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

4.5 Diffusion and Viscous Transport of Water 81
10 −6 m). This is not a good assumption, as pointed out in Sect. 4.1. DTHO in the
pore fluid is definitely lower, and the path length is greater than ℓ due to tortuosity.
As the fractional pore area is Pdiffusionℓ/DTHO, the ratio ℓ/DTHO in the pore
liquid will be much larger than in a water film having the same thickness as the
MX membranes. However, ℓ/DTHO is probably not affected by pH, and for the
sake of argument we have added selected fractional pore areas to Fig. 4.8. Since
permeance of MX membranes in Na + form increased with pH, Apore/Amembrane
also increased. Apore/Amembrane is proportional to the fractional volume of water
in the membrane (volume of water/total volume of membrane), and this is a quantitative
measure of swelling (Kedem and Katchalsky 1961). The absolute values of
Apore/Amembrane are in error, but the increase of Apore/Amembrane with pH reflects
the change in water content of MX. The fractional volume of water in the MX is
independent of pH when the MX is in Ca 2+ form, or when carboxyl groups are not
ionised (Fig. 4.8).
Having established that total pore area increases with increasing pH, as long as
the MX is in Na + form, we can now test if this is due to larger pore radii or to
an increase in number of pores. Size of pores can be estimated using (4.13) when
Pdiffusion and Pviscous are known. Volume flux of water was measured using an apparatus
made from glass (Schönherr 1976a) and a number of solutes differing in size. All
measurements were made with identical buffers on both sides and with the osmotic
solutes in the outer compartment facing the morphological outer surface of the MX.
The volume flux was measured in a calibrated capillary (0.24µlmm −1 ) connected to
the outer compartment. The entire apparatus was submerged in a water bath maintained
at 25 ± 0.02 ◦ C, and only the tips of the capillaries protruded over the surface
of the water bath. Temperature control is critical, since water volume of water varies
greatly with temperature. A 0.01moll −1 citric acid and Na2HPO4 buffer was used
in the pH range of 3–7 and 0.01moll −1 disodiumtetraborate (borax) adjusted with
HCl was used at pH 9. With these buffers in donor and receiver, the MX membranes
are in the Na + form. Solute concentrations were 0.5molkg −1 with urea, glucose and
sucrose, and with raffinose 0.25molkg −1 were used, which is close to the solubility
limit.
Viscous or volume fluxes of water were determined at pH 3, 6 and 9 with urea
glucose, sucrose and raffinose, and Pviscous was calculated from (4.10). The same
set of membranes was used for all pH values and solutes. Pviscous increased with
increasing pH and solute size, and asymptotically approached the maximum value
of Pviscous (Fig. 4.9). As the differences in Pviscous between sucrose and raffinose
were small, Schönherr (1976a) assumed that at all pH values MX membranes were
impermeable to raffinose, and permeance measured with raffinose represented maximum
permeance. Solutes larger than raffinose were not included in the work. Here
we use an approach for estimating maximum Pviscous that is superior to that which
would be obtained with hydrostatic pressure or with solutes to which the membranes
are impermeable. By fitting a parabola to the data points, Pmaximum viscous can be
obtained and the above assumption can be tested. The curves fitted to the data points
(Fig. 4.9a) represent the hyperbola where θ is a constant, and Pmaximum viscous is the maximum
permeance that would be obtained when solute radius (rsolute) approaches