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：

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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f（k）的一阶反应进行了研究：（i）确定性n阶反应，（ii）具有矩形f（k）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R（t）。其第一级- [R _∞ - ˚F（ķ）由的检查得到ř（吨）公式或逆Laplace变换。模型（i）的反应阶数与一阶Gamma f（k）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f（k）s。在拉伸指数下的模型（iii）呈现出堆砌的一阶f（k）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f（k）s。导致相同R（t的动力学描述）不能相互区分。但是，一阶f（k）可以在可比较的域中研究。