Abstract This study examines a one-dimensional Stefan problem describing the sorption of a finite amount of swelling solvent in a glassy polymer. The polymer is initially in a dry non-swollen state, where the polymer network is dense. The polymer is then injected with a critical concentration of a swelling solvent, causing polymer chain relaxation to occur. A moving boundary separating the swollen rubbery polymer from the dry glassy polymer is created, whose speed is defined by a kinetic law. The form of the kinetic law is typically assumed to be linear, but this is a nonphysical restriction, and thus we consider the case for a general exponent. We present formal asymptotic expansions, for both small and large times as well as for small and large values of the control parameter, as well as considering the heat balance integral method. These approximations are compared with a numerical scheme, which uses a boundary immobilisation technique and correctly identifies the appropriate starting solution.

中文翻译：

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在玻璃状聚合物中吸附有限量溶胀溶剂的近似溶液技术

摘要 本研究考察了描述玻璃状聚合物中有限量溶胀溶剂吸附的一维 Stefan 问题。聚合物最初处于干燥的非溶胀状态，其中聚合物网络是致密的。然后将聚合物注入临界浓度的溶胀溶剂，导致聚合物链松弛。产生了一个将溶胀的橡胶状聚合物与干燥的玻璃状聚合物分开的移动边界，其速度由动力学定律定义。动力学定律的形式通常被假定为线性的，但这是一个非物理限制，因此我们考虑一般指数的情况。我们提出了形式渐近扩展，无论是小时间还是大时间以及控制参数的小值和大值，并考虑热平衡积分方法。