物质从厚膜中释放的亚扩散模型
Subdiffusive model of substance releasing from a thick membrane
摘要：
本文从理论和实验两方面研究了亚扩散物质从厚膜中释放的过程。理论模型采用具有分数阶时间导数的亚扩散方程和膜表面的特定边界条件。使用一个特殊的\textit{ansatz}，我们发现分析公式描述的时间演变的浓度曲线和量的物质仍然在膜中。将理论函数与实验结果进行拟合，估算了聚乙二醇2000在琼脂糖凝胶中的亚扩散系数。
英文摘要：
We study both theoretically and experimentally the process of subdiffusive substance releasing from a thick membrane. The theoretical model uses the subdiffusion equation with fractional time derivative and specific boundary conditions at the membrane surfaces. Using a special \textit{ansatz} we find analytical formulas describing the time evolution of concentration profiles and an amount of the substance remains in the membrane. Fitting the theoretical functions to the experimental results, we estimate the subdiffusion coefficient of polyethylene glycol 2000 in agarose hydrogel.
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