Moisture Diffusion and Temperature History Models for Thin Organic Coatings Exposed to Ambient Air
William C. Thomas, Christopher C. White, Mark R. VanLandingham
Baseline models are developed for predicting moisture concentration and temperature in extremely thin polymeric films bonded to impermeable substrate materials. These simplified models are based on analytical rather than numerical solutions to circumvent formulation difficulties and calculation constraints associated with the latter approach for thin coatings. Such coatings typically are less than 100 |m thick with permeances in the range of 10-9 10-12 kg/m2-Pa-s. The temperature model is applicable to coatings on metallic or other substrate materials when the latter have thermal resistances (thickness divided by thermal conductivity) less than approximately 10-3 C-m2/W. The objectives in developing the new models are to accurately predict time-varying moisture concentration profiles, spatially average moisture contents, and temperature history in thin coatings that are exposed to moist ambient air. The models are intended to be an initial tool for examining the effects of the ambient environment on performance and durability of polymer coatings; for designing exposure tests and correlating results; and for conducting parametric investigations on the effects of various material properties and environmental conditions. The governing equation for moisture transfer is based on one-dimensional diffusion and uses the gradient of water-vapor pressure as the driving force. The front surface of the coating accounts for convective mass exchange with ambient air that has a time-dependent relative humidity from periodic measurements. The back surface is assumed to be impermeable, corresponding to paint or other coatings bonded to impervious materials. Justifiable simplifications and superposition are used to obtain a mathematically exact solution in the form of analytical expressions. An aggregated-capacity temperature model is justified and used for temperature calculations. Heat exchange at the front surface is based on periodic measurements of ambient temperature, wind speed (to estimate convection coefficients), sky temperature, and solar irradiation. The model allows either a similar or adiabatic condition at the back surface. The analysis shows that moisture transfer is dominated by diffusion within coatings rather than by convective mass transfer resistance at the exposed surface. Based on the ranges of coating permeability and thickness investigated, this observation means that the moisture concentration at the exposed surface can be safely taken as the equilibrium content corresponding to the immediate vapor pressure (or relative humidity) in the ambient air. Consequently, weather factors that affect the transient surface mass transfer coefficient, which are wind speed and precipitation, have a negligible effect on moisture content and distribution within the coating. The principal results generated are the hourly averaged mean moisture content and temperature of the coatings over the entire time of exposure. Predicted results are compared to the limited data available to establish the credibility of the models. Measurements of moisture content and temperature of coatings during long-term exposure to actual outdoor conditions are lacking. The models developed can be useful in designing and supporting such exposure tests. Uses include estimating the effects on mean moisture concentration and temperature histories of different weather measurement frequency and how long earlier environmental conditions persist, i.e., have a significant effect on the current moisture concentration and temperature.
To Be Determined
analytical modeling, coatings, diffusion, models, moisture, outdoor exposure, service life, thermal, transport