Adsorption of Cu (II) on the Surface of Nonconventional Biomass: A Study on Forced Convective Mass Transfer in Packed Bed Column

Table 3

Various breakthrough equations used in present investigation.

Model	Equation	Symbols representation
Bohart-Admas	𝐶𝑡𝐶𝑖=exp𝑘ba𝐶𝑖𝑡−𝑘ba𝑁0𝑍𝑊	Where 𝐶𝑡, 𝐶𝑖, 𝑘ba, 𝑁0, 𝑍, and 𝑊 were concentration of zinc at time 𝑡, initial concentration of zinc, kinetic constant (L/mg⋅min), saturation concentration (g/L), bed height of column (cm), flow rate of the fluid (mL/h)
Wolborska model	𝐶𝑡𝐶𝑖𝛽=exp^𝑎𝐶𝑖𝑡𝑁0−𝛽𝑎𝑍𝑊	Where 𝛽𝑎 is kinetic coefficient of external mass transfer (L/h), and the rest of all the parameters are the same as shown in Bohart-Admas model
Modified dose response model	𝐶𝑡𝐶𝑖1=1−1+𝑉eff/𝑏mdr^𝑎mdr	Where 𝑉eff is the volume (L) of metal ion solution, and 𝑎mdr and 𝑏mdr are model constants
Thomas model	𝐶𝑡𝐶𝑖=11+exp𝑘Th𝑞0(𝑀/𝐹)−𝑘Th𝑡	Where 𝑞0, 𝑘Th, 𝐶𝑡, 𝐶𝑖, 𝑀, and 𝐹 are metal uptake capacity (mg/g), model constant (L/mg⋅h), metal ion concentration at time 𝑡 (mg/L), influent metal ion concentration (mg/L), mass of the biomass packed in the column (g), and 𝐹 (mL/h) is the flow rate of metal solution through packed bed