Physical Chemistry of Foods

5.2.2 Mass Diffusion

So far, we have tentatively assumed that all molecules and particles are
randomly distributed throughout the volume available. If there are two (or
more) substances present, say solute and solvent, concentration differences
can occur for a number of reasons. If so, the heat motion causes the
molecules to attain a (more) random distribution, i.e., the concentration
differences will eventually disappear, except over very small distances. The
process is thus entropy driven. The rate at which it occurs is generally
described by Fick’s laws. Fick postulated in his first law that thediffusional
transport rateis proportional to the concentration gradient according to

dm

dt

¼
DA

qc

qx



t

ð 5 : 17 Þ

where dmis the amount of solute transported in the direction ofxthrough
the areaAof a cross section perpendicular tox. The amountmcan be given
in any unit of substance, and the concentrationcmust be taken in the same
units per unit volume. From Eq. (5.17) Fick’s second law can be derived,
which gives the change incwith time at any place as a function of the local
concentration gradient

qc

qt



x

¼D

q^2 c

qx^2



t

ð 5 : 18 Þ

Total mass transport and concentration profiles as a function of time
can be obtained from these differential equations. The solution greatly

TABLE5.3 Diffusion CoefficientsðDÞof Some Molecules and

Particles in Water at Room Temperature and Times Needed for

These Species to Diffuse over Various Distances in a Given

Direction,D 1

D

Diffusion time forD 1 ¼

Species m^2 ?s
^1 10 nm 1mm 0.1 mm 1 cm

Water 1 : 7? 10 
^90 : 03 ms 0.3ms 3s 8h

Sucrose 4 : 7? 10 
^100 : 1 ms 1 ms 11 s 30 h

Serum albumin 6 : 1? 10 
^110 : 8 ms 8 ms 82 s 10 d

Emulsion dropleta 4 : 2? 10 
^13 0.1 ms 1 s 3 h 4 y

aDiameter 1mm.