Transient solute transport with sorption in Poiseuille flow

Abstract

Previous work on solute transport with sorption in Poiseuille flow has reached contradictory conclusions. Some have concluded that sorption increases mean solute transport velocity and decreases dispersion relative to a tracer, while others have concluded the opposite. Here we resolve this contradiction by deriving a series solution for the transient evolution that recovers previous results in the appropriate limits. This solution shows a transition in solute transport behavior from early to late time that is captured by the first-and zeroth-order terms. Mean solute transport velocity is increased at early times and reduced at late times, while solute dispersion is initially reduced, but shows a complex dependence on the partition coefficient k at late times. In the equilibrium sorption model, the time scale of the early regime and the duration of the transition to the late regime both increase with ln k for large k. The early regime is pronounced in strongly-sorbing systems (k ≫ 1). The kinetic sorption model shows a similar transition from the early to the late transport regime and recovers the equilibrium results when adsorption and desorption rates are large. As the reaction rates slow down, the duration of the early regime increases, but the changes in transport velocity and dispersion relative to a tracer diminish. In general, if the partition coefficient k is large, the early regime is well-developed and the behavior is well characterized by the analysis of the limiting case without desorption.

Convective carbon dioxide dissolution in a closed porous medium at low pressure

“…Instead, a series solutions can be obtained via Cauchy's residue theorem (Duffy 2004). This requires the poles, s k , of (3.4), which are given implicitly by the roots of Zhang et al 2017). From the definition of the inverse Laplace transform and Jordan's Lemma (Schiff 1999), the solution is then given by…”

Dispersion of charged solute in charged micro‐ and nanochannel with reversible sorption

“…In this work, we focus on the development of the analytical solution, and details of the numerical method can be found in Zhang and Wang and Zhang, Hesse, et al. .…”

“…In Zhang, Hesse, et al. , the authors derived a series solution for transport velocity and dispersion coefficient for solute transport in a soprtive , uncharged channel by combining the Method of Moments and Laplace transform. In this case, the same method cannot be applied to seek a transient solution due to the complexity introduced by the electrical interaction.…”

“…Here, α and β are the coefficients dependent on the EDL and is a kernel function dependent on both velocity distribution and EDL. is the contribution of molecular diffusion to dispersion . Besides, dispersion can be generated by shear flow and surface sorption, which corresponds to the first and second part in D L , respectively.…”

“…Recently, Zhang, Hesse, et al. obtained a transient solution for solute dispersion in a sorptive, uncharged channel by combining the Method of Moments and Laplace transform. However, to the authors’ knowledge, a general expression for dispersion in a charged channel with sorption has never been obtained.…”