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Instability in Thin Liquid Film Flow Over an Uneven, Periodic Incline in the Presence of Surfactant

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posted on 2024-06-19, 00:46 authored by Eugene Zivkov

We consider gravity-driven fluid flow down a wavy inclined surface in the presence of surfactant. The periodicity of the bottom topography allows us to leverage Floquet theory to determine the correct form for the solution to the linearized governing partial differential equations. The result is that perturbations from steady state are wavelike, and a dispersion relation is identified which relates the wavenumber of an initial perturbation, κ, to its complex frequency, ω. The real part of ω ultimately determines the stability of the flow. We observe that the addition of surfactant generally has a stabilizing effect on the flow, but has a destabilizing effect for small wavenumbers. These results are compared and validated against nonlinear results, which are obtained by numerically solving the governing equations directly. The linear and nonlinear analyses show good agreement, except at small wavenumbers, where the linear results could not be replicated.

History

Language

eng

Degree

  • Master of Science

Program

  • Applied Mathematics

Granting Institution

Ryerson University

LAC Thesis Type

  • Thesis

Thesis Advisor

J.P. Pascal

Year

2022

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    Applied Mathematics (Theses)

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