Physical Chemistry of Foods

Note In principle, the ‘‘equilibrium’’ size of the flat film can also
be calculated.
Somesample calculationsare in Table 13.1, where bothpLandshave
been varied. It is seen that for small drops and not very low interfacial
tension, We<1, except in the cream layer in a centrifuge. For large drops
and smallgvalues, We may be larger than unity. It is to be expected that for
We<1, drops are far more stable to coalescence than for We>1, mainly
because the film area is much smaller [cf. Formula (13.30)]. Moreover, small
We tends to go along with relatively largeg, which in itself decreases the
chance of film rupture.
Few studies have been published in which We has been systematically
varied. Nevertheless, it is clear from what is known that for high We
coalescence tends to be much faster than for low We. Studies in which
interfacial tension was varied have especially shown this. Fundamental
studies on coalescence often involve large droplets (some mm in diameter),
where clearly We 4 1. It is very difficult, if possible at all, to translate
results so obtained into coalescence in real food emulsions, where generally
We <1. The same holds for centrifugal tests to determine coalescence,
aimed at rapid prediction of the stability of the emulsion; as is well known to

TABLE13.1 Role of Weber Number [Eq. (13.31)] in Coalescence of

Emulsion Droplets (Calculated Examples)

Laplace pressure pL¼ 2 g=a

g¼12 mN?m
^1 , a¼ 0 : 25 mm pL& 105 Pa

g¼3mN?m
^1 , a¼ 6 mm pL& 103 Pa

Local stress s¼external stress 6 L¼sEa/h

1. Van der Waals attractiona s¼A= 12 ph^3
   A¼ 5? 10
   ^21 J,h¼10 nm s& 102 Pa
   A¼ 5? 10
   ^21 J,h¼3nm s& 5? 103 Pa


2. Hydrodynamic shear stress s¼ZCa=h
   ZC¼ 102 Pa,a/h¼ 100 s& 104 Pa


3. Stress in a sediment layer s¼jsedDrgHa=h
   Dr¼70 kg?m
   ^3 ,H¼10 mm,a/h¼ 100 s& 5? 102 Pa
   Same in centrifuge at 1000g s& 5? 105 Pa
   aHere it is assumed that strong repulsion starts at interparticle distanceh.