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This study presents a further examination of the relationship between the Langmuir kinetics and the Lagergren (first-order) and the second-order rate models of batch adsorption. The earlier work of Liu and Shen on the transformation of the Langmuir kinetic equation to a linear combination of the Lagergren rate expression and the second-order rate expression was given a rational treatment and solutions of the transformed equation were obtained. Based on the solutions, correct relationships between the Langmuir equation and the first-order and second-order equations were established and the significance of the relationships discussed. [ABSTRACT FROM AUTHOR]

Highlights: [•] Studies aimed to develop rational models are based on questionable assumptions. [•] Usually, empirical rate expressions are used in many of the earlier studies. [•] There is a lack of reliable and accurate experimental data confirming the assumptions. [•] Future research should focus on cake depolarization and develop correlations for its prediction. [•] Possible topics of studies along the pragmatic approach are outlined. [ABSTRACT FROM AUTHOR]

Abstract: An assessment of the validity of the laws of filtration and their applications in filtration studies was made. It shows that the assumptions used in formulating some of the filtration rate expressions are incorrect. Furthermore, the experimentally determined relationship between d 2 t/dV 2 and dV/dt was often found to be inconsistent or disagree with the laws of filtration. While applying the laws of filtration may provide information useful to develop empirical models of filtration performance, the same information can be readily obtained using alternative procedures and similar models may be developed with even greater ease independent of the laws of filtration. [Copyright &y& Elsevier]

Abstract: Cake filtration, often referred to as dead-end filtration is used to separate microbial solids from aqueous solutions. In order to scale up such processes, it is necessary to determine the specific resistance and compressibility of the microbial cell cakes. Equations obtained from conventional cake filtration theory must be applied with particular care in such situations with due regard to the assumptions made in deriving them. This communication is intended to present a brief account of the conventional theory and to provide an examination of the filtration flux equation and the conditions under which this equation may or may not be used. Methods to obtain specific filtration resistance from water permeation through formed filter cakes must account for the concentration profiles within these cakes and the fact that they may not correspond to those obtained during a conventional filtration process. [Copyright &y& Elsevier]