Mathematical modelling of the influence of physico-chemical properties on heavy metal adsorption by biosorbents.

Adsorption rate is a critical parameter in the design of effective biosorbent treatment systems for heavy metals removal. Though numerous studies have identified the physico-chemical properties of biosorbents that exert influence on the adsorption rate, such influence has not been mathematically defined, limiting the effective design of adsorption systems. This study quantifies the influence of biosorbent physico-chemical properties including, specific surface area, surface functional groups, pore size, pore volume and zeta potential on the adsorption rate in relation to three divalent metal cations. Mathematical equations were developed to predict the influence of physico-chemical properties on pseudo second order kinetic constant and thereby predict the adsorption rate. Tea factory waste and coconut shell biochar were mixed in different weight percentages to vary the physico-chemical properties under consideration. Four different initial metal ion concentrations were used. Relationship between pseudo second order kinetic constant at each concentration with physico-chemical properties was quantified using regression analysis. The experimental analysis revealed that among the physico-chemical properties, acidic surface functional groups had the most profound influence on sorption mechanisms. Reliability and accuracy of the predictive models were significantly improved when separate models were developed for two ranges of initial metal ion concentrations. The outcomes of this study will contribute to the effective design and optimization of biosorbent mixtures with the capacity to remove Pb, Cu and Cd in wastewater.