Appendix F. LIST OF SYMBOLS

Dimensions (M, mass; L, distance; T, time) are given in brackets. 

1. A_aq is cross-sectional aquifer area perpendicular to the groundwater flow direction [L²]. 
2. A_soil is cross-sectional area perpendicular to the vertical infiltration in the soil column [L²]. 
3. B is aquifer thickness [ft]. 
4. c is residual between two successive Gauss-Sedial iterations. 
5. C₀ is liquid phase solute concentration in the infiltration water [mg/L]. 
6. C_aq is concentration of horizontal groundwater influx [mg/L]. 
7. C_w is concentration of a contaminant in liquid (water) phase [mg/L]. 
8. C_a is concentration of a contaminant in vapor (air) phase [mg/L]. 
9. C_mx(i) is mixed concentration in groundwater [W/V]. 
10. C_s is concentration of a contaminant in solid phase [mg/Kg]. 
11. C_s(z,0) is initial solid-phase concentration [mg/Kg]. 
12. D is combined dispersion coefficient. 
13. D_a is gaseous phase diffusion coefficient in the pore air [ft²/yr]. 
14. D_air is diffusion coefficient of the contaminant in the free air [ft²/yr]. 
15. D_w is dispersion coefficient for the liquid phase contaminant in the pore water [ft²/yr]. 
16. f_oc is fraction organic carbon of the soil [g/g]. 
17. K_d is distribution coefficient between the solid phase and liquid phase [ml/g]. 
18. K_H is dimensional form of Henry's Law constant [atm-m3/mol]. 
19. K_oc is organic carbon-water partition coefficient [ml/g]. 
20. h is head potential [L]. 
21. H is Henry's partition coefficient between the air phase and water phase [dimensionless]. 
22. H_d is penetration depth [ft]. 
23. _di is adjusted penetration depth for each column [L]. 
24. h_i,j is value of the head at the lattice point at (I,j)[L].
25. i is discretized soil column cell (column index in finite difference grid). 
26. j is row index in finite difference grid. 
27. k is time level. 
28. K is hydraulic conductivity [L/T]. 
29. L is horizontal length dimension of the waste [ft]. 
30. L_u is vertical distance from the source to the observation point (i.e., the water table) [L]. 
31. m is iteration index. 
32. M is total contaminant mass per unit volume of the soil. 
33. n is total porosity of the soil: equals the sum of water filled porosity and air filled porosity. 
34. N is head to a reasonable number of points. 
35. q_a is air flow velocity [ft/yr]. 
36. q_aq is the Darcy velocity in the aquifer [ft/yr]. 
37. q_x is specific flow rate in x direction [L/T]. 
38. q_y is specific flow rate in y direction [L/T]. 
39. q_w is water flow velocity (recharge rate) [ft/yr]. 
40. R is universal gas constant (R = 8.2�10^-5 atm-m³/mol�K). 
41. t is time [yr]. 
42. T is absolute temperature (�K = 273.16 + �C). 
43. t₀ is duration of solute release [yr]. 
44. V is flow function. 
45. z is vertical coordinate with positive being downward. 
46. a_L is longitudinal dispersivity of the vadose zone [ft]. 
47. a_v is transverse (vertical) dispersivity of the aquifer [ft]. 
48. Dt is time increment. 
49. Dx is distance of lattice point in horizontal space [L]. 
50. Dy is distance of lattice point in vertical space [L]. 
51. g is decay rate of the solute source due to either degradation or flushing by the infiltration [1/yr]. 
52. m is first order decay rate of a contaminant : in this model, for simplicity, it is assumed that m_w = m_a = m_s = m. 
53. m_w is first order decay rate of a contaminant in water phase [1/yr]. 
54. m_a is first order decay rate of a contaminant in gaseous phase [1/yr]. 
55. m_s is first order decay rate of a contaminant in solid phase [1/yr]. 
56. v is seepage velocity. 
57. q is combined retardation factor. 
58. q_w is volumetric water content (volume of water / total volume) [ft³/ft³]. 
59. q_a is air-filled porosity (volume of air / total volume) [ft³/ft³]. 
60. r_b is bulk density of the soil [gr/cm³].