Travelling-wave similarity solutions for an unsteady shear-stress-driven dry patch in a flowing film

• Main Authors: Yazariah M. Yatim, Duffy, Brian R., Wilson, Stephen K.
• Format: Article
• Language: English
• Published: Universiti Kebangsaan Malaysia 2013
• Online Access: http://journalarticle.ukm.my/6315/1/13_Yazariah.pdf; http://journalarticle.ukm.my/6315/; http://www.ukm.my/jsm/
• Institution: Universiti Kebangsaan Malaysia

We investigate unsteady flow of a thin film of Newtonian fluid around a symmetric slender dry patch moving with constant velocity on an inclined planar substrate, the flow being driven by a prescribed constant shear stress at the free surface of the film (which would be of uniform thickness in the absence of the dry patch). We obtain a novel unsteady travelling-wave similarity solution which predicts that the dry patch has a parabolic shape and that the film thickness increases monotonically away from the dry patch.