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Title Thin fluid films subject to external airflows / Colin Paterson.
Name Paterson, Colin .
Abstract We use lubrication theory to analyse the steady flow of thin ridges, rivulets and rings of fluid and, in particular, we study the behaviour when the fluid is in the presence of an external airflow. Firstly, a thin ridge on an inclined planar substrate subject to a spatially varying pressure gradient due to an external airflow is considered. The effect of increasing the strength of the external airflow, and of increasing the inclination of the substrate to the horizontal, on a ridge of prescribed constant volume is investigated, and we identify and quantify the conditions for the ridge to de-pin at one or both of its contact lines. Secondly, we describe the possible pinning and subsequent de-pinning of a thin rivulet with constant nonzero contact angle as well as the possible de-pinning and subsequent re-pinning of a thin rivulet with constant width as they flow with prescribed volume flux in the azimuthal direction from the top to the bottom of a large horizontal cylinder. Thirdly, this problem is extended to include the effects of a prescribed uniform azimuthal surface shear stress arising from an external airflow in the direction opposing gravity. Lastly, we consider a thin ring of fluid with constant width and constant mass that flows in the azimuthal direction all the way round a large horizontal cylinder (a "full ring" of fluid) subject to a prescribed uniform azimuthal surface shear stress due to an external airflow. In particular, there is a maximum mass of fluid above which no full-ring solution exists, and we show that backflow near the cylinder surface is possible.
Publication date 2013
Name University of Strathclyde. Dept. of Mathematics and Statistics.
Thesis note Thesis PhD University of Strathclyde 2013 T13565
System Number 000003274

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