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Representation of Kinetics Models in Batch Flotation as Distributed First-Order Reactions
Minerals ( IF 2.2 ) Pub Date : 2020-10-15 , DOI: 10.3390/min10100913
Luis Vinnett , Kristian E. Waters

Four kinetic models are studied as first-order reactions with flotation rate distribution f(k): (i) deterministic nth-order reaction, (ii) second-order with Rectangular f(k), (iii) Rosin–Rammler, and (iv) Fractional kinetics. These models are studied because they are considered as alternatives to the first-order reactions. The first-order representation leads to the same recovery R(t) as in the original domain. The first-order R-f(k) are obtained by inspection of the R(t) formulae or by inverse Laplace Transforms. The reaction orders of model (i) are related to the shape parameters of first-order Gamma f(k)s. Higher reaction orders imply rate concentrations at k ≈ 0 in the first-order domain. Model (ii) shows reverse J-shaped first-order f(k)s. Model (iii) under stretched exponentials presents mounded first-order f(k)s, whereas model (iv) with derivative orders lower than 1 shows from reverse J-shaped to mounded first-order f(k)s. Kinetic descriptions that lead to the same R(t) cannot be differentiated between each other. However, the first-order f(k)s can be studied in a comparable domain.

中文翻译:

浮选中动力学模型作为分布式一阶反应的表示

四个动力学模型作为浮选速率分布为fk)的一阶反应进行了研究:(i)确定性n阶反应,(ii)具有矩形fk)的二阶反应,(iii)Rosin–Rammler,和( iv)分数动力学。研究这些模型是因为它们被认为是一阶反应的替代方案。一阶表示可导致与原始域相同的恢复Rt)。其第一级- [R - ˚Fķ)由的检查得到ř)公式或逆Laplace变换。模型(i)的反应阶数与一阶Gamma fk)s的形状参数有关。较高的反应阶数表示一阶域中的速率浓度为k≈0。模型(ii)显示了反向J形的一阶fk)s。在拉伸指数下的模型(iii)呈现出堆砌的一阶fk)s,而具有导数阶数小于1的模型(iv)显示出从倒J型到堆砌的一阶fk)s。导致相同Rt的动力学描述)不能相互区分。但是,一阶fk)可以在可比较的域中研究。
更新日期:2020-10-16
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