POLLUTEv10 Example 2: Pure Diffusion in a Soil Layer (No Sorption)

This example is a fundamental case used to demonstrate pure diffusion of a conservative contaminant through soil. Unlike more complex landfill scenarios, this example isolates diffusion-only transport, making it ideal for understanding baseline contaminant migration behavior.

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Overview of the Scenario

In this example, contaminant transport occurs through:

• A 4 m thick soil layer
• A constant concentration source at the top boundary
• An underlying aquifer where:
  • Concentration is assumed to be zero (perfect sink)
  • Due to high flushing velocity, the aquifer is not explicitly modeled

Key simplifications:

• ❌ No advection (Darcy velocity = 0)
• ❌ No sorption (Kd = 0)
• ✅ Transport driven entirely by molecular diffusion

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Conceptual Model

The system represents a classic one-dimensional diffusion problem:

• Top boundary → constant concentration source
• Bottom boundary → zero concentration (instant removal)
• Transport mechanism → Fickian diffusion

This setup is widely used in environmental engineering to:

• Validate numerical models
• Understand contaminant lag times
• Benchmark analytical solutions

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Input Parameters

Property	Symbol	Value	Units
Darcy Velocity	va	0	m/a
Diffusion Coefficient	D	0.01	m²/a
Distribution Coefficient	Kd	0	cm³/g
Soil Porosity	n	0.4	–
Dry Density	ρd	1.5	g/cm³
Soil Thickness	H	4	m
Sub-layers	–	4	–
Base Concentration	cb	0	g/L

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Governing Equation

Transport is governed by Fick’s Second Law of Diffusion:

$\frac{\partial C}{\partial t} = D \frac{\partial^2 C}{\partial x^2}$∂t∂C​=D∂x2∂2C​

Where:

• C = concentration
• t = time
• D = diffusion coefficient
• x = depth

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Graphical Output: Depth vs Concentration for Different Times

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PDF Report

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Analytical Insight

Because:

• Kd = 0 → no retardation
• va = 0 → no advection

The system behaves as a pure diffusion medium, meaning:

• Travel time depends only on diffusion coefficient and thickness
• No delay from sorption or flow
• Faster breakthrough compared to real soils with adsorption

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Key Results

• Rapid contaminant migration relative to sorbing systems
• Smooth concentration gradients over time
• No retardation effects observed
• Steady-state defined by linear gradient

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Conclusions

• Diffusion alone can drive significant contaminant movement
• Absence of sorption represents a worst-case mobility scenario
• Useful for validating transport models and comparing against more complex cases

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Engineering Insights

• This example represents a baseline condition — real-world systems usually show slower transport due to:
  • Sorption (Kd > 0)
  • Lower effective diffusion
• The assumption of a perfect sink at the base is conservative and ensures:
  • Maximum downward flux
• Dividing the soil into sub-layers improves numerical accuracy in POLLUTEv10

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Applications

• Landfill liner performance comparisons
• Risk assessments for conservative contaminants
• Model calibration and validation
• Teaching and demonstration of diffusion principles

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