The Ostwald ripening stage of a phase transformation process with allowance for synchronous operation of various mass transfer mechanisms (volume diffusion and diffusion along the block boundaries and dislocations) and the initial condition for the particle-radius distribution function is theoretically studied. The initial condition is taken from the analytical solution describing the intermediate stage of a phase transition process. The present theory focuses on relaxation dynamics from the beginning of the ripening process to its final asymptotic state, which is described by the previously constructed theories (Slezov VV. et al. 1978 J. Phys. Chem. Solids39, 705–709. (doi:10.1016/0022-3697(78)90002-1) and Alexandrov & Alexandrova 2020 Phil. Trans. R. Soc. A378, 20190247. (doi:10.1098/rsta.2019.0247)). An evolutionary behaviour of particle growth rates dependent on various mass transfer mechanisms and time is analytically described. The boundaries of the transition layer, which surround the blocking point, are found. The fundamental and relaxation contributions to the particle-radius distribution function are derived for the simultaneous occurrence of various mass transfer mechanisms. The left branch of this function is shifted to smaller particle radii whereas its right branch extends to the right of the blocking point as compared with the asymptotic universal distribution function. The theory under consideration well agrees with experimental data.

This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

理论研究了相变过程的奥斯特瓦尔德熟化阶段，同时考​​虑了各种传质机制（体积扩散和沿块边界和位错的扩散）和粒子半径分布函数的初始条件的同步操作。初始条件取自描述相变过程中间阶段的解析解。目前的理论侧重于从成熟过程开始到其最终渐近状态的松弛动力学，这由先前构建的理论（Slezov VV.等人1978 J. Phys. Chem. Solids 39 , 705-709）描述。 doi:10.1016/0022-3697(78)90002-1) 和 Alexandrov & Alexandrova 2020 Phil. Trans. R. Soc. A378 , 20190247. (doi:10.1098/rsta.2019.0247))。分析描述了依赖于各种传质机制和时间的粒子生长速率的演化行为。找到围绕阻塞点的过渡层的边界。粒子半径分布函数的基本贡献和弛豫贡献是针对同时发生的各种传质机制得出的。与渐近通用分布函数相比，该函数的左分支移动到较小的粒子半径，而其右分支延伸到阻塞点的右侧。所考虑的理论与实验数据非常吻合。

本文是主题问题“复杂系统中的传输现象（第 1 部分）”的一部分。