Analytical solutions of transient concentration of degraded components inside cylindrical and slab-type PLGA particles immersed in infinite medium were derived by solving reaction-diffusion equations of autocatalytic reaction using eigenfunction expansion method. The resulting average concentrations were compared with the modeling results of spherical PLGA particles by Versypt and her colleagues to study the effect of particle morphology on the autocatalytic reaction. Mass transfer resistance inside and outside of the particles was also considered using Biot number, and its effects on the concentration inside particles with various morphologies were also studied by solving reaction-diffusion equation. To predict transient concentration in surrounding medium, coupled differential equations were solved for the three shapes of PLGA particles by assuming finite volume of the decomposition system. Mathematical solutions were obtained by Laplace transform, and the results were compared for the PLGA particles with different shapes depending on Thiele modulus and particle volume fraction.

中文翻译：

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基于反应扩散方程解析解的各种形貌聚合物微粒自催化降解建模

利用本征函数展开法求解自催化反应的反应扩散方程，推导出了浸没在无限介质中的圆柱状和板状PLGA粒子内部降解组分瞬态浓度的解析解。Versypt 及其同事将所得平均浓度与球形 PLGA 颗粒的建模结果进行比较，以研究颗粒形态对自催化反应的影响。还使用Biot数考虑了颗粒内部和外部的传质阻力，并通过求解反应扩散方程研究了其对各种形貌颗粒内部浓度的影响。为了预测周围介质中的瞬时浓度，通过假设分解系统的体积有限，求解了三种形状的 PLGA 颗粒的耦合微分方程。通过拉普拉斯变换获得数学解，并根据蒂勒模量和粒子体积分数对具有不同形状的 PLGA 粒子的结果进行比较。