Paterson, C. and Wilson, S. K. and Duffy, B. R. (2013) Pinning, depinning and repinning of a slowly varying rivulet. European Journal of Mechanics B/Fluids . (Submitted)

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Abstract
The solutions for the unidirectional flow of a thin rivulet with prescribed volume flux down an inclined planar substrate are used to describe the locally unidirectional flow of a rivulet with constant width (i.e. pinned contact lines) but slowly varying contact angle as well as the possible pinning and subsequent depinning of a rivulet with constant contact angle and the possible depinning and subsequent repinning of a rivulet with constant width as they flow in the azimuthal direction from the top to the bottom of a large horizontal cylinder. Despite being the same locally, the global behaviour of a rivulet with constant width can be very different from that of a rivulet with constant contact angle. In particular, while a rivulet with constant nonzero contact angle can always run from the top to the bottom of the cylinder, the behaviour of a rivulet with constant width depends on the value of the width. Specifically, while a narrow rivulet can run all the way from the top to the bottom of the cylinder, a wide rivulet can run from the top of the cylinder only to a critical azimuthal angle. The scenario in which the hitherto pinned contact lines of the rivulet depin at the critical azimuthal angle and the rivulet runs from the critical azimuthal angle to the bottom of the cylinder with zero contact angle but slowly varying width is discussed. The pinning and depinning of a rivulet with constant contact angle, and the corresponding situation involving the depinning and repinning of a rivulet with constant width at a nonzero contact angle which generalises the depinning at zero contact angle discussed earlier, are described. In the latter situation, the mass of fluid on the cylinder is found to be a monotonically increasing function of the constant width.
Item Type:  Article 

Subjects:  D  G > General 
Research Groups:  Oxford Centre for Collaborative Applied Mathematics 
ID Code:  1712 
Deposited By:  Peter Hudston 
Deposited On:  30 Jul 2013 13:08 
Last Modified:  29 May 2015 19:24 
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