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Publication# Numerical Analysis of Apparatus-Induced Dispersion for Density-Dependent Solute Transport in Porous Media

Abstract

The effects of apparatus-induced dispersion on nonuniform, density-dependent flow in a cylindrical soil column were investigated using a finite-element model. To validate the model, the results with an analytical solution and laboratory column test data were analysed. The model simulations confirmed that flow nonuniformities induced by the apparatus are dissipated within the column when the distance to the apparatus outlet exceeds 3R/2, where R represents the radius of the cylindrical column. Furthermore, the simulations revealed that convergent flow in the vicinity of the outlet introduces additional hydrodynamic dispersion in the soil column apparatus. However, this effect is minimal in the region where the column height exceeds 3R/2. Additionally, it is found that an increase in the solution density gradient during the solute breakthrough period led to a decrease in flow velocity, which stabilized the flow and ultimately reduced dispersive mixing. Overall, this study provides insights into the behaviour of apparatus-induced dispersion in nonuniform, density-dependent flow within a cylindrical soil column, shedding light on the dynamics and mitigation of flow nonuniformities and dispersive mixing phenomena.

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Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion, is a type of fluid flow where advective inertial forces are small compared with viscous forces. The Reynolds number is low, i.e. . This is a typical situation in flows where the fluid velocities are very slow, the viscosities are very large, or the length-scales of the flow are very small. Creeping flow was first studied to understand lubrication. In nature, this type of flow occurs in the swimming of microorganisms and sperm.

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In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the flow velocity vector is the flow speed and is a scalar. It is also called velocity field; when evaluated along a line, it is called a velocity profile (as in, e.g., law of the wall).

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Flow measurement is the quantification of bulk fluid movement. Flow can be measured using devices called flowmeters in various ways. The common types of flowmeters with industrial applications are listed below: Obstruction type (differential pressure or variable area) Inferential (turbine type) Electromagnetic Positive-displacement flowmeters, which accumulate a fixed volume of fluid and then count the number of times the volume is filled to measure flow. Fluid dynamic (vortex shedding) Anemometer Ultrasonic flow meter Mass flow meter (Coriolis force).

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