Contact line instabilities of rotating, viscous droplets

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Roper, Tom William (2024) Contact line instabilities of rotating, viscous droplets. PhD thesis, University of Nottingham.

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Abstract

In this thesis, we investigated the stability of the contact line of an initially ax- isymmetric, fixed volume of viscous fluid upon a flat rotating disc, centred on the axis of rotation. We performed an experimental analysis, concerning the onset and formation of the instabilities at the contact line. The instability at the con- tact line is characterised by an integer number of fingers given by the dominant wavenumber, which is found to be proportional to both the volume and rotation rate in the investigated parameter range.

To complement the experimental results, we performed a linear stability analysis within the lubrication limit of small contact angle. We determined the stability of the free surface for which the fluid is at rest within a rotating frame of ref- erence, subject to small axisymmetric and non-axisymmetric perturbations. We found that the rotating droplet is unconditionally unstable, with the dominant wavenumber increasing with both rotational and gravitational effects when cap- illary effects are included. The growth rates of experimentally prevalent modes and equilibrium solutions both show good qualitative and quantitative agreement with the experimental data simultaneously.

We considered further cases where the contact angle is not small, meaning a lu- brication approximation cannot be employed. Using a finite element method to solve the resulting system, we showed that under these circumstances the insta- bility at the contact line is characterised by a rolling motion. This is found to be contrary to the form of instability under a lubrication approximation, where instability occurs via slip of the contact line radially outwards.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Scase, Matthew
Billingham, John
Turnbull, Barbara
Keywords: fluids, fluid mechanics, finite element method
Subjects: Q Science > QA Mathematics > QA801 Analytic mechanics
T Technology > TA Engineering (General). Civil engineering (General) > TA 357 Fluid mechanics
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 77609
Depositing User: Roper, Tom
Date Deposited: 24 Jul 2024 04:41
Last Modified: 24 Jul 2024 04:41
URI: https://eprints.nottingham.ac.uk/id/eprint/77609

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