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

Solutions 51
2.7 Summary
In this chapter we have presented three basic transport models, and we have shown
how permeance (P), diffusion coefficients (D) and first-order rate constants (k) can
be calculated from measurements of mass flux and membrane thickness. We have
pointed out that it is not a good practice to compare data on mass transfer across
cuticles from different species and various solutes when data are given as percent
penetrated during a single arbitrary time interval. Such data can not be related to
properties of cuticles or solutes.
Most problems can be handled by analogy to the above models and equations.
In the chapters to follow, some additional equations are presented for analysing flux
data. If new problems should arise which have not been treated here, the readers
will find assistance in the books by Crank (1975), Crank and Park (1968), Cussler
(1984), Hartley and Graham-Bryce (1980) and Vieth (1991).
Problems
1. What are the numerical values of the resistance in cell wall (P = 1.38 ×
10 −4 ms −1 ) and cuticle (P = 1.46×10 −7 ms −1 ), and what is the total resistance?
2. What are the steady state fluxes of urea and sucrose across a cell wall with
ℓ = 1µm when the concentration difference between donor and receiver is
1 × 10 −3 moll −1 ? The diffusion coefficient of sucrose in water is 5.23 × 10 −10
m 2 s −1 .
3. In calculations (2.15), we assumed that 2,4-D was either in the donor or in the
receiver solutions. Since K is 600, some of the 2,4-D must have been in the
cuticle. How much was it, and did this omission significantly affect permeance?
Use a specific weight of the cuticle of 1,000kgm −3 .
4. If the experiment shown in Fig. 2.9 had been terminated after 2 or 3 days, which
permeance would have resulted using the steady state assumption, and how much
would it differ from the true value?
5. Diffusion of lipophilic solutes in cuticular waxes is a very slow process, and
diffusion coefficients in the range of 10 −18 to 10 −21 m 2 s −1 have been measured.
How long would it take to reach Mt/M0 = 0.5 if the wax layer is 2µm thick?
Solutions
1. The resistance of the cell wall is 7,246sm −1 , and the resistance of the cuticle
is 6.849 × 10 6 sm −1 . The sum of the two resistances is 6.857 × 10 6 sm −1 , and
this is not significantly different from the resistance of the cuticle. Hence, the
resistance of the cell wall is negligible.