vi LIST OF SYMBOLS a geometry constant; 1 for planar, 2 for cylindrical, 3 for spherical a,t isotherm constant for cation i a01 constant in Equation 69 a2i constant in Equation 69 Ai_ collocation constant to replace gradient A, equivalent fraction of cation A in solution phase A_ equivalent fraction of cation A in solid phase bi isotherm constant for cation i Bj_ collocation constant to replace Laplacian operator B, equivalent fraction of cation B in solution phase Bz equivalent fraction of cation B in solid phase ci concentration of cation i in liquid, meq/mL Ci dimensionless concentration of cation i in liquid, ei/c0i Cdi concentration of cation i in bulk liquid, meq/mL Cpi concentration of cation i in liquid in macropores, meq/mL c,i solubility of cation i in Equations 7, 10 and 11, meq/mL; concentration of cation i in liquid at the particle surface, meq/mL c0_ initial concentration of cation i in liquid, vaeq/mL Dci micropore diffusivity for cation i, cm2/s D_i 30(l'e)q01/ec_ d i impeller diameter, cm Dn liquid diffusivity for cation i, em2/s Dpi maeropore diffusivity for cation i, em2/s D_i surface diffusivity for cation i, cm2/s ix _i Coiel,/(1-ep)qo_0 p density of particles, g/cm3

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