Page 14 - AN INTRODUCTION TO SURFACE CHEMISTRY By ERIC KEIGHTLEY RIDEAL

CAPILLARY RISE METHOD 9
respectively. Since the resultant energy change must be zero,
we have
(c,-,)2mr Sh = grh (p -- p,) h,

·. _?(-@)
·. gr(-,)

Now c-0=a,cosa where a is the angle of contact,
·. ,_2a,cosa
·· @rKo-p»)
If the tube is not infinitesimal in radius, the calculation becomes
more difficult, because we shall have to consider not only the form
of the meniscus (in order to calculate its volume) but also the
direction in which that form tends to change under the disturbance
imagined. The general problem has been solved by Rayleigh
(Proe. oy. Soc. A, xCI1. 184, 1915) for sufficiently small tubes
with the result
2a cos a
=r(h+r/3--01288r/l + 01312r/l).
99-PA
(¢
For very large tubes Rayleigh finds
rN_.",osss1 +0279s Ir
,
a 1V2 rV2 2 a
2a cos a
where ye This formula is accurate enough for any
9(P-»)
~rN
practical purpose i >
.
6
a
For intermediate values of r/a, or for tubes of intermediate size,
no general formula has been given. Bashforth and Adams have
however published tables from which the form of any capillary
surface may be calculated, and with the aid of these Sugden has
further calculated a table of values of r/b for all values of r/la
between 0 and 6. b is here the radius of curvature at the crown
.
d .
I
h
h
I
or fth e memscus, and since = 20-1cosa accurately, the capillary
,,
;
99-P,