Water Journal : Water Journal May 2012
refereed paper water MAY 2012 67 pipeline cleaning & maintenance 3. Constant diffusivity The diffusivity could vary with position in the coating. Solids are sometimes characterised as having a 'skin' (Crank, 1975; Hansen, 2004), e.g. due to more rapid curing of the epoxy at the exposed surface. Conversely, the coating properties may be affected by the presence of the substrate at the non-exposed face (van den Brand et al., 2004; Crank and Park, 1968; Huldén and Hansen, 1985). The diffusivity can also vary as a function of concentration, which is common for a range of coatings (Barrer, 1951; Hansen, 2004); in this case an average effective diffusivity is obtained (Crank, 1975). Variation with temperature also occurs (Huldén and Hansen, 1985; Vieth, 1991). 4. Diffusion in coating controlling Diffusion within the liquid phase is not likely to impose a constraint, especially with the flow present in typical installations. However, in some systems the resistance at the interface significantly affects the penetration rate (Barrer, 1951). The most problematic manifestation of this exhibits a false 'equilibrium' at intermediate times, which soon yields to further sorption (Crank, 1975); the plateau could easily be misinterpreted as the equilibrium state, which would underestimate the true final uptake that would apply in service. 5. Constant concentration at surface Given a high diffusivity in the fluid phase and continually replenished 'solution', this assumption would be met except for the obvious diurnal and seasonal variations. For design purposes a representative 'average' would be used. If coupons are to be exposed in the laboratory, it is important to ensure an adequate reservoir of acid, so that its concentration will not be appreciably diminished due to absorption into the specimen. 6. Negligible efflux from coating The diffusivity and solubility in the pipe wall ought to be much less than that of the coating, suggesting flux out of the coating can be neglected. However, the possibility remains that the diffusing species could be consumed in a degradation reaction. As a first approximation, it would be assumed that any such reaction is slow, so that only diffusion in the coating need be considered, as in assumption 4. (Alternative equations can be derived for the case of fast reaction.) It is not necessary for an assumption to exactly reflect the reality; it need only be an adequate approximation. Discussion The theory of diffusion based on Fick's law is well known, and equations for this system have been available for around 100 years. They are readily implemented in commonly available software applications. Incorrect applications of the formulae produce erroneous results, on which evaluations cannot be founded. Even though not all materials will obey Fick's law precisely, often it will be an adequate approximation. Correct application of the theory will at least allow recognition of exceptions, in which alternative models of 'anomalous' diffusion are required. Such models are detailed in the references provided. To assess susceptibility to degradation, quantification of diffusivities is not sufficient. The solubility should also be estimated. This could be estimated from the diffusion experiment, from separate experiments, or perhaps from literature reports. The relative importance of the diffusivity and solubility depends on the mode and kinetics of degradation. In order to determine the mode of degradation, microscopic examination and chemical assays are valuable. Conclusions To assess coating stability, one should: (i) know the mechanism of degradation of the coating or pipe; (ii) identify parameter(s) to characterise the mechanism; (iii) choose the correct theory and correctly apply it to evaluate parameter(s). Of course, other factors will also weigh on the decision, such as the cost of the coating and ease of application. Acknowledgements I am grateful for the support of CSIRO, and for the invaluable services of our librarians. I also thank Lachlan Mason at University of Melbourne for cross-checking the work. The Author Dr David I Verrelli (email: David.Verrelli@csiro.au) is a Postdoctoral Fellow at CSIRO Process Science and Engineering, based in Clayton, Victoria. References Alfrey T, Jr., Gurnee EF & Lloyd WG, 1966: Diffusion in glassy polymers. Journal of Polymer Science Part C: Polymer Symposia 12 (Perspectives in Polymer Science), pp 249--261. 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Hansen CM, 2004: Aspects of solubility, surfaces and diffusion in polymers. Progress in Organic Coatings 51(1):], pp 55--66. Hansen CM & Just L, 2001: Water transport and condensation in fluoropolymer films. Progress in Organic Coatings 42(3--4), pp 167--178. Hansen CM & Just L, 2002: Erratum to "Water transport and condensation in fluoropolymer films". [Prog. Org. Coat. 142 (2001) 167--178]. Progress in Organic Coatings 44(3), p 259. Hill AV, 1928: The diffusion of oxygen and lactic acid through tissues. Proceedings of the Royal Society of London. Series B, Containing papers of a biological character 104(9), pp 39--96. Huldén M & Hansen CM, 1985: Water permeation in coatings. Progress in Organic Coatings 13(3--4), pp 171--194. Ivanova KI, Pethrick RA & Affrossman S, 2001: Hygrothermal aging of rubber modified and mineral filled dicyandiamide cured digylcidyl ether of bisphenol A epoxy resin. I. Diffusion behavior. Journal of Applied Polymer Science 82(14), pp 3468--3476. Legghe E, Aragon E, Bélec L, Margaillan A & Melot D, 2009: Correlation between water diffusion and adhesion loss: Study of an epoxy primer on steel. Progress in Organic Coatings 66(3), pp 276--280. Liu H, Uhlherr A & Bannister MK, 2004: Quantitative structure--property relationships for composites: prediction of glass transition temperatures for epoxy resins. Polymer 45(6), pp 2051--2060. Liu W, Hoa SV & Pugh M, 2008a: Water uptake of epoxy--clay nanocomposites: Experiments and model validation. Composites Science and Technology 68(9), pp 2066--2072. Liu W, Hoa SV & Pugh M, 2008b: Water uptake of epoxy--clay nanocomposites: Model development. Composites Science and Technology 68(1), pp 156--163. Musto P, Mascia L, Ragosta G, Scarinzi G & Villano P, 2000: The transport of water in a tetrafunctional epoxy resin by near-infrared Fourier transform spectroscopy. Polymer 41(2), pp 565--574. Valix M & Bustamante H, 2011: Sulfuric acid permeation in epoxy mortar coatings. 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