Traveling Wave Solutions for Case Ii Diffusion in Polymers
نویسنده
چکیده
Case II diiusion of penetrant liquids in polymer lms is characterized by constant-velocity propagation of a phase interface. We review the development of viscoelastic models describing Case II diiusion and then present a phase plane analysis for traveling wave solutions. For simpliied, piecewise-constant coeecient models we give closed form analytic solutions showing the dependence on various physical parameters in both viscous and viscoelastic diiusive systems. We will also compare the results of our analysis with results from numerical simulations of more general models.
منابع مشابه
Traveling waves for anomalous diffusion in polymers
case II diffusion of a penetrant through a polymer matrix is characterized by constant front speed. Hence, a traveling-wave analysis is appropriate for the model equations. For the previously validated model analyzed here, conditions on the molecular and stress diffusion coefficients are obtained which guarantee the existence of a traveling wave. Conditions are derived under which an interior m...
متن کاملTraveling Wave Solutions for Bistable Differential-Difference Equations with Periodic Diffusion
We consider traveling wave solutions to spatially discrete reaction-diffusion equations with nonlocal variable diffusion and bistable nonlinearities. To find the traveling wave solutions we introduce an ansatz in which the wave speed depends on the underlying lattice as well as on time. For the case of spatially periodic diffusion we obtain analytic solutions for the traveling wave problem usin...
متن کاملTraveling Wave Solutions of 3D Fractionalized MHD Newtonian Fluid in Porous Medium with Heat Transfer
In the present paper, we get exact solutions of Magnetohydrodynamic (MHD) of the fractionalized three-dimensional flow of Newtonian fluid with porous and heat transfer through the traveling wave parameter. The governing equations are produced dependent on established Navier-stokes equations which can be diminished to ordinary differential equation by wave parameter ξ=ax+by+nz+Utα/Γ(α...
متن کاملSome new exact traveling wave solutions one dimensional modified complex Ginzburg- Landau equation
In this paper, we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the one-dimensional modified complex Ginzburg-Landau equation by using the $ (G'/G) $ expansion method, homogeneous balance method, extended F-expansion method. By using homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by j...
متن کاملExistence of traveling wave solutions in a diffusive predator-prey model.
We establish the existence of traveling front solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-II functional response. The traveling front solutions are equivalent to heteroclinic orbits in R(4) and the small amplitude traveling wave train solutions are equivalent to small amplitude periodic orbits in R...
متن کامل