# Interdisciplinary Applied Mathematics

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2y cos в r

and thus the rise of liquid is inversely proportional to the micropipe radius. For example, for a 10-micron glass pipe, there may be a rise of water of up to about 100 microns.

As we    have    seen in the    example of    Figure    8.2,    the    contact    angle    в is a

significant factor in capillarity. When a liquid droplet is in contact with a solid surface, the value of the contact angle reflects the type of interaction between the    liquid    and    the    solid.    The    shape    of    a small    liquid    droplet    on

a homogeneous substrate is usually a spherical cap. The contact angle is approximately constant if there are no impurities, temperature gradients, or surface defects, and it is determined by the Laplace-Young equation (8.2).    The    point    (or line)    of contact,    as shown    in    the    sketch    of Figure    8.3,

is subject to three different surface tensions. Because of equilibrium at the contact point (or line), we have

(8.6)

o

o

Ysg = Yis + Ygicos в,

where Ysg denotes the surface tension between solid and gas, Yls between liquid    and    solid, and    Ygl    between gas and    liquid.    This    equation    is    often

referred to as Young’s law. 11

 Substance Air Water dyn/cm dyn/cm °C 7 or 7 or mN/m mN/m Water 10 74.2 20 72.8 30 71.2 40 69.6 Benzene 20 28.9 35 Ethyl ether 20 17 10.7 Glycerol 20 63.4 < 0 Mercury 20 487 375 Скачать в pdf «Interdisciplinary Applied Mathematics» Н. В. Камышова; С.-Петерб. национал. исслед. ун-т информ. технологий, механики и оптики, Ин-т холода и биотехнологийМетки учебные пособия