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The Dynamics of Capillary Flow

Authors: Edward W. Washburn;

The Dynamics of Capillary Flow

Abstract

Penetration of Liquids into Cylindrical Capillaries.---The rate of penetration into a small capillary of radius $r$ is shown to be: $\frac{\mathrm{dl}}{\mathrm{dt}}=\frac{P({r}^{2}+4\ensuremath{\epsilon}r)}{8\ensuremath{\eta}l}$, where $P$ is the driving pressure, $\ensuremath{\epsilon}$ the coefficient of slip and $\ensuremath{\eta}$ the viscosity. By integrating this expression, the distance penetrated by a liquid flowing under capillary pressure alone into a horizontal capillary or one with small internal surface is found to be the square root of ($\frac{\ensuremath{\gamma}\mathrm{rt}\ifmmode\cdot\else\textperiodcentered\fi{}cos\ensuremath{\theta}}{2\ensuremath{\eta}}$), where $\ensuremath{\gamma}$ is the surface tension and $\ensuremath{\theta}$ the angle of contact. The quantity ($\frac{\ensuremath{\gamma}cos\ensuremath{\theta}}{2\ensuremath{\eta}}$) is called the coefficient of penetrance or the penetrativity of the liquid.Penetration of Liquids into a Porous Body.---(1) Theory. If a porous body behaves as an assemblage of very small cylindrical capillaries, the volume which penetrates in a time $t$ would be proportional to the square root of ($\frac{\ensuremath{\gamma}t}{\ensuremath{\eta}}$). (2) Experiments with mercury, water and other liquids completely verify the theoretical deductions.Dynamic capillary method of measuring surface tension is described. It possesses certain advantages on the static method of capillary rise.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6K
Top 0.01%
Top 0.01%
Top 10%