Improved understanding of bimolecular reactions in deceptively simple homogeneous media: From laboratory experiments to Lagrangian quantification

Abstract

Medium heterogeneity affects reaction kinetics by controlling the mixing of reactant particles, but the linkage between medium properties and reaction kinetics is difficult to build, even for simple, relatively homogeneous media. This study aims to explore the dynamics of bimolecular reactions, aniline 1 1,2-naphthoquinone-4-sulfonic acid ! 1,2-naphthoquinone-4-aminobenzene, in relatively homogeneous flow cells. Laboratory experiments were conducted to monitor the transport of both conservative and reactive tracers through columns packed with silica sand of specific diameters. The measured tracer breakthrough curves exhibit subdiffusive behavior with a late-time tail becoming more pronounced with decreasing sand size, probably due to the segregated flow regions formed more easily in columns packed with smaller size sand. Numerical analysis using a novel Lagrangian model shows that subdiffusion has a twofold effect on bimolecular reactions. While subdiffusion enhances the power-law growth rate of product mass by prolonging the exposure of reactant particles in the depletion zone, the global reaction rate is constrained because subdiffusion constrains the mobility of reactant particles. Reactive kinetics in deceptively simple homogeneous media is therefore controlled by subdiffusion, which is sensitive to the dimensions of packed sand.

A fractional-order tempered-stable continuity model to capture surface water runoff

“…relatively uniform soils and smooth surface) in this experiment, the flow velocity can vary along the soil surface (Deng et al, 2006) where the delayed flow forms the late-time tailing. It is also noteworthy that we observed similar late-time tailing behavior in tracer transport through relatively uniform and saturated soils repacked in sand columns (Zhang et al, 2014). To further check the sensitivity of the tailing behavior to model parameters, we add two more model results with ¼ 0.80 and ¼ 0.30 s À1 for model (1), and ¼ 0.75 and ¼ 0.15 s À1 for model (2) (see the gray and dashed lines in Figure 5(a) and (b)).…”

Modeling mixed retention and early arrivals in multidimensional heterogeneous media using an explicit Lagrangian scheme

“…Anomalous transport with retention or early arrivals have been well documented in many disciplines, motivating the development of nonlocal physical models such as the fractional advection‐dispersion equation (fADE) [ Metzler and Klafter , ; Kilbas et al ., ; Herrmann , ]. In hydrology, anomalous diffusion due to retention has been observed for tracers transport in soils [ Pachepsky et al ., ; Levy and Berkowitz , ; Bromly and Hinz , ; Cortis and Berkowitz , ; Delay et al ., ; Hunt et al ., ], rocks [ LaBolle and Fogg , ; Kosakowski , ; Pedretti et al ., ; Ronayne , ], and streams [ Czernuszenko et al ., ; González‐Pinzón et al ., ], while anomalous diffusion with early arrivals has been found for conservative tracer transport in soils [ Zhang et al ., ], streams [ Deng et al ., , ; Kim and Kavvas , ], bed load or suspended sediment transport in rivers [ Stark et al ., ; Houssais and Lajeunesse , , among many others], and solutes moving along fractured media at various scales [ Benson et al ., ; Reeves et al ., , b; Zhang et al ., ]. The fADE is found to be superior to the second‐order advection‐dispersion equation (ADE) in quantifying the observed non‐Fickian transport behavior [ Benson et al ., , 2004; Schumer et al ., ; Zhang et al ., ].…”

Incorporating Super‐Diffusion due to Sub‐Grid Heterogeneity to Capture Non‐Fickian Transport

“…Laboratory experiments of conservative tracer transport through repacked sand columns were conducted recently to explore the anomalous dynamics at the Darcy scale (Zhang et al ). One glass tube with internal dimensions of 100 cm in length and 4 cm in diameter was packed with coarse sand, and transport of Brilliant Blue FCF (BBF) was then monitored with various flow rates through the saturated column.…”