,
(A1)
where C
(concentration of Cl-), D (diffusion coefficient), P
(porosity), and V (rate of pore-water flow relative to sediment/water
interface) may be functions of time and depth. The diffusion coefficient is
described as a function of pore-water viscosity (
)
and sediment tortuosity (
)
as
.
(A2)
D0 is
the diffusion coefficient at a reference temperature T0 at
which the viscosity of the pore water is 0.
The temperature dependence of
is taken from Out and Los (1980) for 0.7 molal NaCl solutions. The tortuosity
term (McDuff and Ellis, 1979) is approximated by
2
= PF, (A3)
where F (formation factor) is expressed as an exponential function of pore space (P),
F = P-n, (A4)
with n = 1.8 (average value for deep-sea sediments, Manheim and Waterman, 1974).
Assuming steady-state porosity conditions, the rate of flow of pore water is described by:
,
(A5)
where P
,
W,
and Va
are porosity, rate of particle flux relative to the sediment surface, and
externally induced rate of pore-water flow relative to the sediment/water
interface at the depth of fully compacted sediment, respectively. W
is calculated from
.
(A6)
The principle of conservation of mass gives
.
(A7)
The partial differential equation is solved by the upwind Crank-Nicolson formula (e.g., Greenspan and Casulli, 1988).
The diffusion coefficient for HDO was assumed equal to that of H2O (Harris and Woolf, 1980). The Cl- was modeled by means of the diffusion coefficient for NaCl(aq), which changes by less than 1.1% over the range of concentrations encountered here (Rard and Miller, 1979).
