ParticleMobility

{
  "reference": {
    "notes": "source_ref: Aerosol.jl@c8c640bb636b22f2425460e9ed5cba50793bfee1:src/single_particle_dynamics.jl:230\nUpstream `ParticleMobility` is an MTK `@component` with one constant (π_val), three `@parameters` (D_p, μ, C_c) and one variable (B). The single equation is:\n  • B ~ C_c / (3 * π_val * μ * D_p)  (Eq. 9.78 — particle mechanical mobility)\nThe equation is algebraic (no derivatives), making this an observed-only component.\n\nObservability classification: observed-only — the single output B is given by one algebraic equation in which B appears only on the LHS. B migrates as `type: state` with an explicit `equations` entry, matching the sibling single_particle_dynamics.jl migrations mean_free_path.esm, slip.esm, electrical_mobility.esm, stokes.esm and aerodynamic_diameter.esm. Test scenarios use `time_span: [0, 1]` and sample at t=0.\n\nConstant π_val (3.141592653589793) migrates as `type: parameter` carrying its numeric default, consistent with the sibling single_particle_dynamics.jl migrations (π_val is a `type: parameter` in mean_free_path.esm and electrical_mobility.esm). The name is not one of the ESS schema's reserved physical-constant names (R, k_B, N_A), so it is preserved verbatim from the source.\n\nAll three `@parameters` and the constant appear in the equation, so `parameters(sys)` collects the full set — no unused-parameter pruning is needed.\n\nTolerance rationale (model-level rel=1e-9): observed-only algebraic system (no ODE integration); the B equation is a single division of C_c by a product of parameters (with π in the denominator). Expected values are computed in float64 with the same arithmetic; floating-point round-off is ~1e-15. 1e-9 leaves comfortable headroom."
  },
  "tolerance": {
    "rel": 1e-09
  },
  "variables": {
    "π_val": {
      "type": "parameter",
      "units": "1",
      "default": 3.141592653589793,
      "description": "Pi (dimensionless)"
    },
    "D_p": {
      "type": "parameter",
      "units": "m",
      "default": 1e-06,
      "description": "Particle diameter"
    },
    "μ": {
      "type": "parameter",
      "units": "kg/(m*s)",
      "default": 1.8e-05,
      "description": "Dynamic viscosity of air"
    },
    "C_c": {
      "type": "parameter",
      "units": "1",
      "default": 1.0,
      "description": "Slip correction factor (dimensionless)"
    },
    "B": {
      "type": "unknown",
      "units": "s/kg",
      "description": "Particle mobility"
    }
  },
  "equations": [
    {
      "lhs": "B",
      "rhs": {
        "op": "/",
        "args": [
          "C_c",
          {
            "op": "*",
            "args": [
              {
                "op": "*",
                "args": [
                  {
                    "op": "*",
                    "args": [
                      3,
                      "π_val"
                    ]
                  },
                  "μ"
                ]
              },
              "D_p"
            ]
          }
        ]
      }
    }
  ],
  "tests": [
    {
      "id": "default_conditions",
      "description": "Default conditions: D_p = 1.0e-6 m (1 μm particle), μ = 1.8e-5 kg/(m·s), C_c = 1.0. The mechanical mobility B = C_c/(3π μ D_p) ≈ 5.8946e9 s/kg — the steady drift velocity per unit applied force.",
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "B",
          "time": 0.0,
          "expected": 5894627521.9220495
        }
      ]
    },
    {
      "id": "slip_corrected_micron",
      "description": "1 μm particle with the physically appropriate slip correction C_c = 1.164 (the Cunningham value for D_p = 1 μm at λ ≈ 6.5e-8 m) at default viscosity. B = C_c/(3π μ D_p) ≈ 6.8613e9 s/kg. Mirrors the upstream `ParticleMobility B = C_c/(3πμD_p)` test, which uses exactly D_p = 1.0e-6 m, μ = 1.8e-5 kg/(m·s) and C_c = 1.164.",
      "parameter_overrides": {
        "C_c": 1.164
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "B",
          "time": 0.0,
          "expected": 6861346435.517265
        }
      ]
    },
    {
      "id": "large_particle",
      "description": "Large particle (D_p = 1.0e-5 m = 10 μm) in the near-continuum regime, with the lower slip correction C_c = 1.016 appropriate to that size. B ∝ 1/D_p, so the 10× larger diameter drops the mobility roughly tenfold to ≈ 5.9889e8 s/kg. Mirrors the large-particle case of the upstream `ParticleMobility size dependence` test.",
      "parameter_overrides": {
        "D_p": 1e-05,
        "C_c": 1.016
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "B",
          "time": 0.0,
          "expected": 598894156.2272801
        }
      ]
    },
    {
      "id": "small_particle",
      "description": "Small particle (D_p = 1.0e-7 m = 100 nm), with the larger slip correction C_c = 2.85 appropriate to that size. B ∝ 1/D_p and C_c is well above unity, so the mobility rises to ≈ 1.6800e11 s/kg — more than two decades above the large-particle value, confirming that mechanical mobility decreases with particle size (the comparison made by the upstream `ParticleMobility size dependence` test).",
      "parameter_overrides": {
        "D_p": 1e-07,
        "C_c": 2.85
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "B",
          "time": 0.0,
          "expected": 167996884374.77844
        }
      ]
    },
    {
      "id": "high_viscosity",
      "description": "Doubled dynamic viscosity (μ = 3.6e-5 kg/(m·s)) at default particle size and slip correction. B ∝ 1/μ, so doubling the viscosity halves the mobility to ≈ 2.9473e9 s/kg — exactly half the default-conditions value.",
      "parameter_overrides": {
        "μ": 3.6e-05
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "B",
          "time": 0.0,
          "expected": 2947313760.9610248
        }
      ]
    }
  ],
  "analyses": [
    {
      "id": "size_dependence",
      "description": "Sweep particle diameter D_p from 10 nm to 10 μm (log scale) at default viscosity (μ = 1.8e-5 kg/(m·s)) and slip correction held at unity (C_c = 1.0) to isolate the geometric dependence. The mechanical mobility B = C_c/(3π μ D_p) ∝ 1/D_p falls by three decades across the range — smaller particles are mechanically more mobile, drifting faster under a given applied force. This is the size-dependence behavior exercised by the upstream `ParticleMobility size dependence` test.",
      "initial_state": {},
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "D_p",
            "range": {
              "start": 1e-08,
              "stop": 1e-05,
              "count": 50,
              "scale": "log"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "mobility_vs_diameter",
          "type": "line",
          "description": "Particle mechanical mobility B vs particle diameter (log x-axis) — B ∝ 1/D_p, so the curve drops three decades from ≈ 5.9e11 s/kg at 10 nm to ≈ 5.9e8 s/kg at 10 μm at fixed slip correction.",
          "x": {
            "variable": "D_p",
            "label": "D_p (m)"
          },
          "y": {
            "variable": "B",
            "label": "B (s/kg)"
          }
        }
      ]
    }
  ]
}