An empirical correlation of the longitudinal and transverse dispersion coefficients for flow through random particle packs

Modeling of Microplastics Migration in Soil and Groundwater: Insights into Dispersion and Particle Property Effects

“…When a particle passes through the 2D aquifer model, MPs migrate to another location under the influence of ADE. Generally, for low values of the Reynolds number, the coefficients of transverse dispersion and longitudinal dispersion were approximately the same and equal to the effective molecular diffusion coefficient. , Especially, the change of particle velocity Δ u in the Stokes drag law caused by dispersion effects could be defined as normalΔ bold-italicu = N L 2 d L · v par t normalΔ t = N L 2 d normalL · bold-italicv boldpar Δ t = N L 2 D normalL Δ t where Δ u represents variable particle velocity, v par is the particle velocity in the current time step, and Δ t denotes the time step length in the present time step. Here, the dispersion coefficient D L could be expressed as d L · v par .…”

“…Generally, for low values of the Reynolds number, the coefficients of transverse dispersion and longitudinal dispersion were approximately the same and equal to the effective molecular diffusion coefficient. 53,54 Especially, the change of particle velocity Δu in the Stokes drag law caused by dispersion effects could be defined as…”

Dispersion of pollutants in a porous medium with finite thickness and variable dispersion coefficients

“…(2) below: where α (x) is the dispersivity and is the molecular diffusion caused by molecular motion and particle collisions; with τ ≤ 1: tortuosity of the porous medium, is the effective dispersion. Asymptotic dispersivity is responsible for the heterogeneity of porous media and it initially increases with the distance traveled and eventually approaches an asymptotic value, Yan et al. (2015) .…”

“…is the molecular diffusion caused by molecular motion and particle collisions; with τ ≤ 1: tortuosity of the porous medium, e D is the effective dispersion. Asymptotic dispersivity is responsible for the heterogeneity of porous media and it initially increases with the distance traveled and eventually approaches an asymptotic value, Yan (2015). Since the asymptotic dispersion coefficient depends on the distance, such a relation can be expressed equation ( 3) below:…”

“…A comparative study was carried out between distance-dependent dispersion and constant dispersion, simulating experimental data on the transport of solutes in the soil's column with a constant mass transfer coefficient. Yan (2015) proposed an empirical correlation describing the interaction of asymptotic behaviors of longitudinal and transverse dispersion of the solute for flow through packets of random particles. Dagan (1984) used a similar approximation by satisfying a diffusion equation with time-dependent apparent dispersion coefficients to determine the expected value of the concentration.…”