## 2 Methodology
### Batch Adsorption Studies
#### 2.4.4 Detailed Adsorption Studies  
In this section, studies such as the point of zero charge, isotherm, kinetics, desorption, and regeneration were conducted using only the adsorbent that demonstrated better performance in preliminary adsorption studies, i.e., biochar/rGO/DES-glycerol.  
The point of zero charge was determined by investigating the isoelectric point of the adsorbent under study over a pH range of 2-12.  
Isotherm and Kinetic Studies  
The isotherm and kinetics studies were conducted by investigating the effect of the initial concentration and contact time. The experiments were carried out using concentrations of 5, 10, 15, 20, 50, and 100 mg L\({}^{-1}\) at an optimum pH of 2. The mixtures were agitated at 150 rpm for 6 h at room temperature. For each concentration, small aliquots of the bulk sample were drawn at predetermined intervals and filtered for the analysis of the remaining amount of the initial pollutant concentration using UV vis.  
To explore the adsorption interaction and evaluate the equilibrium, the experimental data obtained after the study of the initial concentration effect were fitted with models such as [PERSON] (Equation (3)) and Freundlich (Equation (4)) equilibrium isotherms [22; 23].  
\[\text{Langmuir equation }\rightarrow\ q_{e}=\frac{q_{m}b_{K}C_{e}}{\left(1+b_{k}C_{e} \right)^{aK}} \tag{3}\]  
\[\text{Freundlich equation }\rightarrow\ q_{e}=K_{F}C_{e}^{n} \tag{4}\]  
where \(C_{e}\) is the residual ZDV/phenol concentration in the solution (mg L\({}^{-1}\)), \(q_{e}\) is the ZDV/phenol concentration in the adsorbent (mg g\({}^{-1}\)), \(K_{F}\) (mg/g)/(mg/L), \(n\) is the Freundlich constant, and \(n\) (dimensionless) is the heterogeneity factor. \(q_{m}\) is the maximum ZDV/phenol adsorption quantity per gram of adsorbent (mg g\({}^{-1}\)) and KL is the Langmuir adsorption equilibrium constant (L mg\({}^{-1}\)).  
To determine the adsorption dynamics, rate, mechanism, and transport of the pollutants (under study) onto different adsorbents, the experimental data obtained during the studies of contact time were fitted with kinetics models such as the Pseudo-first order (PFO), Pseudo-second order (PSO) [24], and Weber-Morris intraparticle diffusion models (IPD) [25]. The adequacy of the model that explains the data was determined by the R\({}^{2}\) value of the non-linear regression analysis' proximity to unity.  
\[\text{PFO equation }\rightarrow\ q_{t}=q_{e}-e^{-k1t} \tag{5}\]  
\[\text{PSO equation }\rightarrow\ q_{t}=\frac{q_{e}^{2}k_{2}t}{1+k_{2}q_{e}t} \tag{6}\]  
\[\text{IPD }\rightarrow\ q_{t}=k_{ld}t^{1/2}+C \tag{7}\]  
Desorption and Regeneration Studies  
It is vital to avoid producing secondary waste by dumping discarded (contaminated) adsorbents into the environment. The adsorbents' reusability was examined to renew the adsorbents and isolate the contaminants. Desorption experiments were performed by introducing 0.5 g of the adsorbent (biochar/rGO/DES-glycerol) to 40 mL of 10 mg L\({}^{-1}\) ZDV and 50 mg L\({}^{-1}\) phenol. The solutions were shaken for 24 h at room temperature. The pollutant equilibrium concentration was obtained after filtering the solutions. The saturated adsorbents were dried in an oven at 80 \({}^{\circ}\)C. In conical flasks, 0.05 g of saturated adsorbents was weighed, 10 mL of ethanol was added, and the flasks were agitated for 30 min. The initial concentration of the pollutants (ZDV and phenol) was determined using the collected filtrates.  
The following equation was used to determine the desorption efficiency:  
\[\text{Desorption efficiency}=\frac{\text{Cdes}}{\text{Cads}}\times 100 \tag{8}\]  
where Cdes is the concentration of ZDV/phenol adsorbed on the adsorbents (mg L\({}^{-1}\)) and Cads is the concentration of dye adsorbed on the adsorbent in the initial cycle (mg L\({}^{-1}\)).