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Shrinking core model for multispecies uptake onto an ion exchange resin involving distinct reaction fronts

机译:收缩核心模型,用于多物种吸收到涉及不同反应前沿的离子交换树脂上

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A shrinking core model is derived for multispecies ion exchange when the counter-ions advance through the resin at different rates,leading to regions with distinctly different occupancies across the particle profile.The model generalizes an earlier version by accounting for the displacement between the various ions at the interfaces separating the regions.The model is applied to the uptake of Cu~(2+) and Co~(2+) onto an iminodiacetate chelating resin originally containing Na~+ that has been shown to exhibit distinct bands marking the furthest advance of Co~(2+) and Cu~(2+).The model successfully fits reported experimental data for the evolution of the two interface positions throughout the uptake process.Comparison between the pseudo-steady state (PSS) and fully transient transport versions of the model shows that the PSS approximation gives good predictions at the lower counter-ion concentrations considered (approx 0.1 molL~(-1)) except when the interfaces approach the resin centre,as expected.However,at higher concentrations (0.4molL~(-1)),the deviation becomes significant long before the interfaces reach the centre,indicating that the PSS approximation may not be entirely valid under these conditions.Calculation of the ion concentration profiles across the particle shows that there is a net outflow of Co~(2+) from the resin before it reaches the particle centre due to displacement by Cu~(2+).
机译:当抗衡离子以不同的速率穿过树脂时,会生成用于不同种类离子交换的收缩核模型,从而导致整个粒子分布具有明显不同的占据率的区域模型,该模型通过考虑各种离子之间的位移来概括早期版本。该模型适用于将Cu〜(2+)和Co〜(2+)吸收到最初含有Na〜+的亚氨基二乙酸螯合树脂上,该树脂已显示出表现出最远距离的明显谱带。 Co〜(2+)和Cu〜(2+)的模型,该模型成功拟合了报告的实验数据,反映了整个吸收过程中两个界面位置的演变。伪稳态(PSS)与完全瞬态传输版本之间的比较模型的模型表明,PSS近似值在考虑到较低的平衡离子浓度(约0.1 molL〜(-1))时给出了良好的预测,除了当界面接近树脂中心时,如但是,在较高浓度(0.4molL〜(-1))下,在界面到达中心位置之前很长时间,偏差就变得很明显,这表明在这些条件下,PSS近似可能并不完全有效。颗粒表明,由于Cu〜(2+)的位移,Co〜(2+)在到达颗粒中心之前从树脂中净流出。

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