Diffusion kinetics of plane layer swelling

3 DIFFUSION KINETICS OF PLANE LAYER SWELLING Consider two stages of swelling process in a plane layer - the initial and final. In the initial stage, the influence of the opposite layer boundary on the swelling process is inessential and therefore diffusion in a layer of finite thickness at sufficiently small values of time can be considered as the diffusion in half-space. 

At flie very beginning of the swelling process the amount of absorbed hquid is rather small. Henee we may set u(x,t) 0 in the right-hand parts of Eqs. [6.1.25] and [6.1.27] whieh results in 

From fliis follows the expression for the integral process eharacteristies 

These relations define the asymptotie properties of swelling at t 0. 

Since for arbitrary dependence of k(u,l) a boundary-value solution of equation [6.1.23] on the half-line with boundary condition of Eq. [6.1.34] cannot be represented in a similar form, we restriet our consideration to a model problem with diffusion coefficients defined by 

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Figure 6.1.2. Diffusion kinetics of plane layer swelling for diffusion coefficient k(u)=u at 6 = 0.1 andd = 2/9 a,b are power swelling modes at s = 1 and s = 2.5, respectively c - exponential swelling mode (s=5) d - blow-up swelling mode (s = 5.5). Numerals over curves denote correspond to instants of time. [Adapted, by permission, from E. Ya. Denisyuk, V. V. Tereshatov, Vysokomol. soed., A42, 74 (2000)].

In this section, we have developed a geometrically and physically nonlinear model of swelling processes for an infinite plane elastomeric layer and obtained approximate solutions describing different stages of swelling at large deformations of a polymeric matrix. We have identified the strain-stress state of the material caused by diffusion processes and analyzed its influence on the swelling kinetics. 

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