Table 5.

Descriptions of kinetic models

Kinetic model	Description
Pseudo-first order [120]	Adsorption is the difference equilibrium adsorption and the adsorbed capacity at time multiplied by the rate constant of the adsorption. The rate of adsorption is proportional to this driving force linearly
Pseudo-second order [121]	Adsorption is the difference between the equilibrium adsorption capacity and the adsorbed capacity multiplied by the rate constant. However, in this model, the rate of adsorption is proportional to the square of the driving force indicating each adsorbate occupies two adsorption sites
Elovich [122]	This model looks into this from a chemisorption kinetics perspective by describing the reduction in rate of adsorption due to increase in surface coverage with time
Avrami [123]	This model is adapted from Avrami’s kinetic decomposition model which is used to evaluate the reaction rate as the fraction of adsorption at time, and the rate constant. It also considers multiple adsorption sites
Weber and Morris [124]	The equation for the Weber and Morris intraparticle diffusion model is based on some assumptions. Firstly, it assumes that the resistance to mass transfer is only significant at the beginning of the diffusion. Secondly, the concentration governs the radial diffusion process, only constant diffusion occurs in the process
Diffusion-chemisorption [125]	The diffusion-chemisorption model can be used to describe the sorption of adsorbate onto the heterogeneous surface. The model correlates the rate of change of concentration in solid phase to the rate of mass of transfer of pollutant in fluid phase to the biosorption side
Bangham [126]	It is a logarithmic model used to evaluate the ability of pore diffusion in the adsorption process
Boyd [127]	This model studies if adsorption is taking place by film diffusion or intra-particle diffusion as it assumes that the boundary of the adsorbent has a significant impact on the diffusion of the solute