Fluid mechanics of liquid drops and thin-films


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The natural world is rich with fluids, like liquids, polymers, gels, which are governed by physical laws of motion. The present dissertation is a detailed theoretical, experimental, and numerical study of the complex phenomenon exhibited by liquid drops and liquid thin-films. Studying these systems is important both from fundamental and applied science perspectives.

The first topic of the dissertation is on using pendant droplet tensiometry to measure surface tension of biological fluid secreted by N. rafflesiana pitcher plant. The values of pitcher fluid surface tension is found to be significantly lower than water. In parallel, experiments performed by our collaborators on insect drowning inside pitcher fluid and water indicated that insects find it difficult to come out of pitcher fluid in comparison to water. Lower surface tension of pitcher fluid is presented to be a potential explanation for this.

The second topic is on finding an analytical solution for the resonant frequency of an inviscid sessile drop with small Bond number (surface tension dominates gravity) and a fixed contact line on a flat horizontal plate. The governing equations are expressed in terms of a toroidal coordinate system which yields solutions involving hypergeometric functions. The predictions show excellent agreement with experimental data reported in the literature, particular for drops with low contact angles and higher modes of vibration.

The third topic is to find the underlying physics of filamentous structures formed when sticky pitcher fluids are dewetted on a substrate. By using polyethylene oxide (PEO) aqueous solutions on a polydimethyl siloxane (PDMS) substrate, thin-film dynamics is investigated. Linear stability analysis of the thin-film yields a theoretical critical film thickness at an early stage. When the measured film thickness is smaller than this value, the film is unstable and forms filaments. It is then followed by investigating the intermediate stage thin-film dynamics to theoretically predict the spacing between the filaments. Agreement of the theory is fairly good in comparison to the experiments reported in the literature and performed in the lab.

Wilson, D Ian
Fluid mechanics, Frugal science, Navier-Stokes equations, Physical singularities, Pitcher fluids, Soft matter, Toroidal coordinates
Doctor of Philosophy (PhD)
Awarding Institution
University of Cambridge
S.S. was funded by the Cambridge India Ramanujan Scholarship from the Cambridge Commonwealth, European and International Trust and SERB, Govt. of India.