where, C – effluent concentration (mg/L); C0 – influent concentration (mg/L); K – adsorption rate coefficient (L/mg/min); N – adsorption capacity coefficient (mg/L); x – bed depth (cm); u – linear velocity (cm/min); and t – time (min).
The constants K and q0 were determined from a plot of Ct/C0 against t for a given set of conditions. The amount of dye adsorbed mg/g was evaluated through the factor N (adsorption capacity coefficient in mg/L). This parameter was converted to adsorption capacity of the adsorbent packed in the column by considering the volume of dye solution treated with respect to the amount of adsorbent used. The Bohart–Adams model plot for the adsorption of DR23 onto PPAC is shown
Adsorption rate coefficient (K) is an indication of volume of influent treated by unit amount of adsorbent at unit time. On increasing the concentration more solute molecules form greater concentration gradient which ultimately reduces the adsorption rate coefficient from 2.7 × 10−3 to 0.9 × 10−3 L/mg/min. When the flow rate increased from 5 to 15 mL/min the adsorption rate coefficient increases from 0.8 × 10−3 to 3.0 × 10−3 L/mg/min and it does not show any variation while increasing the bed height from 5 to 10 cm.
The adsorption capacity coefficient (N) increases while increasing the influent concentration from 25 to 75 mg/L due to more availability of solute molecules in the vicinity of adsorbent. The derivative adsorption capacity of the adsorbent (qBA) calculated from N is also increase with respect to concentration. The experimental and calculated adsorption capacity has good correlation with low Sd. The Bohart–Adams model describes the adsorption data of DR23 onto PPAC column with a good fit. Out of the three models tested for the adsorption of DR23 onto PPAC column, the YN model provides excellent fit with very high r2 (0.9844–0.9953) and low Sd (0.09–0.37).