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

Format

PDF

Identifier

DP0029004

Language

English

Release Date

12-15-2024

Document Type

Thesis

Campus Location

Orlando (Main) Campus

Subjects

Bubbles--Dynamics; Bubbles--Mathematical models; Bubbles--Thermodynamics; Fluid dynamics--Mathematical models; Surface tension--Mathematical models

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