6.2 Advection, Dispersion, and Diffusion in Aquatic Systems

Water pollution moves through aquatic systems in complex ways. Advection, dispersion, and diffusion transport contaminants differently, affecting how far and fast they spread. Understanding these processes helps predict and manage pollution's impact on water bodies.

Mathematical models and equations describe contaminant transport, allowing scientists to calculate concentrations over time and space. Factors like flow velocity, turbulence, and mixing processes influence how pollutants move and behave in various aquatic environments.

Transport Processes in Aquatic Systems

Advection, dispersion, and diffusion concepts

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• Advection transports contaminants via bulk fluid motion primarily moving pollutants long distances in rivers and streams (Mississippi River)
• Dispersion spreads contaminants due to velocity variations caused by turbulence and shear stress mixing pollutants in complex flow patterns (urban stormwater runoff)
• Diffusion moves contaminants from high to low concentration areas through random molecular motion significant in slow or stagnant waters (pollutant gradient in a lake)

Mathematical models for contaminant transport

• One-dimensional advection-dispersion equation describes concentration changes over time and space $\frac{\partial C}{\partial t} = -v\frac{\partial C}{\partial x} + D\frac{\partial^2 C}{\partial x^2}$
  • C represents contaminant concentration
  • t denotes time
  • v indicates average flow velocity
  • x measures distance
  • D signifies dispersion coefficient
• Fick's first law of diffusion quantifies diffusive flux $J = -D\frac{\partial C}{\partial x}$
  • J represents diffusive flux
• Darcy's law for groundwater flow calculates specific discharge $q = -K\frac{dh}{dl}$
  • q denotes specific discharge
  • K represents hydraulic conductivity
  • dh/dl indicates hydraulic gradient

Factors Affecting Contaminant Transport

Flow effects on contaminant movement

• Flow velocity increases advective transport rate and affects contaminant residence time in systems (fast-flowing rivers vs. slow-moving estuaries)
• Turbulence enhances mixing, dispersion, and increases effective diffusion coefficient (whitewater rapids)
• Mixing processes include:
  1. Vertical mixing in rivers and lakes
  2. Lateral mixing in wide channels
  3. Tidal mixing in estuaries
• Reynolds number indicates flow regime using formula $Re = \frac{vL}{\nu}$
  • v denotes flow velocity
  • L represents characteristic length
  • ν signifies kinematic viscosity

Factors in plume behavior

• Plume characteristics shape and extent influenced by dominant transport processes creating concentration gradients (industrial effluent discharge)
• Péclet number measures ratio of advective to diffusive transport $Pe = \frac{vL}{D}$
• Temporal plume evolution shows initial advection dominance with increasing dispersion and diffusion importance over time
• Spatial variations in plume behavior include near-field vs. far-field effects and boundary interactions (shorelines, sediment-water interface)
• Attenuation processes reduce contaminant concentrations through sorption to sediments, biodegradation, and chemical reactions (oil spill degradation)