface tension on bubble growth are investigated. This research shows that, in general, bubble growth in the isothermal case is faster than in the polytropic case. Furthermore, strong surface tension severely limits bubble growth. As surface tension increases, the cutoff radius approaches the initial radius of the bubble, totally suppressing bubble growth and shortening the length of time before bubble growth is cut off. Overall, this thesis concludes that bubble growth is strongly affected by the bubble's thermodynamics and environment and lays the foundation to study the effects of other environmental factors on bubble growth, such as fluid compressibility.
Completion Date
2024
Semester
Fall
Committee Chair
Shivamoggi, Bhimsen
Degree
Master of Science (M.S.)
College
College of Sciences
Department
Mathematics
Degree Program
Mathematical Science
Format
Identifier
DP0029004
Language
English
Release Date
12-15-2024
Access Status
Thesis
Campus Location
Orlando (Main) Campus
STARS Citation
Kulenguski, Kacie, "Mathematical Developments for Bubble Dynamics" (2024). Graduate Thesis and Dissertation post-2024. 40.
https://stars.library.ucf.edu/etd2024/40
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