Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg, 620000, Russian Federation.
Philos Trans A Math Phys Eng Sci. 2020 May 15;378(2171):20190246. doi: 10.1098/rsta.2019.0246. Epub 2020 Apr 13.
A non-stationary integro-differential model describing the dissolution of polydisperse ensembles of crystals in channels filled with flowing liquid is analysed. The particle-size distribution function, the particle flux through an arbitrary cross-section of the channel, the particle concentration profile, as well as the disappearance intensity of particles are found analytically. It is shown that a nonlinear behaviour of solutions is completely defined by the source term of particles introduced into the channel. In particular, the model approximately describes the processes of dissolution and transport of drug microcrystals to the target sites in a living organism, taking into account complex dissolution kinetics of drug particles. This article is part of the theme issue 'Patterns in soft and biological matters'.
分析了一个描述在充满流动液体的通道中溶解多分散晶体集合体的非定常积分微分模型。通过通道任意横截面的颗粒通量、颗粒浓度分布以及颗粒消失强度的解析求解。结果表明，溶液的非线性行为完全由引入通道的颗粒源项决定。特别是，该模型近似描述了药物微晶体在活体内溶解和输送到靶部位的过程，同时考虑了药物颗粒复杂的溶解动力学。本文是“软物质和生物物质中的模式”主题的一部分。
