Kinetics, as a fundamental requirement of nearly all industrial activities and engineering researches, plays a great role in leaching processes. Although there are many pieces of research on its application, there is not a clear pathway for investigating the kinetics of leaching and researchers usually follow different strategies in their studies. The conventional investigation techniques, which usually do not consider the mixed mechanisms and possibility of any change in the mechanism, normally include many calculations, plots, and inadequate capabilities to detect changes in the controlling mechanism of leaching. In this review, the main mathematical models of leaching and all possible scenarios are presented and discussed. The effect of various leaching parameters (including leaching agent, temperature, particle size, agitation, and solid to liquid ratio) on the rate of dissolution is summarized. Besides, two main approaches of rate determination step (single controlling mechanism and combined resistances method) are described and compared by reporting related equations and suitable examples. A technique to detect any changes in the leaching controlling mechanism is introduced and the alternatives to confirm the results are described. Additional models and equations were suggested for the cases that there is no agreement between data and the conventional models. Also, situations which are ignored in simple models (e.g., reversibility of the leaching reactions, adsorption and desorption of leached species, influence of charge and surface potential, existence of multiple reactants in the solid, galvanic effect, wide particle size distribution, etc.) to develop more legalistic models are discussed. Considering various possible mechanisms in the kinetics of leaching, equations are derived for industrial leaching reactors.

中文翻译：

---

浸出动力学：综述

动力学作为几乎所有工业活动和工程研究的基本要求，在浸出过程中发挥着重要作用。尽管对其应用有很多研究，但没有明确的途径来研究浸出动力学，研究人员通常在研究中遵循不同的策略。传统的调查技术通常不考虑混合机制和机制发生任何变化的可能性，通常包括许多计算、绘图和检测浸出控制机制变化的能力不足。在这篇综述中，介绍和讨论了浸出的主要数学模型和所有可能的情况。各种浸出参数（包括浸出剂、温度、粒度、搅拌、和固液比）对溶解速率的影响进行了总结。此外，通过报告相关方程和合适的例子，描述和比较了速率确定步骤的两种主要方法（单一控制机制和组合电阻法）。介绍了一种检测浸出控制机制中任何变化的技术，并描述了确认结果的替代方法。对于数据与传统模型不一致的情况，建议使用其他模型和方程。此外，在简单模型中忽略的情况（例如，浸出反应的可逆性、浸出物质的吸附和解吸、电荷和表面电位的影响、固体中存在多种反应物、电偶效应、宽粒度分布等）。) 以发展更多的法律模式进行了讨论。考虑到浸出动力学中的各种可能机制，推导出工业浸出反应器的方程。