ABSTRACT
The terms diffusion and permeability are frequently confused and misused. For example, Barrer (1941) in the preface of his book defines permeability constant in contradictory ways in successive sentences and both are incorrect. In the case of diffusion of gases and water, confusing systems of units have been employed. Taylor et al. (1936) define a coefficient as g/hr/cm/mmHg and Barrer (1941) uses cc(vapour at N.T.P.)/sec/cm2/cmHg/mm thick. The use of more than one solidus leads to ambiguity and may, for example, disguise that the thickness term is in the numerator and Machin (1980) does, indeed, manage to invert this term. Other errors can also easily occur. Thus Beament (1958) writes mmHg when cmHg is intended and this is repeated by Machin (1980). Also Machin & Lampert (1987) use both the coefficients mg h−1 cm−2 torr−1 and cms−1 without relating them.
It seems, therefore, that it would be useful to derive, rigorously, simple relationships between the parameters involved in the diffusion of water across oil and wax layers and to relate these to the diffusion of water across insect cuticles.
Now, in the situation where there is essentially pure water on one side of the wax layer and dry air on the other, Δp/p* = 1 and equation 8 is much simplified and is identical to the equation used by Schatzberg (1965). If J ′ is expressed as kgs−1 m−2, δ as m and ρ as kgm−3, then D is m2s−1 and Pd is m s−1. These are the units in which these coefficients should always be expressed.
Although a permeability coefficient can be readily determined, a diffusion coefficient requires further information. If the solubility of water is unknown or ignored, the products Da or DKp are found. In Table 1, a series of quantities and units that have been employed are defined and conversion factors to convert them to preferred quantities and units are given.
Using the data of Taylor et al. (1936) and making the appropriate conversion, the value of DKp for hydrocarbon wax is 0·32×10−15m2s−1 at 21 °C, a very low absolute value that must partially reflect a low solubility of water in wax (solubility not given). Values for the liquid hydrocarbon hexadecane are given by Schatzberg (1965), who also measured the solubility of water in liquid hydrocarbons (Schatzberg, 1963). His value for the diffusion coefficient is 4·16×10−9m2s−1 at 25°C and for the solubility corresponds to a partition coefficient of 41·7×10−6 (v/v). This diffusion coefficient is rather greater than that for water in water (Kohn, 1965). The product DKp is 173×10−15m2s−1. This is considerably greater than the value for hydrocarbon wax. However, the molecular interactions that result in a solid state would undoubtedly reduce both the diffusion coefficient and solubility of water.
The data on hydrocarbons can be compared to data on insect cuticles. Only the epicuticular layers seem to be significant in waterproofing. In the cockroach, Beament (1958) has interpreted the waterproofing layers as a thick unorganized fluid grease layer (δ = 0·25 μm) and a much thinner solid packed layer (δ = 100 Å = 10 nm). The overall permeability calculated from the data of Beament (1958) using equation 8 is 1·3×10−9ms−1. Taking the thickness as 0·25μm, this corresponds to a value of DKp of 0·33×10−15m2s−1, the same as for solid hydrocarbon wax. It seems unlikely that a liquid grease could have a value as low as this. A much higher value, similar to a liquid hydrocarbon, would be expected. Beament (1958) also measured the rate of water loss through a thin solid packed layer derived from the grease and the value of DKp that can be estimated from this is 0·070 ×10−15 m2s−1, a value considerably less than that of solid hydrocarbon wax. However, even with such a layer in series with the grease layer, an unreasonably low value of DKp in the grease layer has to be postulated. The problem is, in fact, greater than this as recent estimates of water permeability in the cockroach are much less. The permeability calculated from the data of Noble-Nesbitt & Al-Shukur (1987) is as low as 0-39x10−9ms−1 and from the data of Machin & Lampert (1987) is only 0·10×10−9ms−1. Permeabilities as low as these cannot be explained in terms of our current knowledge of the system.
ACKNOWLEDGEMENTS
We wish to thank Dr J. F. Thain for useful comments on the manuscript.