Page 18 - AN INTRODUCTION TO SURFACE CHEMISTRY By ERIC KEIGHTLEY RIDEAL

DROP WEIGHT METHOD 13
Tate (Phil. Mag. xxv11. 176, 1864) discovered empirically that the
weight of a drop of liquid falling from the end of a tube was pro-
portional to the radius of the tube and the surface tension of the
liquid.
The theoretical formula for the maximum weight of a cylindrical I
drop hanging from a tube in equilibrium was shown to be
a.nra
by Worthington (Proo. Roy. Soc. XXX11. 362, 1881; Phil. Mag.
1884, 1885) and Rayleigh (Phil. Mag. XL111. 321, 1899).
Rayleigh showed however that in practice this equation required
modification and found for tubes of moderate radius that a better
agreement was obtained by the relationship
W38r.
For very small or very large tubes however the value of the
constant " 38 rises well above 4,
Morgan and his co-workers (J.A.0.S. 1908--1913) have published
a number of papers in support of " Tate's laws" claiming that
under suitable conditions W • Kra where K is a constant, 'This
view however cannot be substantiated.
This variation is of course due to the fact that the actual de-
tachment of the drop is an extremely complicated dynamical
process (ef. Perrot, J. Chaim. Phy8. xv. 164, 1917)
Lohstein (Zeit. f. Physikal. Chem. Lx1v. 686, 1908) and Harkins
(J.A.C.S. XXXv111. 228, 1916, et seqp.) assumed that the weight
of an " ideal " drop should be given by the relationship
Wu2nra
and that for actual drops an empyrie factor had to be introduced,
the L~hnstein correction. This factor was dependent on the radius
of the tip and the nature of the liquid under investigation. The
L~hnstein equation in its final form is accordingly
r
2a
W 2nraf where a'=--,
u
a P
The function was found to be approximately a cubic function of'
(
being unity when'approaches 0 falling to a minimum of about
a
06 when '=.1l and rising thereafter continuously.
a