surface often is heterogeneous. Nevertheless the uptake of water
from the air can occur even if the solid matter itself cannot dissolve
any water, although the pores must be very fine.Several finepowdersof such materials exhibit increasing stickiness—
which is caused by interparticle attraction—at increasing water activity,
often starting above aW & 0.9. This is presumably due to capillary
condensation, producing tiny water bridges between particles.
Question 1
Figure 10.23a shows two vessels each containing an amount of liquid. Are these
stable situations or will the liquids start to move? If so, in what direction?
Answer
Left figure, liquid moves to the left. Right figure, to the right. Explain.
Question 2
Figure 10.23b shows a cylindrical thread of liquid in air that has obtained a shape as
indicated. At what place is the Laplace pressure higher, at A or at B? What will
happen with the liquid, assuming no external forces to act? Do you know of a
situation in which this happens?
Answer
Assume that the original cross-sectional radius of the cylinderr¼1 unit. Then the
amplitude of the ‘‘wave’’ on the cylinder&0.4, so the radiiR 1 at A and B are 0.6 and
1.4, respectively. At A,R 2 ¼5, and at B,R 2 ¼5. Consequently at A,pL&1/0.6 –
1/5¼1.47, whereas at B,pL&1/1.4þ1/5¼0.91. Although one of the principal
radii of curvature is negative near A, the pressure at A is higher than that at B;
consequently, liquid will flow from A to B. The thread is unstable and will eventually
break up into drops. This is what commonly happens when a thin stream of water
falls from a faucet, because—according to Rayleigh—any developing varicose wave
of wavelength> 2 prwill cause the Laplace pressure to be higher in the narrow than
in the wide parts of the thread.