An Accurate and Comprehensive Model of Thin Fluid Flows with Inertia on Curved Substrates

A.J. Roberts, Li. Zhenquan

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)
129 Downloads (Pure)


Consider the three dimensional flow of a viscous Newtonian fluidupon a curved two dimensional substrate when the fluid film is thinas occurs in many draining, coating and biological flows. We derivea comprehensive model of the dynamics of the film, the model beingexpressed in terms of the film thicknen and the average lateral velocity Pu. Based upon centre manifold theory, we are assured thatthe model accurately and systematically includes the effects of thecurvature of substrate, gravitational body force, fluid inertia and dissipation.The model resolves wave-like phenomena in the dynamics ofviscous fluid flows over arbitrarily curved substrates such as cylinders,tubes and spheres. We briefly illustrate its use in simulating dropformation on cylindrical fibres, wave transitions, three dimensionalinstabilities, Faraday waves, viscous hydraulic jumps, flow vortices ina compound channel and flow down and up a step. These modelsare the most complete models for thin film flow of a Newtonian fluid;many other thin film models can be obtained by different restrictionsand truncations of the model derived here.
Original languageEnglish
Pages (from-to)33-73
Number of pages41
JournalJournal of Fluid Mechanics
Publication statusPublished - Apr 2006


Dive into the research topics of 'An Accurate and Comprehensive Model of Thin Fluid Flows with Inertia on Curved Substrates'. Together they form a unique fingerprint.
  • Buildings (Journal)

    Li, Z. (Reviewer)

    10 Jan 202431 Jan 2024

    Activity: Publication peer-review and editorial workPeer review responsibility, including review panel or committee

Cite this