SCSB#000: Water and Chemical Transport in the Field Transport Tables

Table 1. Selected equilibrium and kinetic type models for heavy metal retention in soils (from Selim and Amacher, 1997).

	Model	Formulation²
Equilibrium Type
	Linear	S = K_d C
	Freundlich	S = K_d C^b
	General Freundlich	S/S_max = [w C/(1 + w C)]b
	Rothmund-Kornfeld ion exchange	S_i/S_T = K_RK (C_i/C_T)ⁿ
	Langmuir	S/S_max = w C/[1 + w C]
	General Langmuir Freundlich	S/S_max = (w C)b /[1 + (w C)b ]
	Langmuir with Sigmoidicity	S/S_max = w C /[1 + w C + s /C]
Kinetic Type
	First-Order	¶ S/¶ t = k_f (q /r_b) C - k_b S
	n-th Order	¶ S/¶ t = k_f (q /r_b) Cⁿ - k_b S
	Irreversible (sink/source)	¶ S/¶ t = k_s (q /r_b) (C - C_p)
	Second-order irreversible	¶ S/¶ t = k_s (q /r_b) C (S_max - S)
	Langmuir Kinetic	¶ S/¶ t = k_f (q /r_b) C (S_max - S) - k_b S
	Elovich	¶ S/¶ t = A exp(-BS)
	Power	¶ S/¶ t = K (q /r _b)CⁿS^m
	Mass Transfer	¶ S/¶ t = K (q /r _b) (C - C*)

²A, B, b, C*, C_p, K, K_d, K_RK, k_b, k_f, k_s, n, m , S_max, w , b , and s are adjustable model parameters, r _bis the soil bulk density, q is the volumetric soil water content, and C_T is the total solute concentration and S_T is the total amount sorbed of all competing species.