Wall Loss Tutorial: Spherical vs Rectangular Chambers¶

Learn how to configure wall loss strategies, compare chamber geometries, and chain wall loss with coagulation and condensation. All examples run quickly (≤30 s) with small grids and reuse helper functions to avoid recomputing simulations.

Setup¶

• Uses particula public APIs from par.dynamics re-exports.
• Time grid: 0–30 min with 30 s spacing (61 points).
• Distribution: preset discrete radius bins (small and fast).
• Plots: minutes on x-axis; log-scale concentrations.

In [ ]:

import numpy as np
from matplotlib import pyplot as plt

import particula as par

np.set_printoptions(precision=3, suppress=True)
TIME_STEP = 30.0  # seconds
TOTAL_TIME = 1800.0  # seconds (30 minutes)
N_STEPS = int(TOTAL_TIME / TIME_STEP)
TIME_GRID = np.linspace(0.0, TOTAL_TIME, N_STEPS + 1)
TEMPERATURE = 298.15  # K
PRESSURE = 101325.0  # Pa

import numpy as np from matplotlib import pyplot as plt import particula as par np.set_printoptions(precision=3, suppress=True) TIME_STEP = 30.0 # seconds TOTAL_TIME = 1800.0 # seconds (30 minutes) N_STEPS = int(TOTAL_TIME / TIME_STEP) TIME_GRID = np.linspace(0.0, TOTAL_TIME, N_STEPS + 1) TEMPERATURE = 298.15 # K PRESSURE = 101325.0 # Pa

In [ ]:

def build_aerosol() -> par.Aerosol:
    """Create a small discrete aerosol with an empty atmosphere."""
    particles = par.particles.PresetParticleRadiusBuilder().build()
    atmosphere = par.gas.Atmosphere(
        temperature=TEMPERATURE,
        total_pressure=PRESSURE,
        partitioning_species=[],
        gas_only_species=[],
    )
    return par.Aerosol(atmosphere=atmosphere, particles=particles)


def run_wall_loss(strategy: par.dynamics.WallLossStrategy, sub_steps: int = 1):
    """Execute wall loss over the shared time grid."""
    aerosol = build_aerosol()
    wall_loss = par.dynamics.WallLoss(wall_loss_strategy=strategy)
    series = np.zeros_like(TIME_GRID)
    series[0] = aerosol.particles.get_total_concentration()
    for idx in range(1, TIME_GRID.size):
        aerosol = wall_loss.execute(
            aerosol, time_step=TIME_STEP, sub_steps=sub_steps
        )
        series[idx] = aerosol.particles.get_total_concentration()
    return series, aerosol


def plot_decay(times_min, *series_with_labels):
    fig, ax = plt.subplots(figsize=(6, 4))
    for series, label, style in series_with_labels:
        ax.plot(times_min, series / series[0], style, label=label, linewidth=2)
    ax.set_xlabel("Time (min)")
    ax.set_ylabel("Normalized concentration")
    ax.set_yscale("log")
    ax.grid(True)
    ax.legend()
    plt.tight_layout()
    return fig, ax


times_minutes = TIME_GRID / 60.0
baseline_aerosol = build_aerosol()
print("Initial bins:", baseline_aerosol.particles.get_radius().size)
print("Initial total conc (1/m^3):",
      f"{baseline_aerosol.particles.get_total_concentration():.3e}")

def build_aerosol() -> par.Aerosol: """Create a small discrete aerosol with an empty atmosphere.""" particles = par.particles.PresetParticleRadiusBuilder().build() atmosphere = par.gas.Atmosphere( temperature=TEMPERATURE, total_pressure=PRESSURE, partitioning_species=[], gas_only_species=[], ) return par.Aerosol(atmosphere=atmosphere, particles=particles) def run_wall_loss(strategy: par.dynamics.WallLossStrategy, sub_steps: int = 1): """Execute wall loss over the shared time grid.""" aerosol = build_aerosol() wall_loss = par.dynamics.WallLoss(wall_loss_strategy=strategy) series = np.zeros_like(TIME_GRID) series[0] = aerosol.particles.get_total_concentration() for idx in range(1, TIME_GRID.size): aerosol = wall_loss.execute( aerosol, time_step=TIME_STEP, sub_steps=sub_steps ) series[idx] = aerosol.particles.get_total_concentration() return series, aerosol def plot_decay(times_min, *series_with_labels): fig, ax = plt.subplots(figsize=(6, 4)) for series, label, style in series_with_labels: ax.plot(times_min, series / series[0], style, label=label, linewidth=2) ax.set_xlabel("Time (min)") ax.set_ylabel("Normalized concentration") ax.set_yscale("log") ax.grid(True) ax.legend() plt.tight_layout() return fig, ax times_minutes = TIME_GRID / 60.0 baseline_aerosol = build_aerosol() print("Initial bins:", baseline_aerosol.particles.get_radius().size) print("Initial total conc (1/m^3):", f"{baseline_aerosol.particles.get_total_concentration():.3e}")

Basic spherical wall loss¶

Spherical chamber with modest eddy diffusivity and radius. Uses two sub-steps to demonstrate clamping behavior in the runnable.

In [ ]:

spherical_strategy = par.dynamics.SphericalWallLossStrategy(
    wall_eddy_diffusivity=1e-3,
    chamber_radius=0.5,
    distribution_type="discrete",
)
spherical_series, spherical_aerosol = run_wall_loss(
    spherical_strategy, sub_steps=2
)
print("Final conc (spherical):", f"{spherical_series[-1]:.3e} 1/m^3")

spherical_strategy = par.dynamics.SphericalWallLossStrategy( wall_eddy_diffusivity=1e-3, chamber_radius=0.5, distribution_type="discrete", ) spherical_series, spherical_aerosol = run_wall_loss( spherical_strategy, sub_steps=2 ) print("Final conc (spherical):", f"{spherical_series[-1]:.3e} 1/m^3")

In [ ]:

_ = plot_decay(
    times_minutes,
    (spherical_series, "Spherical (0.5 m)", "b-"),
)

_ = plot_decay( times_minutes, (spherical_series, "Spherical (0.5 m)", "b-"), )

Geometry comparison: spherical vs rectangular¶

Equal-volume comparison: a 0.5 m radius sphere (~0.52 m^3) vs a rectangular chamber with dimensions (1.0, 0.72, 0.72) m.

In [ ]:

rectangular_strategy = par.dynamics.RectangularWallLossStrategy(
    wall_eddy_diffusivity=1e-3,
    chamber_dimensions=(1.0, 0.72, 0.72),
    distribution_type="discrete",
)
rect_series, _ = run_wall_loss(rectangular_strategy)
fig_cmp, _ = plot_decay(
    times_minutes,
    (spherical_series, "Spherical (0.5 m)", "b-"),
    (rect_series, "Rectangular (1.0x0.72x0.72 m)", "r--"),
)
fig_cmp.axes[0].set_title("Geometry comparison")

rectangular_strategy = par.dynamics.RectangularWallLossStrategy( wall_eddy_diffusivity=1e-3, chamber_dimensions=(1.0, 0.72, 0.72), distribution_type="discrete", ) rect_series, _ = run_wall_loss(rectangular_strategy) fig_cmp, _ = plot_decay( times_minutes, (spherical_series, "Spherical (0.5 m)", "b-"), (rect_series, "Rectangular (1.0x0.72x0.72 m)", "r--"), ) fig_cmp.axes[0].set_title("Geometry comparison")

Advanced chaining: coagulation + wall loss¶

Demonstrates runnable composition with the | operator. Uses the same time grid and small bin counts to keep runtime low.

In [ ]:

coag_strategy = par.dynamics.BrownianCoagulationStrategy(
    distribution_type="discrete"
)
coagulation = par.dynamics.Coagulation(coagulation_strategy=coag_strategy)
coag_wall = coagulation | par.dynamics.WallLoss(wall_loss_strategy=spherical_strategy)

aerosol_wall_only = build_aerosol()
aerosol_coag_wall = build_aerosol()
wall_only_series = np.zeros_like(TIME_GRID)
coag_wall_series = np.zeros_like(TIME_GRID)
wall_only_series[0] = aerosol_wall_only.particles.get_total_concentration()
coag_wall_series[0] = aerosol_coag_wall.particles.get_total_concentration()

for idx in range(1, TIME_GRID.size):
    aerosol_wall_only = par.dynamics.WallLoss(
        wall_loss_strategy=spherical_strategy
    ).execute(aerosol_wall_only, time_step=TIME_STEP)
    aerosol_coag_wall = coag_wall.execute(
        aerosol_coag_wall, time_step=TIME_STEP
    )
    wall_only_series[idx] = aerosol_wall_only.particles.get_total_concentration()
    coag_wall_series[idx] = aerosol_coag_wall.particles.get_total_concentration()

_ = plot_decay(
    times_minutes,
    (wall_only_series, "Wall loss only", "b-"),
    (coag_wall_series, "Coagulation | Wall loss", "g--"),
)

coag_strategy = par.dynamics.BrownianCoagulationStrategy( distribution_type="discrete" ) coagulation = par.dynamics.Coagulation(coagulation_strategy=coag_strategy) coag_wall = coagulation | par.dynamics.WallLoss(wall_loss_strategy=spherical_strategy) aerosol_wall_only = build_aerosol() aerosol_coag_wall = build_aerosol() wall_only_series = np.zeros_like(TIME_GRID) coag_wall_series = np.zeros_like(TIME_GRID) wall_only_series[0] = aerosol_wall_only.particles.get_total_concentration() coag_wall_series[0] = aerosol_coag_wall.particles.get_total_concentration() for idx in range(1, TIME_GRID.size): aerosol_wall_only = par.dynamics.WallLoss( wall_loss_strategy=spherical_strategy ).execute(aerosol_wall_only, time_step=TIME_STEP) aerosol_coag_wall = coag_wall.execute( aerosol_coag_wall, time_step=TIME_STEP ) wall_only_series[idx] = aerosol_wall_only.particles.get_total_concentration() coag_wall_series[idx] = aerosol_coag_wall.particles.get_total_concentration() _ = plot_decay( times_minutes, (wall_only_series, "Wall loss only", "b-"), (coag_wall_series, "Coagulation | Wall loss", "g--"), )

Concise condensation + wall loss snippet¶

Shows a lightweight condensation strategy chained with wall loss over a short window (10 min). Parameters are intentionally small to keep runtime ≤1 s.

In [ ]:

condensation_strategy = par.dynamics.CondensationIsothermalBuilder()
condensation_strategy.set_molar_mass(0.12, "kg/mol")
condensation_strategy.set_diffusion_coefficient(1e-5, "m^2/s")
condensation_strategy.set_accommodation_coefficient(0.9)
condensation_strategy.set_update_gases(False)
condensation = par.dynamics.MassCondensation(
    condensation_strategy=condensation_strategy.build()
)
wall_loss_runnable = par.dynamics.WallLoss(wall_loss_strategy=spherical_strategy)
cond_wall = condensation | wall_loss_runnable

short_time = np.linspace(0.0, 600.0, 21)  # 10 min, 30 s spacing
cond_series = np.zeros_like(short_time)
aerosol_cond = build_aerosol()
cond_series[0] = aerosol_cond.particles.get_total_concentration()

for idx in range(1, short_time.size):
    aerosol_cond = cond_wall.execute(
        aerosol_cond, time_step=short_time[1] - short_time[0]
    )
    cond_series[idx] = aerosol_cond.particles.get_total_concentration()

_ = plot_decay(
    short_time / 60.0,
    (cond_series, "Condensation | Wall loss (10 min)", "m-"),
)

condensation_strategy = par.dynamics.CondensationIsothermalBuilder() condensation_strategy.set_molar_mass(0.12, "kg/mol") condensation_strategy.set_diffusion_coefficient(1e-5, "m^2/s") condensation_strategy.set_accommodation_coefficient(0.9) condensation_strategy.set_update_gases(False) condensation = par.dynamics.MassCondensation( condensation_strategy=condensation_strategy.build() ) wall_loss_runnable = par.dynamics.WallLoss(wall_loss_strategy=spherical_strategy) cond_wall = condensation | wall_loss_runnable short_time = np.linspace(0.0, 600.0, 21) # 10 min, 30 s spacing cond_series = np.zeros_like(short_time) aerosol_cond = build_aerosol() cond_series[0] = aerosol_cond.particles.get_total_concentration() for idx in range(1, short_time.size): aerosol_cond = cond_wall.execute( aerosol_cond, time_step=short_time[1] - short_time[0] ) cond_series[idx] = aerosol_cond.particles.get_total_concentration() _ = plot_decay( short_time / 60.0, (cond_series, "Condensation | Wall loss (10 min)", "m-"), )

Assertions and sanity checks¶

Quick guards to keep the notebook honest during headless execution.

In [ ]:

# Geometry parameter validation
try:
    par.dynamics.SphericalWallLossStrategy(
        wall_eddy_diffusivity=1e-3, chamber_radius=-1.0
    )
    raise AssertionError("Expected ValueError for negative radius")
except ValueError:
    pass

try:
    par.dynamics.RectangularWallLossStrategy(
        wall_eddy_diffusivity=1e-3, chamber_dimensions=(0.0, 1.0, 1.0)
    )
    raise AssertionError("Expected ValueError for non-positive dimension")
except ValueError:
    pass

# Concentration non-negativity after simulations
assert np.all(spherical_series >= 0.0)
assert np.all(rect_series >= 0.0)
assert np.all(wall_only_series >= 0.0)
assert np.all(coag_wall_series >= 0.0)
assert np.all(cond_series >= 0.0)

print("Assertions passed: parameter guards and non-negativity checks.")

# Geometry parameter validation try: par.dynamics.SphericalWallLossStrategy( wall_eddy_diffusivity=1e-3, chamber_radius=-1.0 ) raise AssertionError("Expected ValueError for negative radius") except ValueError: pass try: par.dynamics.RectangularWallLossStrategy( wall_eddy_diffusivity=1e-3, chamber_dimensions=(0.0, 1.0, 1.0) ) raise AssertionError("Expected ValueError for non-positive dimension") except ValueError: pass # Concentration non-negativity after simulations assert np.all(spherical_series >= 0.0) assert np.all(rect_series >= 0.0) assert np.all(wall_only_series >= 0.0) assert np.all(coag_wall_series >= 0.0) assert np.all(cond_series >= 0.0) print("Assertions passed: parameter guards and non-negativity checks.")

Summary¶

• Built reusable helpers to construct aerosols and run wall loss quickly.
• Compared spherical vs rectangular chambers over a shared time grid.
• Demonstrated chaining with coagulation and a concise condensation variant.
• Added inline assertions for invalid geometry and non-negative concentrations.