The present study develops comprehensive drop size distribution by coupling numerical modeling with experimental data to optimize the heavy metal extraction in a modified rotating disc contactor column. Droplet behavior was illustrated based on the maximum entropy principle, population balance model, normal and log-normal functions. For case studies, the vanadium extraction from sulfate solution by mixtures of D2EHPA and TBP extractants and metal stripping from the loaded organic phase by ammonium solution was employed as the reactive agents to generate chemical reactions. The modeling results indicated that the agitation speed and mass transfer direction have more profound influences on the drop size distribution, whereas only partially associated with the phase flow rates. Mathematical optimizations based on the Lagrange multipliers method are conducted to formulate the new correlations in terms of the maximum entropy principle (MEP). The population balance model (PBM) was utilized to characterize the distribution internal coordinate with main parameters in the breakage and coalescence of drops. From output results for drop size distribution, the population balance approach validated significantly with the experimental data for reactive systems in an MRDC column.

本研究通过将数值建模与实验数据相结合来开发综合液滴尺寸分布，以优化改进的转盘接触器塔中的重金属提取。基于最大熵原理、种群平衡模型、正态和对数正态函数来说明液滴行为。在案例研究中，使用 D2EHPA 和 TBP 萃取剂的混合物从硫酸盐溶液中萃取钒，以及通过铵溶液从负载的有机相中萃取金属作为反应剂来产生化学反应。建模结果表明，搅拌速度和传质方向对液滴尺寸分布有更深远的影响，而与相流速仅部分相关。进行基于拉格朗日乘子法的数学优化以根据最大熵原理 (MEP) 制定新的相关性。利用群体平衡模型（PBM）来表征液滴破裂和聚结中主要参数的分布内坐标。从液滴尺寸分布的输出结果来看，总体平衡方法通过 MRDC 塔中反应系统的实验数据得到了显着验证。