I am looking for any mathematical equation which can describe release of volatiles from any substrate preferably a polymer.
To model the release of volatile from the polymer matrix you could use empirical or phenomenological models. Rate kinetic equations are quite common for the former; for the latter you can easily refer to Crank's Mathematics of Diffusion book and perhaps, fit an appropriate analytical solution.
See examples-
http://escholarship.org/uc/item/0t76c1pg#page-1
Cayot et al 2008 Measurement of transport phenomena of volatile compounds: A review, Food Research International, 41:349–362.
There would be diffusion in the substrate, so I would use a diffusion equation in it for the valatiles (different volatiles may have different diffusion coefficients). The evaporation will occur at the surface of the substrate: assuming that there is (forced or natural) convection we could assume zero partial pressure for the volatiles in air, and the rate would be proportional to the concentration of the volatiles at the surface. Since evaporation is an endothermic reaction, it will be (1) temperature dependent, and (2) cooling the surface. If the cooling is negligible, then temperature would be an exogenous input to the model. Under certain assumptions, the model could be simplified; for example, if the substrate is relatively thin then a one-dimensional diffusion equation would be enough for diffusion through the thickness of the substrate. fleshing all this out into a complete model would require a bit more information about the configuration of the system and applicability of the above assumptions.
Dear Luis Felipe Velázquez León, My requirement is a model that can describe the process of volatilization from liquid to vapor phase with respect to time in the form of mass fraction ratio. thanks
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Materials Science
- Materials Chemistry