Coagulation Basic 2: PDF (Builder + Coagulation)¶

This notebook shows Brownian coagulation for a continuous/PDF distribution using the public builder pattern:

1. Build a Brownian coagulation strategy with distribution_type="continuous_pdf".
2. Wrap it in par.dynamics.Coagulation.
3. Run a short, lightweight step on a PDF aerosol and visualize change.

Grid sizes and time horizon are kept small for quick execution (<120 s).

In [ ]:

# In Colab uncomment the following command to install particula:
#!pip install particula[extra] --quiet
import matplotlib.pyplot as plt
import numpy as np
import particula as par

# In Colab uncomment the following command to install particula: #!pip install particula[extra] --quiet import matplotlib.pyplot as plt import numpy as np import particula as par

Build a PDF aerosol¶

We build a lognormal PDF on a modest grid. PDF units are m⁻³·m⁻¹ (number per volume per size).

In [ ]:

# Radius bins (log-spaced)
radius_bins = np.logspace(-8, -6, 140)  # m

# Lognormal PDF (concentration per unit size)
concentration_pdf = par.particles.get_lognormal_pdf_distribution(
    x_values=radius_bins,
    mode=np.array([120e-9]),
    geometric_standard_deviation=np.array([1.5]),
    number_of_particles=np.array([8e8]),  # m^-3 total when integrated
)

# Atmosphere (ambient)
atmosphere = (
    par.gas.AtmosphereBuilder()
    .set_temperature(25, "degC")
    .set_pressure(1, "atm")
    .build()
)

# PDF particle representation
particles_pdf = (
    par.particles.PresetParticleRadiusBuilder()
    .set_distribution_type("pdf")
    .set_radius_bins(radius_bins, radius_bins_units="m")
    .set_concentration(concentration_pdf, concentration_units="m^-3")
    .set_density(np.array([1_000.0]), density_units="kg/m^3")
    .set_charge(np.zeros_like(radius_bins))
    .build()
)

aerosol_pdf = par.Aerosol(atmosphere=atmosphere, particles=particles_pdf)

# Radius bins (log-spaced) radius_bins = np.logspace(-8, -6, 140) # m # Lognormal PDF (concentration per unit size) concentration_pdf = par.particles.get_lognormal_pdf_distribution( x_values=radius_bins, mode=np.array([120e-9]), geometric_standard_deviation=np.array([1.5]), number_of_particles=np.array([8e8]), # m^-3 total when integrated ) # Atmosphere (ambient) atmosphere = ( par.gas.AtmosphereBuilder() .set_temperature(25, "degC") .set_pressure(1, "atm") .build() ) # PDF particle representation particles_pdf = ( par.particles.PresetParticleRadiusBuilder() .set_distribution_type("pdf") .set_radius_bins(radius_bins, radius_bins_units="m") .set_concentration(concentration_pdf, concentration_units="m^-3") .set_density(np.array([1_000.0]), density_units="kg/m^3") .set_charge(np.zeros_like(radius_bins)) .build() ) aerosol_pdf = par.Aerosol(atmosphere=atmosphere, particles=particles_pdf)

Configure coagulation (continuous PDF)¶

In [ ]:

coagulation_strategy = (
    par.dynamics.BrownianCoagulationBuilder()
    .set_distribution_type("continuous_pdf")
    .build()
)
coagulation_process = par.dynamics.Coagulation(
    coagulation_strategy=coagulation_strategy
)

print(coagulation_process)

coagulation_strategy = ( par.dynamics.BrownianCoagulationBuilder() .set_distribution_type("continuous_pdf") .build() ) coagulation_process = par.dynamics.Coagulation( coagulation_strategy=coagulation_strategy ) print(coagulation_process)

Execute a short coagulation step¶

In [ ]:

time_step = 200  # seconds
sub_steps = 10

pdf_before = aerosol_pdf.particles.get_concentration()
radii = aerosol_pdf.particles.get_radius()

aerosol_pdf_after = coagulation_process.execute(
    aerosol_pdf, time_step=time_step, sub_steps=sub_steps
)
pdf_after = aerosol_pdf_after.particles.get_concentration()

time_step = 200 # seconds sub_steps = 10 pdf_before = aerosol_pdf.particles.get_concentration() radii = aerosol_pdf.particles.get_radius() aerosol_pdf_after = coagulation_process.execute( aerosol_pdf, time_step=time_step, sub_steps=sub_steps ) pdf_after = aerosol_pdf_after.particles.get_concentration()

Plot: PDF concentration before/after¶

In [ ]:

fig, ax = plt.subplots(figsize=(8, 5))
ax.plot(radii, pdf_before, label="Before", color="tab:blue")
ax.plot(radii, pdf_after, label="After", color="tab:orange")
ax.set_xscale("log")
ax.set_xlabel("Particle radius (m)")
ax.set_ylabel(r"PDF concentration ($m^{-4}$)")
ax.set_title("PDF coagulation (Brownian, continuous)")
ax.legend()
ax.grid(alpha=0.3)
plt.show()

fig, ax = plt.subplots(figsize=(8, 5)) ax.plot(radii, pdf_before, label="Before", color="tab:blue") ax.plot(radii, pdf_after, label="After", color="tab:orange") ax.set_xscale("log") ax.set_xlabel("Particle radius (m)") ax.set_ylabel(r"PDF concentration ($m^{-4}$)") ax.set_title("PDF coagulation (Brownian, continuous)") ax.legend() ax.grid(alpha=0.3) plt.show()

Summary¶

• Strategy: BrownianCoagulationBuilder().set_distribution_type( "continuous_pdf").build()
• Runnable: par.dynamics.Coagulation
• Representation: PDF (continuous number concentration per size)
• Runtime guardrails: small grid, short horizon