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

32 2 Quantitative Description of Mass Transfer
In this chapter, we consider mass transfer across homogeneous membranes.
We define variables and transport parameters, and introduce quantitative transport
models. Cuticles are not homogeneous, but our analysis of chemistry–structure–
permeability relationships is based on these concepts and calculations.
2.1 Models for Analysing Mass Transfer
The flow of molecules (F) across an interface, a membrane or a stagnant layer is
expressed as amount (M) per time. Mol per second or mass per second are frequently
used. The choice depends on the specific situation. If the flow is divided by the
area (A) across which transport takes place, the flux (J) is obtained with units of
molm −2 s −1 or kgm −2 s −1 . For a net flow to occur, there must be a driving force.
This may be a difference of concentration (C in molm −3 or kgm −3 ) or a difference
in pressure (MPa).
When solvent or solutes are labelled with stable or radioactive isotopes, a flux
can be measured even in the absence of a concentration difference. In this case,
the driving force is the difference in concentration of isotope. This is a very attractive
alternative, because the flux and the difference in concentration are very easy
to measure, and there is no need to establish a concentration or a pressure difference
across the membrane. Random motion of a molecule marked by stable ( 18 O)
or radioactive isotopes ( 3 H, 14 C) in an environment of identical but unlabelled
molecules is called self-diffusion.
The choice of the model depends on what we want to find out and which information
is available. This can be explained on the basis of an idealised experimental
setup. A typical transport apparatus is shown in Fig. 2.1. The membrane may be a
synthetic polymer, a cuticle or a stagnant layer of water. Those who find it difficult
to visualise a stagnant water film separating stirred solutions can think of a gel of
10% gelatine or agar-agar. Transport across a stagnant water film is the simplest
case, as there is a water continuum between the two solutions and the membrane.
The solute is always surrounded by water. If the membrane is made up of a dense
non-porous polymer such as polyethylene, the solute must leave the water phase and
enter the polymer, which is not aqueous.
There are basically two ways to study mass transport:
(1) The difference in concentration remains practically constant. This type of experimental
setup is called “steady state”.
(2) The concentrations of the compartments change with time. This affects the
mathematics but not the choice of model. We shall explain these models and
their characteristics on the basis of simple experiments.
We want to analyse permeability of a gelatine membrane to urea. Urea is a nonvolatile
solid, and it must be dissolved in water. The membrane is inserted between
the compartments which are open for taking samples (Fig. 2.1). This also assures
equal pressure on both sides of the membrane.