New turbulent flow and eddy dispersion mechanism to interpret dispersivity in homogeneous soils in miscible displacement experiments

For a homogeneous soil, the traditional laminar flow and well-known Taylor diffusion mechanism cannot interpret dispersivity (linear relationship between dispersion coefficient and pore-water velocity). The objective of this study was to propose a new mechanism and mathematical model based on fluid mechanics.

Due to the roughness of the wall of a soil capillary tube, a new turbulent flow is proposed to be eddies at the wall and laminar flow at the main stream of a soil capillary tube. A new eddy dispersion mechanism is that the behavior of solute in the eddies follows random walks and the solute mixes instantly between the wall and main stream in a tube at the microscale. The new turbulent flow and eddy dispersion occur when the pore-water velocity is greater than a critical value. Transition to the new mechanism from a laminar flow in the tube and molecular diffusion is described by a plateau-linear model. It was tested by published datasets of pore-water velocity and dispersion coefficient in miscible displacement experiments on a loam and a sandy loam.

The plateau-linear model fit the published datasets. The estimate of dispersivity was 0.135 cm. The transition of water flow and dispersion process occurred at the critical pore-water velocity 0.216 cm h⁻¹ or Reynolds number of the order of 10⁻⁶.

Dispersivity in homogeneous soils was interpretated by the turbulent water flow and the eddy dispersion mechanism. It is determined by the structure of rough wall in a soil capillary tube at the miscroscale.