| Autor: |
HODGES, S. R., JENSEN, O. E., RALLISON, J. M. |
| Předmět: |
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| Zdroj: |
Journal of Fluid Mechanics; Feb2004, Vol. 501 Issue 1, p279-301, 23p |
| Abstrakt: |
Liquid of viscosity μ moves slowly through a cylindrical tube of radius R under the action of a pressure gradient. An immiscible force-free drop having viscosity λμ almost fills the tube; surface tension between the liquids is γ. The drop moves relative to the tube walls with steady velocity U, so that both the capillary number Ca = μ U/γ and the Reynolds number are small. A thin film of uniform thickness ε R is formed between the drop and the wall. It is shown that Bretherton's (1961) scaling ε ∝ Ca2/3 is appropriate for all values of λ, but with a coefficient of order unity that depends weakly on both λ and Ca. The coefficient is determined using lubrication theory for the thin film coupled to a novel two-dimensional boundary-integral representation of the internal flow. It is found that as λ increases from zero, the film thickness increases by a factor 42/3 to a plateau value when Ca-1/3 ll λ ll Ca-2/3 and then falls by a factor 22/3 as λ → ∞. The multi-region asymptotic structure of the flow is also discussed. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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