LangmuirAdsorption

{
  "reference": {
    "citation": "Seinfeld, J. H. and Pandis, S. N. (2006) Atmospheric Chemistry and Physics, 2nd Edition, Chapter 14, Section 14.5.3, Eq. 14.44 — Langmuir monolayer adsorption isotherm. Migrated from Aerosol.jl src/organic_aerosol.jl `LangmuirAdsorption` (esm-znc).",
    "notes": "source_ref: Aerosol.jl@main:src/organic_aerosol.jl:249\nUpstream `LangmuirAdsorption` is an MTK `@component` with two parameters (V_m, b), and two variables (p, V). The equation is:\n  • V ~ V_m * b * p / (1 + b * p)  (Eq. 14.44 — Langmuir isotherm)\nThe equation is algebraic (no derivatives), making this an observed-only component.\n\nObservability classification: observed-only — the single output V is given by an algebraic equation in terms of input p. Test scenarios use `time_span: [0, 1]` and sample at t=0.\n\nESM representation note: in the upstream MTK component p is an `@variable` supplied externally as the input; in this .esm it is represented as a `parameter` (not a state) so the system is well-posed under the schema's equation-count rule (one equation per state) and to match the observed-only pattern used elsewhere in this rig (see components/aerosol/organic/bet.esm). Tests vary p via `parameter_overrides`, and the `pressure_sweep` example sweeps p as a parameter dimension.\n\nTolerance rationale (model-level rel=1e-9): observed-only algebraic system (no ODE integration); the equation involves multiplication and division. Floating-point round-off is ~1e-15. 1e-9 leaves comfortable headroom."
  },
  "tolerance": {
    "rel": 1e-09
  },
  "variables": {
    "V_m": {
      "type": "parameter",
      "units": "m^3",
      "default": 1.0,
      "description": "Gas volume for monolayer formation"
    },
    "b": {
      "type": "parameter",
      "units": "Pa^-1",
      "default": 1.0,
      "description": "Adsorption constant"
    },
    "p": {
      "type": "parameter",
      "units": "Pa",
      "default": 1.0,
      "description": "Gas partial pressure. Input parameter — the observed-only model has one algebraic equation for V given p."
    },
    "V": {
      "type": "unknown",
      "units": "m^3",
      "description": "Volume of gas adsorbed"
    }
  },
  "equations": [
    {
      "lhs": "V",
      "rhs": {
        "op": "/",
        "args": [
          {
            "op": "*",
            "args": [
              "V_m",
              "b",
              "p"
            ]
          },
          {
            "op": "+",
            "args": [
              1,
              {
                "op": "*",
                "args": [
                  "b",
                  "p"
                ]
              }
            ]
          }
        ]
      }
    }
  ],
  "tests": [
    {
      "id": "default_conditions",
      "description": "Default conditions: V_m = 1.0 m^3, b = 1.0 Pa^-1, p = 1.0 Pa. V = 1.0*1.0*1.0 / (1 + 1.0*1.0) = 1.0/2.0 = 0.5 m^3.",
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_overrides": {
        "p": 1.0
      },
      "assertions": [
        {
          "variable": "V",
          "time": 0.0,
          "expected": 0.5,
          "tolerance": {
            "rel": 1e-06
          }
        }
      ]
    },
    {
      "id": "high_pressure_saturation",
      "description": "High pressure: p = 1e6 Pa. V approaches V_m = 1.0 m^3 (saturation). V = 1.0*1.0*1e6 / (1 + 1.0*1e6) ≈ 0.999999.",
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_overrides": {
        "p": 1000000.0
      },
      "assertions": [
        {
          "variable": "V",
          "time": 0.0,
          "expected": 0.999999,
          "tolerance": {
            "rel": 0.001
          }
        }
      ]
    },
    {
      "id": "low_pressure_henry",
      "description": "Low pressure: p = 1e-6 Pa. Henry's law limit — V ≈ V_m * b * p = 1.0*1.0*1e-6 = 1e-6 m^3.",
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_overrides": {
        "p": 1e-06
      },
      "assertions": [
        {
          "variable": "V",
          "time": 0.0,
          "expected": 1e-06,
          "tolerance": {
            "rel": 0.001
          }
        }
      ]
    }
  ],
  "analyses": [
    {
      "id": "pressure_sweep",
      "description": "Sweep gas partial pressure from 0.01 Pa to 100 Pa to show the characteristic Langmuir isotherm shape (saturation approach as p increases).",
      "initial_state": {},
      "parameters": {
        "V_m": 1.0,
        "b": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "p",
            "range": {
              "start": 0.01,
              "stop": 100.0,
              "count": 50
            }
          }
        ]
      },
      "plots": [
        {
          "id": "langmuir_isotherm",
          "type": "line",
          "description": "Langmuir isotherm: V vs p — shows linear Henry's law regime at low p and saturation approach at high p.",
          "x": {
            "variable": "p",
            "label": "p (Pa)"
          },
          "y": {
            "variable": "V",
            "label": "V (m^3)"
          }
        }
      ]
    }
  ]
}