{"id":92156,"date":"2026-04-21T07:00:57","date_gmt":"2026-04-21T07:00:57","guid":{"rendered":"https:\/\/gaeatech.com\/knowledge-center\/?p=92156"},"modified":"2026-04-13T23:38:12","modified_gmt":"2026-04-13T23:38:12","slug":"pollutev10-example-2-pure-diffusion-soil-model","status":"publish","type":"post","link":"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-2-pure-diffusion-soil-model\/","title":{"rendered":"POLLUTEv10 Example 2: Pure Diffusion in a Soil Layer (No Sorption)"},"content":{"rendered":"\n

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

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Overview of the Scenario<\/h2>\n\n\n\n

In this example, contaminant transport occurs through:<\/p>\n\n\n\n

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

      Key simplifications:<\/p>\n\n\n\n

        \n
      • \u274c No advection (Darcy velocity = 0)<\/li>\n\n\n\n
      • \u274c No sorption (Kd = 0)<\/li>\n\n\n\n
      • \u2705 Transport driven entirely by molecular diffusion<\/strong><\/li>\n<\/ul>\n\n\n\n
        \n\n\n\n

        Conceptual Model<\/h2>\n\n\n\n

        The system represents a classic one-dimensional diffusion problem<\/strong>:<\/p>\n\n\n\n

          \n
        • Top boundary \u2192 constant concentration source<\/li>\n\n\n\n
        • Bottom boundary \u2192 zero concentration (instant removal)<\/li>\n\n\n\n
        • Transport mechanism \u2192 Fickian diffusion<\/strong><\/li>\n<\/ul>\n\n\n\n

          This setup is widely used in environmental engineering to:<\/p>\n\n\n\n

            \n
          • Validate numerical models<\/li>\n\n\n\n
          • Understand contaminant lag times<\/li>\n\n\n\n
          • Benchmark analytical solutions<\/li>\n<\/ul>\n\n\n\n
            \n\n\n\n

            Input Parameters<\/h2>\n\n\n\n
            Property<\/th>Symbol<\/th>Value<\/th>Units<\/th><\/tr><\/thead>
            Darcy Velocity<\/td>va<\/td>0<\/td>m\/a<\/td><\/tr>
            Diffusion Coefficient<\/td>D<\/td>0.01<\/td>m\u00b2\/a<\/td><\/tr>
            Distribution Coefficient<\/td>Kd<\/td>0<\/td>cm\u00b3\/g<\/td><\/tr>
            Soil Porosity<\/td>n<\/td>0.4<\/td>–<\/td><\/tr>
            Dry Density<\/td>\u03c1d<\/td>1.5<\/td>g\/cm\u00b3<\/td><\/tr>
            Soil Thickness<\/td>H<\/td>4<\/td>m<\/td><\/tr>
            Sub-layers<\/td>–<\/td>4<\/td>–<\/td><\/tr>
            Base Concentration<\/td>cb<\/td>0<\/td>g\/L<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
            \n\n\n\n

            Governing Equation<\/h2>\n\n\n\n

            Transport is governed by Fick\u2019s Second Law of Diffusion<\/strong>:<\/p>\n\n\n\n

            \u2202<\/mi>C<\/mi><\/mrow>\u2202<\/mi>t<\/mi><\/mrow><\/mfrac>=<\/mo>D<\/mi>\u2202<\/mi>2<\/mn><\/msup>C<\/mi><\/mrow>\u2202<\/mi>x<\/mi>2<\/mn><\/msup><\/mrow><\/mfrac><\/mrow>\\frac{\\partial C}{\\partial t} = D \\frac{\\partial^2 C}{\\partial x^2}<\/annotation><\/semantics><\/math>\u2202t\u2202C\u200b=D\u2202x2\u22022C\u200b<\/p>\n\n\n\n

            Where:<\/p>\n\n\n\n

              \n
            • C<\/em> = concentration<\/li>\n\n\n\n
            • t<\/em> = time<\/li>\n\n\n\n
            • D<\/em> = diffusion coefficient<\/li>\n\n\n\n
            • x<\/em> = depth<\/li>\n<\/ul>\n\n\n\n
              \n\n\n\n

              Graphical Output: Depth vs Concentration for Different Times<\/h2>\n\n\n\n
              \"\"<\/figure>\n\n\n\n
              \n\n\n\n

              PDF Report<\/h2>\n\n\n