Coke is sweetened with a mixture of sucrose and high-fructose corn
syrup. There are therefore at least three types of "sugar" present:
fructose, glucose (from the corn syrup), and sucrose. There will also
be other sugars that were present in the corn syrup. Each of these
sugars will have a slightly different diffusion coefficient, though
because the clucose and fructose are both monosaccharides and have
roughly the same molecular size, their diffusion coefficients will be
very similar. The diffusion coefficient of sucrose, which is a
disaccharide, will be somewhat smaller due to the larger size of the
sucrose molecule.
The 57th edition of the CRC Handbook of Chemistry and Physics provides
diffusion coefficients for sucrose in pure water (infinitely dilute
solution) at 25 C of 0.5226E-05 cm^2/s. In a 0.38 wt. % solution of
sugar, the listed diffusion coefficient for sucrose drops to 0.521E-05
cm^2/s. The diffusion coefficient of glucose in a 0.39% solution is
listed as 0.673E-05 cm^2/s. (All at 25 C). A
Coke, however, has a sugar concentration of around 11-12%, and the
diffusion coeffient should be lower under these conditions. There is
an online "calculator" that calculate the diffusion coefficient for
sucrose in water as a function of concentration at
:http://www.univ-reims.fr/Externes/AVH/MementoSugar/002.htm. This
site returns a diffusion coefficient of 0.61E-05 cm^2/s for sucrose in
pure water, and 0.43E-05 cm^2/s for sucrose in an 11.5% solution. Note
that the pure water value is ~20% higher than that given in the CRC
handbook. Note also that there is an error in the units that the
website specifies. The calculated value shown in the result box is
the diffusion coefficient in units of m^2/s, not in units of
10^-12*m^2/s, as indicated on the website. (Multiply the value in
m^2/s by 10^4 to get the result in units of cm^2/s).
In practical terms, the diffusion coefficient of *anything* in Coke is
likely to be irrelevant to the speed at which a solute mixes unless
the Coke is completely "flat" (i.e, has lost all its carbonation). If
the Coke is actively "fizzing" then the rate at which a solute like
sugar gets mixed will be greatly increased by the advective flow
induced by the rising bubbles.
As for the diffusion of C in Fe, see
http://www.sv.vt.edu/classes/MSE2034_NoteBook/MSE2034_kriz_NoteBook/diffusion/analytic/anal2.html.
This site provides an analytical expression for the diffusion
coefficient of C in body-centered cubic iron (the staple polymorph of
Fe below ~1100 C) as a function of temperature (constrained by data
only up to 800 C, however). |
