Steady symmetric low-Reynolds-number flow past a film-coated cylinder

In this study, we examine a steady two-dimensional slow flow past a rigid cylinder coated with a thin layer of immiscible fluid. The Reynolds number for the external bulk flow is assumed small and flow within the film is driven by the action of the bulk fluid’s tangential viscous stress acting at th...

Full description

Saved in:
Bibliographic Details
Published in:European journal of applied mathematics 2013-02, Vol.24 (1), p.1-24
Main Authors: BAND, L. R., OLIVER, J. M., WATERS, S. L., RILEY, D. S.
Format: Article
Language:English
Subjects:
Applied mathematics
Fluid mechanics
Reynolds number
Thin films
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this study, we examine a steady two-dimensional slow flow past a rigid cylinder coated with a thin layer of immiscible fluid. The Reynolds number for the external bulk flow is assumed small and flow within the film is driven by the action of the bulk fluid’s tangential viscous stress acting at the interface. Using double asymptotic expansions based on the bulk fluid’s Reynolds number and the aspect ratio of the film thickness to the cylinder’s radius, we derive the leading- and first-order equations governing the steady-state film dynamics, and obtain analytical solutions, in terms of the film thickness, for the bulk flow. We solve the governing film equations, finding that solutions feature a drained region. We briefly discuss the influence of the Capillary number and fluid viscosities, and conclude by showing how the presence of the film affects the drag on the film-coated cylinder.
ISSN:0956-7925
1469-4425
DOI:10.1017/S0956792512000289