Nomenclature

(as defined in J. Gruber, "Waves in a Two-Component System: The Oxide Surface as a Variable Charge Adsorbent")
First parentheses give units. (-) means dimensionless.
Last parentheses give number of equation or Figure where symbol first appears or is defined. in the above reference

c ............. electrolyte concentration (mol per Liter of liquid), (18),
c ..............vector of soluble concentration {M, Ht} or {M, H}, (mol per Liter of liquid), (31),
C ..............vector of adsorbed concentrations H(M, H) and M(M, H), (mol per Liter of system volume),
F ..............Faraday constant (96485 Coulomb per mol), (10),
H+ ............H(x * 0, t = 0), (5),
H- .............H(x < 0, t = 0), (5),
Ht- ............Ht(x < 0, t = 0), (27), see also (9),
Hm ............concentration of free proton between 1- and 2-wave, (mol per Liter of liquid), (Figure 1),
Ht(x, t) ......total soluble concentration of protons, (mol per Liter of liquid), (2),
H(x) ..........concentration of free proton, (mol per Liter of liquid), (8),
H(x, t) .......concentration of free proton at location x and time t, (mol per Liter of liquid), (9),
H(M, H) ......adsorbed proton concentration (proton isotherm), (mol per Liter of system volume), (2),
I ................ionic strength, (mol per Liter of liquid), (21),
I ................identity matrix, (32),
k ................index specifying wave, k = 1: 1-wave (slow), k = 2: 2-wave (fast), (Figure1, (25), (26)),
k1 ..............equilibrium formation constant of XOH2 surface complex from XOH and H, (Liter per mol), (13),
k2 ..............equilibrium formation constant of XO surface complex from XOH and H, (mol per Liter), (15),
Kw ..............water dissociation constant, ((mol per Liter of liquid)2), (9),
Kd(c) .........Jacobi matrix of isotherms evaluated at location c in composition space, (-), (32),
M+ .............M(x <= 0, t = 0), (mol per Liter of liquid), (5),
M- ..............M(x < 0, t = 0), (mol per Liter of liquid), (5),
M(M, H) ......adsorbed metal concentration (metal isotherm), (mol per Liter of system volume), (1),
M(x, t) ........soluble metal concentration, (mol per Liter of liquid), (1),
M(x) ...........soluble concentration of metal, (mol per Liter of liquid), (7),
Mm .............concentration of metal between the 1- and 2-wave, (mol per Liter of liquid), (Figure 1),
Maeq(H) .....soluble equivalent metal concentration (at which half the adsorption sites of type a are filled with metal ions) as a function of H, (mol per Liter of liquid), (36),
P(x) ...........Boltzmann distribution as a function of distance from oxide surface, (-), (10),
P(H) ..........analytical approximation of Boltzmann distribution at oxide surface as a function proton concentration, (-), (22), (23),
P0(XO.., c)..Boltzmann distribution at oxide surface as a function of non neutral surface complex concentrations and electrolyte concentration, (-), (18),
PZC ...........point of zero charge on hydrous ferric oxide in pristine water, i.e. at I < 10-4 mol/L PZC =  (k2/k1)1/2, (22),
q ...............flux of water in column of porous medium, (meter per year), (1),
R ...............molar gas constant, (8.314 Joule per(mol Kelvin)), (10),
R(c) ...........retardation matrix evaluated at location c in concentration space, (-), (31),
rk(c) ..........right eigenvector of R(c) corresponding to eigenvalue rhok(c), ((mol year) per (Liter meter)), (IV.13),
t ................time variable, (year), (1),
T ...............absolute temperature, (Kelvin), (10),
XaT ............concentration of adsorption sites of type a, (mol per Liter of system volume), (11),
XT ..............concentration of adsorption sites of any type, (mol per Liter of system volume), (12),
XaO ...........concentration of empty sites of type a, (mol per Liter of system), (11),
XaOL .........concentration of sites of type a covered with L = H, H2, M, (mol per Liter of system), (11),
XOL ...........concentration of any site type covered with L = H, H2, M, (mol per Liter of system), (12),
x ...............space variable (meter), (1),
z ...............charge of ion, (multiple of unit electronic charge), (10).

a ...............site type, (a = s, w), (11),
aa ..............metal-proton exchange constant for site type a, (-), (39),
da ...............denominator in adsorption isotherms (17), (mol per Liter of liquid),
Dc ...............concentration jump across shock, (mol per Liter of liquid), (3)
Dt ................time interval, (year), (3),
Dx ...............distance traveled by shock during period Dt, (meter), (3),
f .................porosity of medium, (-), (1),
r(c) .............eigenvalue of R(c), also called "retardation", (-), (IV.3),
rk(c) ...........retardation of k-rarefaction wave, (-), (33),
sk ...............retardation of k-shock, (-), (V.2),
x(c) ............speed of concentration c, (meter per year), (6),
xk ...............speed of concentration in a k-wave, (meter per year), (28),
y(x) .............electrostatic potential at distance x from oxide surface, (Volt), (10).