Water and Solute Permeability of Plant Cuticles: Measurement and ...

2.1 Models for Analysing Mass Transfer 37
2.1.3 Model 3
Mass transfer across a membrane may also be analysed in analogy to a first order
chemical reaction. In this case, the change in urea concentration in the receiver with
time (molm −3 s −1 ) is taken to be proportional to donor concentration:
∆Creceiver
∆t
= kCdonor. (2.6)
This proportionality coefficient (k) is a rate constant having the dimension s −1 .
Membrane area and thickness do not enter into calculation. Example calculations
will be presented below.
All of these three models have been used in studies of permeability of cuticles.
The choice among the models depends on the particular situation. P, D or k are
parameters which contain information about properties of cuticles and solutes and
their interactions. They are essential when we want to find out why permeability of
cuticles from different genotypes differs, and why it depends on the type of solute
and on environmental factors. These models and equations are simple and straightforward
to use. In spite of this, most researchers in the past measured penetration or
“uptake” during only a single time interval. From these data P, D or k can not be
calculated, and we are left with huge amounts of uncorrelated data.
2.1.4 Conductance and Resistance
Most students are familiar with Ohm’s law, which is analogous to models 1 and 2
except that it deals with electrons rather than molecules (mass transfer). If the ends
of a piece of wire (a conductor of electricity) are connected to a battery, a current
will flow. Current is the number of electrons that flow per unit cross-section of the
wire under a difference of electrical potential (volt):
current = conductance× potential difference. (2.7)
If the length of the conductor is also considered, the factor of proportionality is
called conductivity:
current× lenght = conductivity× potential difference. (2.8)
These equations are of the same type as (2.2) and (2.3), which state that mass flux
(2.2) or mass flux times membrane thickness (2.3) are proportional to concentration
difference. This analogy may ease the apprehension some biologists experience
when dealing with Fick’s law.
The reciprocal of conductance is the electrical resistance, and 1/conductivity is
called resistivity. This convention can also be used with mass conduction. For a
perfect analogy, we rename the permeability coefficient (P) from (2.2) and call it