TY - JOUR

T1 - Pinning, de-pinning and re-pinning of a slowly varying rivulet

AU - Paterson, C.

AU - Wilson, S.K.

AU - Duffy, B.R.

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: The first author (CP) gratefully acknowledges the financial support of the University of Strathclyde via a Postgraduate Research Scholarship. Part of this work was undertaken while the corresponding author (SKW) was a Visiting Fellow in the Department of Mechanical and Aerospace Engineering, School of Engineering and Applied Science, Princeton University, USA, and part of it was undertaken while he was a Visiting Fellow in the Oxford Centre for Collaborative Applied Mathematics (OCCAM), Mathematical Institute, University of Oxford, United Kingdom. This publication was based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). A preliminary version of this work, discussing only the de-pinning of a rivulet with constant width at zero contact angle, appears as OCCAM preprint number 12/43 [35].
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2013/9

Y1 - 2013/9

N2 - 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 de-pinning of a rivulet with constant contact angle and the possible de-pinning and subsequent re-pinning 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 non-zero 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 de-pin 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 de-pinning of a rivulet with constant contact angle, and the corresponding situation involving the de-pinning and re-pinning of a rivulet with constant width at a non-zero contact angle which generalises the de-pinning 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. © 2013 Elsevier Masson SAS. All rights reserved.

AB - 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 de-pinning of a rivulet with constant contact angle and the possible de-pinning and subsequent re-pinning 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 non-zero 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 de-pin 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 de-pinning of a rivulet with constant contact angle, and the corresponding situation involving the de-pinning and re-pinning of a rivulet with constant width at a non-zero contact angle which generalises the de-pinning 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. © 2013 Elsevier Masson SAS. All rights reserved.

UR - http://hdl.handle.net/10754/599197

UR - https://linkinghub.elsevier.com/retrieve/pii/S099775461300023X

UR - http://www.scopus.com/inward/record.url?scp=84878833826&partnerID=8YFLogxK

U2 - 10.1016/j.euromechflu.2013.02.006

DO - 10.1016/j.euromechflu.2013.02.006

M3 - Article

SN - 0997-7546

VL - 41

SP - 94

EP - 108

JO - European Journal of Mechanics - B/Fluids

JF - European Journal of Mechanics - B/Fluids

ER -