# A Numerical Solution of Transport of Mono- and Tri-valent Cations during Steady Water Flow in a Binary Exchange System

• Ro, Hee-Myong (Department of Horticultural Environment, National Horticultural Research Institute) ;
• Yoo, Sun-Ho (Department of Agricultural Chemistry, Seoul National University)
A one-dimensional transport of displacing monovalent ion, $A^+$, and a trivalent ion being displaced, $B^{3+}^ in a porous exchange system such as soil was approximated using the Crank-Nicolson implicit finite difference technique and the Thomas algorithm in tandem. The variations in the concentration profile were investigated by varying the ion-exchange equilibrium constant (k) of ion-exchange reactions, the influent concentrations, and the cation exchange capacity (CEC) of the exchanger, under constant flux condition of pore water and dispersion coefficient. A higher value of k resulted in a greater removal of the native ion, behind the sharper advancing front of displacing ion, while the magnitude of the penetration distance of$A^+$was not great. As the CEC increased, the equivalent fraction of$B^{3+}^ initially in the soil was greater, thus indicating that a higher CEC adsorbed trivalent cations preferentially over monovalent ions. Mass balance error from simulation results was less than 1%, indicating this model accounted for instantaneous charge balance fairly well.