Spherical Wall Loss Strategy Tutorial¶

This notebook demonstrates how to use the strategy-based wall loss API in particula, focusing on WallLossStrategy and SphericalWallLossStrategy.

You will:

• Build a simple radius-based particle distribution using PresetParticleRadiusBuilder.
• Configure SphericalWallLossStrategy for a spherical chamber.
• Integrate wall loss over time and visualize concentration decay.
• See how wall loss strategies can plug into other dynamics components.

For a full chamber forward simulation including dilution and coagulation, see the separate Chamber_Forward_Simulation.ipynb example in this folder.

Prerequisites¶

Before running this notebook, ensure you have:

• Python 3.9 or later
• particula installed (via pip or conda)

In Google Colab you can install particula with:

pip install particula[extra] --quiet

In [29]:

# If running in Colab, uncomment the next line to install particula:
# !pip install particula[extra] --quiet

import numpy as np
from matplotlib import pyplot as plt

import particula as par

# If running in Colab, uncomment the next line to install particula: # !pip install particula[extra] --quiet import numpy as np from matplotlib import pyplot as plt import particula as par

1. Build a lognormal particle distribution¶

We use PresetParticleRadiusBuilder to create a ParticleRepresentation with radius bins, number concentration, and default physical properties.

In [30]:

# Build a simple radius-based particle distribution (discrete bins)
particle = par.particles.PresetParticleRadiusBuilder().build()

print('Radius shape:', particle.get_radius().shape)
print('Concentration shape:', particle.get_concentration().shape)
print(
    'Total concentration (initial):',
    f'{particle.get_total_concentration():.3e} 1/m^3',
)

# Build a simple radius-based particle distribution (discrete bins) particle = par.particles.PresetParticleRadiusBuilder().build() print('Radius shape:', particle.get_radius().shape) print('Concentration shape:', particle.get_concentration().shape) print( 'Total concentration (initial):', f'{particle.get_total_concentration():.3e} 1/m^3', )

Radius shape: (250,)
Concentration shape: (250,)
Total concentration (initial): 1.100e+10 1/m^3

2. Configure the spherical wall loss strategy¶

We now create a SphericalWallLossStrategy instance. This strategy computes a size-dependent wall loss coefficient and applies a first-order loss to the particle concentration.

In [31]:

# Configure spherical wall loss strategy
wall_loss = par.dynamics.SphericalWallLossStrategy(
    wall_eddy_diffusivity=1e-3,  # m^2/s
    chamber_radius=0.5,          # m
    distribution_type='discrete',
)

T = 298.15  # K
P = 101325.0  # Pa

rate = wall_loss.rate(
    particle=particle,
    temperature=T,
    pressure=P,
)

print('Rate array shape:', rate.shape)
print('Example rate[0]:', float(rate.ravel()[0]))

# Configure spherical wall loss strategy wall_loss = par.dynamics.SphericalWallLossStrategy( wall_eddy_diffusivity=1e-3, # m^2/s chamber_radius=0.5, # m distribution_type='discrete', ) T = 298.15 # K P = 101325.0 # Pa rate = wall_loss.rate( particle=particle, temperature=T, pressure=P, ) print('Rate array shape:', rate.shape) print('Example rate[0]:', float(rate.ravel()[0]))

Rate array shape: (250,)
Example rate[0]: -2.2766844125094575e-88

3. Integrate wall loss over time¶

Next, we integrate wall loss for one hour using a fixed time step and track the total number concentration as a function of time.

In [ ]:

# Time integration setup
final_time = 6000.0  # s (= 100 minutes)
dt = 1.0           # s
n_steps = int(final_time / dt)

times = np.arange(n_steps + 1) * dt
total_concentration = np.zeros_like(times, dtype=float)

# Record initial concentration
total_concentration[0] = particle.get_total_concentration()

# Time loop: apply only wall loss
for i in range(1, n_steps + 1):
    particle = wall_loss.step(
        particle=particle,
        temperature=T,
        pressure=P,
        time_step=dt,
    )
    total_concentration[i] = particle.get_total_concentration()

print(
    'Total concentration (final):',
    f'{total_concentration[-1]:.3e} 1/m^3',
)

# Time integration setup final_time = 6000.0 # s (= 100 minutes) dt = 1.0 # s n_steps = int(final_time / dt) times = np.arange(n_steps + 1) * dt total_concentration = np.zeros_like(times, dtype=float) # Record initial concentration total_concentration[0] = particle.get_total_concentration() # Time loop: apply only wall loss for i in range(1, n_steps + 1): particle = wall_loss.step( particle=particle, temperature=T, pressure=P, time_step=dt, ) total_concentration[i] = particle.get_total_concentration() print( 'Total concentration (final):', f'{total_concentration[-1]:.3e} 1/m^3', )

Total concentration (final): 1.009e+10 1/m^3

Plot normalized concentration decay¶

We now plot the normalized total number concentration to visualize how quickly particles are removed by wall loss.

In [33]:

fig, ax = plt.subplots(figsize=(6, 4))

ax.plot(times / 60.0, total_concentration / total_concentration[0])

ax.set_xlabel('Time (min)')
ax.set_ylabel('Normalized total concentration')
ax.set_title('Spherical wall loss: concentration decay')
ax.grid(True)

plt.tight_layout()
plt.show()

fig, ax = plt.subplots(figsize=(6, 4)) ax.plot(times / 60.0, total_concentration / total_concentration[0]) ax.set_xlabel('Time (min)') ax.set_ylabel('Normalized total concentration') ax.set_title('Spherical wall loss: concentration decay') ax.grid(True) plt.tight_layout() plt.show()

Compare initial and final size distributions¶

Because wall loss is size-dependent, different radii experience different loss rates. Here we compare the initial and final size distributions.

In [34]:

# Rebuild the initial distribution for comparison
initial_particle = par.particles.PresetParticleRadiusBuilder().build()

fig, ax = plt.subplots(figsize=(6, 4))

ax.plot(
    initial_particle.get_radius(),
    initial_particle.get_concentration(),
    label='Initial',
)
ax.plot(
    particle.get_radius(),
    particle.get_concentration(),
    label='After wall loss',
)

ax.set_xscale('log')
ax.set_xlabel('Particle radius (m)')
ax.set_ylabel('Number concentration (1/m^3)')
ax.set_title('Size distribution before/after wall loss')
ax.grid(True)
ax.legend()

plt.tight_layout()
plt.show()

# Rebuild the initial distribution for comparison initial_particle = par.particles.PresetParticleRadiusBuilder().build() fig, ax = plt.subplots(figsize=(6, 4)) ax.plot( initial_particle.get_radius(), initial_particle.get_concentration(), label='Initial', ) ax.plot( particle.get_radius(), particle.get_concentration(), label='After wall loss', ) ax.set_xscale('log') ax.set_xlabel('Particle radius (m)') ax.set_ylabel('Number concentration (1/m^3)') ax.set_title('Size distribution before/after wall loss') ax.grid(True) ax.legend() plt.tight_layout() plt.show()

4. Composing wall loss with other dynamics¶

Wall loss strategies follow the same rate / step pattern as other dynamics components (for example, condensation strategies). This makes it easy to combine wall loss with other processes in a single time loop.

The sketch below shows how you might apply wall loss repeatedly. For a complete example that combines condensation with wall loss, see the condensation tutorials in docs/Examples/Dynamics/.

In [35]:

example

# Pseudo-code: combine condensation and wall loss
particle = par.particles.PresetParticleRadiusBuilder().build()

wall_loss = par.dynamics.SphericalWallLossStrategy(
    wall_eddy_diffusivity=1e-3,
    chamber_radius=0.5,
    distribution_type='discrete',
)

# Note: CondensationIsothermal requires a GasSpecies object. For a complete
# example that includes gas-particle condensation, see the condensation
# tutorials in docs/Examples/Dynamics/.

for _ in range(10):
    # Apply wall loss to the particle distribution
    particle = wall_loss.step(
        particle=particle,
        temperature=T,
        pressure=P,
        time_step=dt,
    )

# Pseudo-code: combine condensation and wall loss particle = par.particles.PresetParticleRadiusBuilder().build() wall_loss = par.dynamics.SphericalWallLossStrategy( wall_eddy_diffusivity=1e-3, chamber_radius=0.5, distribution_type='discrete', ) # Note: CondensationIsothermal requires a GasSpecies object. For a complete # example that includes gas-particle condensation, see the condensation # tutorials in docs/Examples/Dynamics/. for _ in range(10): # Apply wall loss to the particle distribution particle = wall_loss.step( particle=particle, temperature=T, pressure=P, time_step=dt, )

Summary¶

In this notebook you:

• Built a lognormal radius-based particle distribution using PresetParticleRadiusBuilder.
• Configured SphericalWallLossStrategy and computed wall loss rates.
• Integrated wall loss over time and visualized concentration decay.
• Saw how wall loss strategies can be composed with other dynamics processes in a shared simulation loop.

For more background on dynamics and wall loss, see the main documentation index (Dynamics and wall loss section) and the chamber wall loss examples in docs/Examples/Chamber_Wall_Loss.