arXiv subjects

D. Ian Wilson

Publications and source records attributed to D. Ian Wilson.

3 recordsLinked to original sources

arXiv2023

Origin of filaments in finite-time in Newtonian and non-Newtonian thin-films

The sticky fluids found in pitcher plant leaf vessels can leave fractal-like filaments behind when dewetting from a substrate. To understand the origin of these filaments, we investigate the dynamics of a retreating thin-film of aqueous polyethylene oxide (PEO) solutions which partially wet polydimethyl siloxane (PDMS) substrates. Under certain conditions the retreating film generates regularly-spaced liquid filaments. The early-stage thin-film dynamics of dewetting are investigated to identify a theoretical criterion for liquid filament formation. Starting with a linear stability analysis of a Newtonian or simple non-Newtonian (power-law) thin-film, a critical film thickness is identified which depends on the Hamaker constant for the fluid-substrate pair and the surface tension of the fluid. When the measured film thickness is smaller than this value, the film is unstable and forms filaments as a result of van der Waals forces dominating its behaviour. This critical film-height is compared with experimental measurements of film thickness obtained for receding films of Newtonian (glycerol-water mixtures) and non-Newtonian (PEO) solutions generated on substrates inclined at angles 0 $^{\circ}$, 30 $^{\circ}$, and 60 $^{\circ}$ to the vertical. The observations of filament and its absence show good agreement with the theory. The evolution of the thin-film shape is modelled numerically to show that the formation of filaments arises because the thin-film equation features a singular solution after a finite-time, hence termed a "finite-time singularity".

cond-mat.soft↗

arXiv2021

Experimental evidence for surface tension origin of the circular hydraulic jump

For more than a century, the consensus has been that the thin-film hydraulic jump that can be seen in kitchen sinks is created by gravity. However, we recently reported that these jumps are created by surface tension, and gravity does not play a significant role. In this paper, {we present experimental data for hydraulic jump experiments conducted in a micro-gravity environment ($\approx 2\%$ of Earth's gravity) (Avedisian \& Zhao 2000; Painter et al. 2007; Phillips et al. 2008). The existence of a hydraulic jump in micro-gravity unequivocally confirms that gravity is not the principal force causing the formation of the kitchen sink hydraulic jump.} We also present thirteen sets of experimental data conducted under terrestrial gravity reported in the literature for jumps in the steady-state for a range of liquids with different physical parameters, flow rates and experimental conditions. There is good agreement with {Bhagat et al.}'s theoretical predictions. We also show that beyond a critical flow rate, $Q_C^* \propto γ^2 /νρ^2 g$, gravity does influence the hydraulic jumps. At lower flow rates, at the scale of the kitchen sink, surface tension is the dominating force. We discuss previously reported phenomenological and predictive models of hydraulic jumps and show that the phenomenological model -- effectively a statement of continuity of radial momentum across the jump -- does not allow the mechanism of the origin of the jump to be identified. However, combining the phenomenological model and {Bhagat et al.}'s theory allows us to predict the height of the jump.

physics.flu-dyn↗

arXiv2020

Natural oscillations of a sessile drop: Inviscid theory

We present a fully analytical solution for the natural oscillation of an inviscid sessile drop of arbitrary contact angle on a horizontal plate for the case for the case of low Bond number, when surface tension dominates gravity. The governing equations are expressed in terms of the toroidal coordinate system which yields solutions involving hypergeometric functions. Resonant frequencies are identified for zonal, sectoral and tesseral vibration modes. The predictions show good agreement with experimental data reported in the literature, with better agreement than the model of \citeauthor{bostwick} (\textit{J. Fluid Mech.}, vol. 760, 2014, 5-38), particularly for flatter drops (lower contact angle) and higher modes of vibration. The impact of viscous dissipation is discussed briefly.

physics.flu-dyn↗