United Arab Emirates

The United Arab Emirates (UAE) is part of the geographic region known as the Middle East. With a land mass of 82,000 square kilometres, predominantly desert and mountains it is bordered by Oman, Saudi Arabia and the Arabian Gulf. The UAE is strategically located due to its proximity to other oil rich Middle Eastern countries such as Kuwait, Iraq, Iran, and Saudi Arabia. The UAE was formed from a federation of seven emirates (Abu Dhabi, Dubai, Sharjah, Ras Al Khaimah, Ajman, Fujuriah, and Um Al Quain) in December 1971 (Ras Al Khaimah did not join the federation until 1972) (Heard-bey, 2004, 370). Abu Dhabi is the political capital, and the richest emirate; while Dubai is the commercial centre. The majority of the population of the various Emirates live along the coast line as sources of fresh water often heavily influenced the site of different settlements. Unlike some near neighbours (Iran and Iraq) the UAE has not undergone any significant political instability since it was formed in 1971. Due to this early British influences the UAE has had very strong political and economic ties with first Britain, and, more recently, the United States of America (Rugh, 2007). Until the economic production of oil in the early 1960’s the different Emirates had survived on a mixture of primary industry (dates), farming (goats and camels), pearling and subsidies from Britain (Davidson 2005, 3; Hvit, 2007, 565) Along with near neighbours Kuwait, Bahrain, Oman, Qatar and Saudi Arabia, the UAE is part of the Gulf Cooperation Council (GCC), a trading bloc. (Hellyer, 2001, 166-168).

Gravity-driven fingering simulations for a thin liquid film flowing down the outside of a vertical cylinder

A numerical study is presented to examine the fingering instability of a gravity-driven thin liquid film flowing down the outer wall of a vertical cylinder. The lubrication approximation is employed to derive an evolution equation for the height of the film, which is dependent on a single parameter, the dimensionless cylinder radius. This equation is identified as a special case of that which describes thin film flow down an inclined plane. Fully three-dimensional simulations of the film depict a fingering pattern at the advancing contact line. We find the number of fingers observed in our simulations to be in excellent agreement with experimental observations and a linear stability analysis reported recently by Smolka & SeGall (Phys Fluids 23, 092103 (2011)). As the radius of the cylinder decreases, the modes of perturbation have an increased growth rate, thus increasing cylinder curvature partially acts to encourage the contact line instability. In direct competition with this behaviour, a decrease in cylinder radius means that fewer fingers are able to form around the circumference of the cylinder. Indeed, for a sufficiently small radius, a transition is observed, at which point the contact line is stable to transverse perturbations of all wavenumbers. In this regime, free surface instabilities lead to the development of wave patterns in the axial direction, and the flow features become perfectly analogous to the two-dimensional flow of a thin film down an inverted plane as studied by Lin & Kondic (Phys Fluids 22, 052105 (2010)). Finally, we simulate the flow of a single drop down the outside of the cylinder. Our results show that for drops with low volume, the cylinder curvature has the effect of increasing drop speed and hence promoting the phenomenon of pearling. On the other hand, drops with much larger volume evolve to form single long rivulets with a similar shape to a finger formed in the aforementioned simulations.

Mathematical modelling of the impaction and spreading of spray droplets on leaves

This thesis concerns the development of mathematical models to describe the interactions that occur between spray droplets and leaves. Models are presented that not only provide a contribution to mathematical knowledge in the field of fluid dynamics, but are also of utility within the agrichemical industry. The thesis is presented in two parts. First, thin film models are implemented with efficient numerical schemes in order to simulate droplets on virtual leaf surfaces. Then the interception event is considered, whereby energy balance techniques are employed to instantaneously predict whether an impacting droplet will bounce, splash, or adhere to a leaf.