Diffusional Deborah number

Another criterion for predicting if the transport in polymeric gels is controlled by diffusion (Fickian) or by relaxation, is to determine the diffusional Deborah number De), which is a ratio between the characteristic polymer relaxation time of the polymer (2) when it is subject to a swelling stress and a characteristic diffusion time (6), defined as the coefficient between the square of the sample thickness (h) and the coefficient of water diffusion in the polymeric gel... 

Mechanism of water penetration in water-soluble cellulose derivatives Solvent transport in glassy amorphous polymers has been shown to undergo varying behavior according to the dominant process diffusion of the penetrant into the polymer or relaxation of the polymer chains [34-37]. A diffusional Deborah number, (DEB)q, has been proposed by Vrentas et al. [38, 39] as a means of characterizing penetrant transport ... 

Kim D, Peppas NA. Concentration and temperature dependence of diffusional deborah number during dodecane transport in crosshnked polystyrene. Korean J ChemEng 1996 13(2) 123-8. 

A convenient method of predicting whether the transport of a solvent in an amorphous polymer is FicMan or non-Fickian is to examine the diffusional Deborah number. Deg. This number is defined as the ratio of a characteristic relaxation time for the polymer-solvent system to the characteristic time of the diffusion process (Vrentas et al., 1975). Fickian transport is observed when either Dee < 0.1 or Dee >10, whereas non-Fickian transport is observed when Dee = 1. 

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