Table 2 Isotherm and kinetics models were used.

From: Production and characterization of magnetic Biochar derived from pyrolysis of waste areca nut husk for removal of methylene blue dye from wastewater

Model name

Equations

Langmuir

\(\:{q}_{e}={q}_{m}{K}_{L}\frac{{C}_{e}}{1+{K}_{L}{C}_{e}}\) (4)

Freundlich

\(\:{q}_{e}={K}_{F}{C}_{e}^{\frac{1}{n}}\) (5)

Kinetic model

 Pseudo-first order

\(\:{q}_{e}={q}_{e}\:(1-\text{exp}(-{k}_{1}t))\) (6)

 Pseudo-second order

\(\:{q}_{e}=\frac{{q}_{e}^{2}{k}_{2}t}{1+{q}_{e}{k}_{2}t}\) (7)

 Elovich

\(\:{q}_{e}=\left(1+{\beta\:}_{E}\right)\times\:\text{l}\text{n}(1+{\alpha\:}_{E}{\beta\:}_{E}t)\) (8)

  1. qe and qm = the amount of dye adsorbed at equilibrium and saturation (mg/g), Ce = equilibrium dye concentration (mg/L), KL=Langmuir adsorption constant, KF and n = Freundlich adsorption constant and Freundlich exponent. k1 = rate constants for the pseudo-first-order (1/h), k2 = rate constants for the pseudo-second-order model (g/mg/h), α = the initial adsorption rate (mg/g/h), β = Elovich constant, qt = the adsorption capacity at time t (mg/g), and C is the intercept.
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