Effects of sorption on transverse mixing in transient flows

Transverse mixing has been identified as a potentially limiting factor for natural attenuation of plumes originating from continuously emitting sources. Under steady-state flow conditions, dispersion is the only process leading to lateral mixing. This process is very slow and cannot explain the lateral spread of plumes observed in the field. When the flow direction fluctuates with time, transverse dispersion is slightly enhanced, but not very pronounced. Under these flow conditions, however, sorption can contribute to mixing into the mean transverse direction. If the reacting compounds differ in their strength of sorption, chromatographic mixing and separation alternate in time-periodic flows. For instantaneous sorption, the plumes may overlap within a stripe of fixed width. In contrast to sorption in local equilibrium, kinetic sorption contributes to mixing also for compounds with identical sorption strength. I derive an analytical expression for the equivalent transverse dispersion coefficient of a kinetically sorbing compound in a spatially uniform flow field undergoing sinusoidal fluctuations in time. This expression may be used for reactive transport calculations in an equivalent domain with constant flow. The effects are the strongest for compounds with a dimensionless partitioning coefficient of about unity, slow sorption kinetics, and slowly fluctuating velocities. For realistic parameters, kinetic sorption contributes to transverse mixing in the same range as heterogeneity.