Concise Physical Chemistry

c11 JWBS043-Rogers September 13, 2010 11:26 Printer Name: Yet to Come

SURFACE TENSION 167

liquid surface

f

σ

dσ

l

dh

FIGURE 11.3 Stretching a two-dimensional liquid bimembrane.

Now consider capillary rise caused by surface tension in a tube of radiusR.The

lengthlof the movable edge in Fig. 11.3 is replaced by the circumferencecof the tube

in which the liquid rises,c= 2 πR; but there is only one circular surface, so the factor

2 drops out of 2γdσonly to reappear as 2πR,sodw=γcdh=γ 2 πRdh.Theforce

opposing capillary rise ismgdue to lifting the mass of liquidmin opposition to

gravitational accelerationg(Fig. 11.4). At equilibrium, the forces are in balance:

mg=γ 2 πR

The volume of suspended liquid is that of a cylinder of heighthand densityρ=m/V.

FromV=πR^2 hfor a cylinder, we getm=ρV=ρπR^2 h:

(ρπR^2 h)g=γ 2 πR

and

γ=

ρRhg

2

mg

2 γπR

FIGURE 11.4 Capillary rise in a tube of radiusR. The equilibrium height of the liquid

column is determined by the balance of the capillary force and the gravitational force.