Skinning During Desorption of Polymers: An Asymptotic Analysis

Edwards, David A.

doi:10.1137/s0036139996311060

Cited by 5 publications

(11 citation statements)

References 25 publications

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“…Because of the relationship between σ and C, we also need layers for the pseudostress. The solutions for σ exhibit maxima for x near but less than s(t), which is consistent with a buildup in stress as the polymer changes states [44][45][46][47]. At x = s(t), a Stefan-like condition was derived to couple the two operators.…”

Section: Discussionsupporting

confidence: 52%

“…Note there is an internal maximum in the pseudostress associated with the change of state from rubber to glass. This maximum has been seen in other theoretical [44][45][46] and experimental [47] studies of these types of systems.…”

Section: Since (33) Does Not Satisfy (212a) There Must Also Be An supporting

confidence: 60%

“…Thus, our model exhibits the phenomena of skinning, behavior also seen in viscoelastic models for polymer-penetrant systems [4,5,18,19,45,46]. Since C g = 0 is less than the interface values, the solution also exhibits desorption overshoot, as described in [33].…”

Section: Discussionmentioning

confidence: 52%

“…Note the increasing pseudostress in the glassy region. These sorts of internal extrema, which are related to the buildup of stress associated with the glass-rubber change of state, have been seen in viscoelastic models of desorption [45,46] and sorption [44] problems, as well as experimentally [47]. The flux contribution from σ in this region overwhelms the contribution from the concentration, thus forming an overall negative flux which continues the desorption of the polymer.…”

Section: Solution Profilesmentioning

confidence: 88%

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A Spatially Nonlocal Model for Polymer Desorption

Edwards

2005

J Eng Math

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Abstract. In order to describe diffusion of a penetrant in a polymer entanglement network, one must incorporate nonlocal effects. Most previous models have included nonlocality in time only; however, by exploiting the disparate length scales in such systems, one can model these effects by a partial integrodifferential equation which is nonlocal in space. When considering the case of diffusion near the glass-rubber transition, a moving boundary separates the polymer into two regions, each governed by a different set of PDEs. The desorption of a semi-infinite polymer is studied using singular perturbation methods. Layers arise at the exposed surface, at the moving boundary, and initially. Analytical and phase-plane solutions are obtained for the solution, which exhibits physically realistic forms of desorption overshoot. Thus, spatially nonlocal models have the potential to replicate experimental systems, and should be considered in concert with other viscoelastic models of polymer-penetrant systems.

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Section: Discussionsupporting

confidence: 52%

Section: Since (33) Does Not Satisfy (212a) There Must Also Be An supporting

confidence: 60%

Section: Discussionmentioning

confidence: 52%

Section: Solution Profilesmentioning

confidence: 88%

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A Spatially Nonlocal Model for Polymer Desorption

Edwards

2005

J Eng Math

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“…Our equations are the same, to leading order, as those for general polymer-penetrant systems derived in detail by Edwards and Cohen [24], [25], Edwards [26], Cairncross and Durning [8], Durning [27], and Durning and Tabor [28]. These models, which are presented in section 2, consist of a set of coupled PDEs for the concentration and stress.…”

Section: Introductionmentioning

confidence: 96%

Desorption Overshoot in Polymer-Penetrant Systems: Asymptotic and Computational Results

Edwards¹,

Cairncross²

2002

SIAM J. Appl. Math.

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Abstract. Many practically relevant polymers undergoing desorption change from the rubbery (saturated) to the glassy (nearly dry) state. The dynamics of such systems cannot be described by the simple Fickian diffusion equation due to viscoelastic effects. The mathematical model solved numerically is a set of two coupled PDEs for concentration and stress. Asymptotic solutions are presented for a moving boundary-value problem for the two states in the short-time limit. The solutions exhibit desorption overshoot, where the penetrant concentration in the interior is less than that on the surface. In addition, it is shown that if the underlying time scale of the equations is ignored when postulating boundary conditions, nonphysical solutions can result. 1. Introduction. Over the past few decades, much experimental and theoretical work has been devoted to the study of polymer-penetrant systems. In particular, the desorption of penetrants from saturated polymer matrices has been examined due to its wide industrial applicability. One unusual feature of such systems is the change in the polymer from a rubbery state when it is nearly saturated to a glassy state when it is nearly dry. As part of the drying process, a glassy skin often develops at the exposed surface of a polymer whose properties are significantly different from the rest of the polymer-penetrant solution There are many different theories for why the skinning process occurs, including phase separation [17], crystallization [18], and diffusion-induced convection [19]. Nevertheless, for the systems we wish to study, most scientists agree that one important factor is a viscoelastic stress in the polymer entanglement network, which can be as important to the transport process as the well-understood Fickian dynamics [20], [21], [22]. The size of this stress is related to the relaxation time of the viscoelastic polymer matrix. In the glassy skin, the relaxation time is finite, so the stress is an important effect, but in the rubbery region the relaxation time is nearly zero [15], [20], [23]. Nevertheless, we will show that in order for the mathematical model to yield physically meaningful results, at some level the short relaxation time in the rubber must also be taken into account.Numerical and analytical solutions are derived here for model equations for the

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Coupled vehicle–skin models for drug release

Barbeiro

Ferreira

2009

Computer Methods in Applied Mechanics and Engineering

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Please cite this article as: S. Barbeiro, J.A. Ferreira, Coupled vehicle-skin models for drug release, Comput. Methods Appl. Mech. Engrg. (2009), doi: 10.1016/j.cma.2009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. ACCEPTED MANUSCRIPT AbstractPercutaneous absorption of a drug delivered by a vehicle source is usually modeled by using diffusion Fick's law. In this case, the model consists in a system of partial differential equations of diffusion type with a compatibility condition on the transition boundary between the vehicle and the skin. Using this model, the fractional drug release in both componentsvehicle and skin -is proportional to the square root of the release time. Often experimental results show that the predicted drug concentration distribution in the vehicle and in the skin by the Fick's model does not agree with experimental data. In this paper we present a nonFickian mathematical model for the introduced percutaneous absorption problem. In this new model the Fick's law for the flux is modified by introducing a non-Fickian contribution defined with a relaxation parameter related to the properties of the components. Combining the flux equation with the mass conservation law, a system of integro-differential equations is established with a compatibility condition on the boundary between the two components of the physical model. The stability analysis is presented. In order to simulate the mathematical model, its discrete version is introduced. The stability and convergence properties of the discrete system are studied. Numerical experiments are also included.

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Skinning During Desorption of Polymers: An Asymptotic Analysis

Cited by 5 publications

References 25 publications

A Spatially Nonlocal Model for Polymer Desorption

A Spatially Nonlocal Model for Polymer Desorption

Desorption Overshoot in Polymer-Penetrant Systems: Asymptotic and Computational Results

Coupled vehicle–skin models for drug release

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