Dispersion of a moving salt‐water boundary advancing through saturated sand

Abstract

When salt water displaces fresh water in sand the boundary between the two liquid phases becomes diffuse after a short period of flow. The dispersion of salt may occur at a much greater rate than can be expected by ion diffusion. The effect has been attributed to a mechanism referred to here as hydrodynamic dispersion, a general phenomenon arising from the fact that the velocity of the moving stream varies from point to point in the porous system. The mathematical treatment of the problem is based upon a statistical theory developed by Scheidegger. Equations have been derived here for the dispersion of salt water injected in the stream. The theory has been tested by displacing pure water with salt water in a column of saturated sand and determining the concentration of effluent as a function of time. The measured concentrations vary with time in approximately the manner predicted by theory.

Nitrate Leaching Under Bare Fallow at a Site in Northern Nigeria

“…As a result of dispersion some nitrate is leached faster and some slower than on the plug displacement model (Day, 1956;Biggar and Nielsen, 1962;Gardner, 1965 ;Kolenbrander, 1970), and the nitrate concentration should therefore become less the deeper it is leached. Analyses showed (Fig.…”

A Model for Predicting the Redistribution of Salts Applied to Fallow Soils After Excess Rainfall or Evaporation

“…Mathematical models based on the principle of miscible displacement of soluble salts in soils have been developed by Day (1956), Day and important for two reasons. Not only does it cause the soil to dry out so that more rainfall is required for through drainage and leachin also causes the upward movement of water and salts by capil ary rise (Marshall and Gurr, 1954; Richards et aZ., 19 6; Wetselaar, 1960).…”

Miscible displacement of nitrate and chloride through soil columns

“…This equation can be evaluated using standard tables of the normal probability integral (Hodgman,195^). Experiments of Day (1956) and Hifai et al, (1956)1 with saturated columns of washed sand, and those of Handy (1959), with sandstone, indicated, for velocities above 2.0 cm/hr, that the above equation adequately predicted the experimental results. Beran (1955) stated that the velocity at which molecular diffusion starts to be of some importance is close to 1 cm/hr.…”

“…Investigators (Taylor, 1953;Hlfal et ^,, 1956) have where Xq is the length of the slug of tracer of concentration Co in the column if no mixing occurred, to is the time for the tracer to enter the column, and N(x) is the normal prob ability integral (Day, 1956). This equation can be evaluated using standard tables of the normal probability integral (Hodgman,195^).…”