Assessment of Food Processing and Pharmaceutical Industrial Wastes as Potential Biosorbents: A Review

Table 3

Main adsorption isotherm models involved in the present study.

Adsorption isotherm model	Model parameters
Freundlich; 𝑞=𝐾𝐹𝐶^1/𝑛; Linear form; log𝑞=log𝐾𝐹+1𝑛log𝐶	𝐾𝐹: Freundlich isotherm constant that indicates adsorption capacity; (mg/g) (L/mg)^𝑛; 𝑛: measure of adsorption intensity or surface heterogeneity (dimensionless); 𝑞: amount adsorbed at equilibrium, mg/g; 𝐶: adsorbate concentration at equilibrium, mg/L
Langmuir; 𝑞𝑞=^𝑚𝐾𝐿𝐶1+𝐾𝐿𝐶; Linear form; 1𝑞=1𝑞𝑚𝐾𝐿𝐶+1𝑞𝑚	𝑞𝑚: maximum binding capacity, mg/g; 𝐾𝐿: Langmuir binding (adsorption) constant, L/mg
Sips; 𝑞𝑞=^𝑚(𝐾𝑠𝐶)^1/𝑛1+(𝐾𝑠𝐶)^1/𝑛; 𝑘𝑞=^𝑠𝐶^𝛽𝑠1+𝑎𝑠𝐶^𝛽𝑠	𝐾𝑠: Sips binding (adsorption) constant, (L/mg)^𝑛; 𝑛: dimensionless exponent constant; 𝛽𝑠 = Sips sorption exponent; 𝑎𝑠 = Sips sorption constant (L/mg)
Dubinin-Astakhov; 𝑞=𝑞𝑚−𝐶exp𝑅𝑇ln𝑠/𝐶𝐸^𝑛	𝐸: mean free energy of adsorption, KJ/mol; 𝑛: Dubinin-Astakhov dimensionless exponent; 𝑇: temperature, K; 𝑅: universal gas constant, KJ/mol·K
BET; 𝑞𝑞=^𝑚𝐶BET𝐶𝐶𝑠−𝐶[1+𝐶BET−1𝐶/𝐶𝑠]; Linear form; 𝐶𝑞𝐶𝑠=1−𝐶𝑞𝑚𝐶BET+𝐶BET−1𝑞𝑚𝐶BET⋅𝐶𝐶𝑠; Alternative form; 𝑞𝑞=^𝑚𝑏𝑠𝐶(1−𝑏𝐿𝐶)(1−𝑏𝐿𝐶+𝑏𝑠𝐶)	𝐶BET: BET isotherm constant which indicates energy of surface interaction, L/mg; 𝐶𝑠: saturation concentration of adsorbate, mg/L; 𝑏𝑠: isotherm constant for BET adsorption in the first layer, L/mg; 𝑏𝐿: isotherm constant for BET adsorption in upper layers, mg/L