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Note on the lifting of liquids by withdrawal

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Abstract

The results of previous studies on the problem of estimating the thickness and the flux of liquid being dragged out of a reservoir by a moving plate are summarized. An asymptotic solution is derived for the limiting case where the effect of surface tension may be neglected. This solution agrees better with the experimental results than that predicted by Jeffreys' theory and serves to explain the phenomenon of a definite maximum flux obtainable in the experiments.

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Abbreviations

A :

constant

C a :

capillary number (μU 0/σ)

D :

dimensional reference length (μU 0/ρg)1/2

g :

acceleration of gravity

Q :

flux per unit width of plate

t :

time

U 0, U min :

speed of withdrawal

x :

coordinate along the plate

ξ, ξ 0, ξ max, ξ min :

thickness of liquid film

μ :

viscosity

ρ :

density

σ :

surface tension at liquid-gas interface

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Authors and Affiliations

  1. Dept. of Mech. Engr., University of California Berkeley, 9 47 20, Cal., USA

    Wen-Fan Lin & E. V. Laitone

Authors
  1. Wen-Fan Lin
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  2. E. V. Laitone
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Lin, WF., Laitone, E.V. Note on the lifting of liquids by withdrawal. Appl. Sci. Res. 25, 171–178 (1972). https://doi.org/10.1007/BF00382293

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  • DOI: https://doi.org/10.1007/BF00382293

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