Simple isotherm models, such as the Langmuir and Freundlich equations, are frequently used to correlate water contaminant adsorption data. In the conventional data fitting approach, the Langmuir and Freundlich equations are fitted to experimental data by minimizing the difference between the measured and calculated adsorbed phase concentrations. However, some isotherm equations are implicit in adsorbed phase concentration. Such isotherms must be converted to explicit forms to allow the use of standard nonlinear regression methods in data correlation. This paper explores the use of the Lambert W function to invert the loading-implicit isotherms of Elovich, Volmer, and Jossens to solve for adsorbed phase concentration as a function of liquid phase concentration.

中文翻译：

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通过 Lambert W 函数反转加载隐式吸附等温线

简单的等温线模型，例如 Langmuir 和 Freundlich 方程，经常用于关联水污染物吸附数据。在传统的数据拟合方法中，Langmuir 和 Freundlich 方程通过最小化测量和计算的吸附相浓度之间的差异来拟合实验数据。然而，一些等温方程隐含在吸附相浓度中。此类等温线必须转换为显式形式，以允许在数据关联中使用标准非线性回归方法。本文探讨了使用 Lambert W 函数来反转 Elovich、Volmer 和 Jossens 的加载隐式等温线，以求解作为液相浓度函数的吸附相浓度。