Answer
What is first needed is the magnitude ofv¼pd 633 =6. Assuming the emulsion to have
been made in a high-pressure homogenizer, its size distribution will be rather wide
(see, e.g., Figure 11.9a); presumably,d 63 will then be 3 to 4 timesd 32 , so we may
estimatevat about 120mm^3. Figure 14.6a indicatesNcat& 3? 1016 m^3. Inserting
these values in Eq. (14.14) yields ymax¼0.925. Figure 14.6b indicates that J 0
& 3? 1013 m^3 ?s^1. Equation (14.16) then yields times of about half a minute and
one hour fory¼0.1 and 0.9, respectively.
In the absence of catalytic impurities, homogeneous nucleation is needed,
which would presumably lead toy&ymax. Equation (14.16) shows that we need to
know the values ofy/ymax; these are pretty close to the values just applied since we
tookymax¼0.925. We can now insert the value ofJhomto obtainy(t). This means
that we only have to find the temperature at whichJhom¼J 0 (15 8 C), and Figure 14.6b
shows this to be about 7 8 C.
It makes no sense to do more precise calculations, since the results will anyway
be approximate because of natural variation in the values ofJandNcat.
Question 2
Suppose that you want to keep a solution of an enzyme in an aqueous buffer at
308 C without freezing (because the freeze concentration would lead to irreversible
enzyme inactivation). How can this be achieved? Assume the number of catalytic
impurities at 308 Ctobe10^11 m^3.
Answer
The best way is to make a W–O emulsion. It is advisable to have an oil phase that
freezes at low temperature, since that prevents settling and possible coalescence of
the drops. The oil should not affect the protein. Tetradecane seems suitable (freezing
point about 6 8 C). An emulsifier has to be added and it should (a) have a low HLB
value (why?), (b) not give rise to surface nucleation at 308 C, and (c) not affect the
protein. It may take some trial and error finding a suitable surfactant. Assume that
‘‘without freezing’’ implies thatymaxshould become at most 0.01. By use of Eq.
(14.14) it follows that the average droplet diameterd 63 then must be below 57mmto
prevent heterogeneous nucleation, which can easily be realized. Figure 14.3 shows
that at 308 CJhomis about 1 m^3 ?s^1 , which gives negligible nucleation in 57mm
drops over several centuries.