Physical Chemistry of Foods

act except hard-core repulsion. The latter is taken care of by assuming that
very strong repulsion prevails below a certain value ofh, often taken as 0.5
or 1 nm. [Ath¼0, Eq. (12.1) would predict the attraction energy to be
infinite.] Another example is a water film between large air bubbles, if the
surfactant present does not cause repulsion and ifhis larger than twice the
thickness of the surfactant layer.

Note It would take far too much space to discuss theLifshits

theoryhere. For the interested reader, we give one example of an

approximate equation (error< 5 %) for the unretarded Hamaker

constant of particles (1) in a medium (3). The equation is often

useful and it reads

A 11 ð 3 Þ&

3

4

kBT

e 1 
e 3

e 1 þe 3

 2

þ

3 hPne

16

ffiffiffi

2

p

ðn^21 
n^23 Þ^2

ðn^21 þn^23 Þ^3 =^2

Hereeis the static (zero frequency) relative dielectric constant;hPis

Planck’s constant, i.e., 6: 626? 10 
^34 J?s; ne is the main UV

adsorption frequency, which equals for most substances involved

2 : 9 
 3 : 0? 1015 s
^1 ;andnis the refractive index for visible light

(generally taken at a wavelength of 589 nm). The first term in the

equation is due to dipole–dipole and dipole–induced dipole

interactions, and the second term is due to London dispersion

forces (unretarded). The first term is always smaller than (3/4)kBT;

the second term can be much larger.

Question 1

Consider a flat film of water, thicknessh¼10 nm, between two large air bubbles.
You may assume that at thathvalue van der Waals attraction is the only interactive
force. Calculate the disjoining pressure in the film, and do this also for a similar oil–
water–oil film.

Answer

As mentioned in Section 12.1, the disjoining pressure is given bypdisj¼
dV/dh.
Differentiating Eq. (12.2) then yieldspdisj¼
A/6ph^3. The disjoining pressure thus is
negative, as it should be for an attractive force. According to Table 12.2, the value of
A 11 , i.e., for water across air, equals 37? 10
^21 J, and the value for air across water is
virtually the same. We thus obtainpdisj¼
2000 Pa, a considerable pressure. The
value of the Hamaker constant for oil across water depends on the type of oil and is