Inertial effects on thin-film wave structures with imposed surface shear on an inclined plane

Sivapuratharasu, M.; Hibberd, Stephen; Hubbard, Matthew E.; Power, H.

Abstract

This study provides an extended approach to the mathematical simulation of thin-film flow on a flat inclined plane relevant to flows subject to high surface shear. Motivated by modelling thin-film structures within an industrial context, wave structures are investigated for flows with moderate inertial effects and small film depth aspect ratio, epsilon. Approximations are made assuming a Reynolds number, Re ~ O(1/epsilon), and depth-averaging used to simplify the governing Navier-Stokes equations. A parallel Stokes flow is expected in the absence of any wave disturbance and a generalisation for the flow is based on a local quadratic profile. This approach provides a more general system which includes inertial effects and is solved numerically. Flow structures are compared with studies for Stokes flow in the limit of negligible inertial effects. Both two-tier and three-tier wave disturbances are used to study film profile evolution. A parametric study is provided for wave disturbances with increasing film Reynolds number. An evaluation of standing wave and transient film profiles is undertaken and identifies new profiles not previously predicted when inertial effects are neglected.

Citation

Sivapuratharasu, M., Hibberd, S., Hubbard, M. E., & Power, H. (2016). Inertial effects on thin-film wave structures with imposed surface shear on an inclined plane. Physica D: Nonlinear Phenomena, 325, 86-97. https://doi.org/10.1016/j.physd.2016.03.008

• Journal Article Type: Article
• Acceptance Date: Mar 13, 2016
• Online Publication Date: Mar 21, 2016
• Publication Date: Jun 15, 2016
• Deposit Date: Mar 7, 2017
• Publicly Available Date: Mar 7, 2017
• Journal: Physica D: Nonlinear Phenomena
• Print ISSN: 0167-2789
• Electronic ISSN: 1872-8022
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 325
• Pages: 86-97
• DOI: https://doi.org/10.1016/j.physd.2016.03.008
• Keywords: Inertial effects; Thin film; Surface shear; Wave structures; Capillarity; Numerical simulation
• Public URL: https://nottingham-repository.worktribe.com/output/796573
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0167278915301494
• Contract Date: Mar 7, 2017