Particle transport in flow through porous media: Advection, longitudinal dispersion, and filtration

A theoretical and experimental investigation of the transport parameters of particles flowing through porous media has been made. These parameters are the particle advective velocity, longitudinal dispersion coefficient, and filter coefficient. The theoretical development used dimensionless numbers to define the transport parameters and incorporated them into an advective-dispersion equation describing particle transport.;Flow experiments were conducted in a 1.5 m vertical column with sand (geo. mean diameter = 381 micron), with suspensions of polystyrene latex particles (three cases, mean diameter = 0.1, 1.0, and 2.8 micron), and with NaCl as the electrolyte (0.4 mM ;The particle advective velocities for the three different sized particles were found to range approximately from 0 to 5.4% greater than the solute velocity, and these values were within a few percent of predictions based on particle and pore radii.;The longitudinal dispersion coefficient for the three different sized particles was found to be a function of only the advective velocity of the particles and grain diameter of the porous bed which confirmed the dimensional analysis argument and closely matched previous solute work.;A solution to the complete advective-dispersion equation for particle transport was derived for the case of a constant filter coefficient. This solution when compared to a similar solution previously derived for solute transport, showed that for small filtration the solutions were identical except for the exponential decay factor due to filtration. A numerical model was developed for the case of a variable filter coefficient.;A dimensional analysis argument for the relationship between the favorable and unfavorable filter coefficient was proposed to be a function of the ratio of the particle diffusion length of an advecting particle and the double layer thickness (which in turn depends on the ionic strength of the water).