marelac (version 2.0)

diffcoeff: Molecular Diffusion Coefficients

Description

Calculates the molecular and ionic diffusion coefficients in $m^2 s^{-1}$, for several inorganic species in seawater at a given salinity, temperature, and pressure.

Based on Chapter 4 in Boudreau (1997)

Usage

diffcoeff(S = 35, t = 25, P = 1.013253,
      species=c("H2O","O2","CO2","H2","CH4","DMS",
      "He","Ne","Ar","Kr","Xe","Rn",
      "N2","H2S","NH3","NO","N2O","CO","SO2",
      "OH","F","Cl","Br","I",
      "HCO3","CO3","H2PO4","HPO4","PO4",
      "HS","HSO3","SO3","HSO4","SO4","IO3","NO2","NO3",
      "H","Li","Na","K","Cs","Ag","NH4",
      "Ca","Mg","Fe","Mn","Ba","Be","Cd","Co",
      "Cu","Hg","Ni","Sr","Pb","Ra","Zn","Al","Ce","La","Pu",
      "H3PO4","BOH3","BOH4","H4SiO4"))

Arguments

S

Salinity, -,

t

Temperature, $^\circ$C,

P

True pressure, bar,

species

character vector with the names of the chemical species whose diffusion coefficient should be calculated.

Value

• A data.frame with the diffusion coefficients $m^2 s^{-1}$ of the selected chemical species.

Details

To correct for salinity, the Stokes-Einstein relationship is used. This is not quite accurate, but is at least consistent.

$H_3PO_4$ : Least (1984) determined D(H3PO4) at 25 deg C and 0 S. Assume that this value can be scaled by the Stokes-Einstein relationship to any other temperature.

$B(OH)_3$ : Mackin (1986) determined D(B(OH)3) at 25 deg C and about 29.2 S. Assume that this value can be scaled by the Stokes-Einstein relationship to any other temperature.

$B(OH)_4$ : No information on this species. Boudreau and Canfield (1988) assume it is 12.5% smaller than B(OH)3.

$H_4SiO_4$ : Wollast and Garrels (1971) found D(H4SiO4) at 25 deg C and 36.1 ppt S. Assume that this value can be scaled by the Stokes-Einstein relationship to any other temperature.

References

Based on Chapter 4 in Boudreau (1997) :

Boudreau BP, 1997. Diagenetic Models and their Implementation. Modelling Transport and Reactions in Aquatic Sediments. Springer. Berlin.

who cites:

for self-diffusion coefficient H2O:

Cohen MH and Turnbull D. 1959. Molecular transport in liquids and glasses. Journal of chemical physics 31 (5): 1164-1169

Krynicki K, Green CD and Sawyer DW, 1978. Pressure and temperature-dependence of self-diffusion in water. Faraday discussions 66: 199-208

for gases O2 and CO2:

Novel relation by Boudreau (1997) based on new compilation of data

for gases He, Ne, Kr, Xe, Rn, H2, CH4:

Jahne B, Heinz G, and Dietrich W, 1987. Measurements of the diffusion coefficients of sparingly soluble gases in water. J. Geophys. Res., 92:10,767-10,776.

for Ar:

Ohsumi T and Horibe Y, 1984. Diffusivity of He and Ar in deep-sea sediments, Earth and Planetary Science Letters 70, 61-68.

for DMS:

Saltzman ES, King DB, Holmen K, and Leck C, 1993. Experimental Determination of the Diffusion Coefficient of Dimethylsulfide in Water, J. Geophys. Res., 98(C9), 16, 481-486.

for other gases (N2, H2S, NH3, NO, N2O, CO, SO2):

Wilke CR and Chang P, 1955. Correlation of diffusion coefficients in dilute solutions. Aiche journal 1 (2): 264-270

with the correction proposed by

Hayduk W and Laudie H, 1974. Prediction of diffusion-coefficients for nonelectrolytes in dilute aqueous-solutions. Aiche journal 20 (3): 611-615

for ions:

Hayduk W and Laudie H, 1974. Prediction of diffusion-coefficients for nonelectrolytes in dilute aqueous-solutions. Aiche journal 20 (3): 611-615

for H3PO4, B(OH)3, B(OH)4, H4SiO4 : see details

See Also

coriolis, viscosity, ssd2rad, vertmean, gravity

Examples

diffcoeff(S = 15, t = 15)/(1e4*3600*24)       # cm2/day
diffcoeff(t = 10, species = "O2")             # m2/s
difftemp <- diffcoeff(t = 0:30)[,1:13]
matplot(0:30, difftemp, xlab = "temperature", ylab = "m2/s",
        main = "Molecular/ionic diffusion", type = "l")
legend("topleft", ncol = 2, cex = 0.8, title = "mean", col = 1:13, lty = 1:13,
       legend = cbind(names(difftemp),
       format(colMeans(difftemp), digits = 4)))

select <- c("O2", "CO2", "NH3", "NH4", "NO3")
diffsal <- diffcoeff(S = 0:35, species = select)
matplot(0:35, diffsal,xlab = "salinity", ylab = "m2/s",
         main = "Molecular/ionic diffusion", type = "l")
legend("topleft", ncol = 2, cex = 0.8, title = "mean",
       col = 1:length(select), lty = 1:length(select),
       legend = cbind(select, format(colMeans(diffsal), digits = 4)))