Kappa Parameter Activity Example¶

Demonstrates using ActivityKappaParameter for computing water activity in hygroscopic aerosol particles using kappa-Kohler theory.

What is the Kappa Parameter?¶

The kappa parameter provides a single-parameter representation of hygroscopicity, relating dry particle volume to water activity. Higher kappa values indicate more hygroscopic species that absorb more water.

What This Example Shows¶

• Creating a kappa parameter activity strategy
• Computing water activity at different water contents
• Understanding kappa values for common aerosol species

In [ ]:

import numpy as np
import particula as par

import numpy as np import particula as par

1. Define Species Properties¶

Set up properties for water and ammonium sulfate. Ammonium sulfate has a kappa value of ~0.61, making it highly hygroscopic.

In [ ]:

# Define species properties for water and ammonium sulfate
# kappa=0 for water (not hygroscopic itself)
# kappa=0.61 for ammonium sulfate (highly hygroscopic)
kappa_values = np.array([0.0, 0.61])
densities = np.array([1000.0, 1770.0])  # kg/m^3
molar_masses = np.array([18.015e-3, 132.14e-3])  # kg/mol

print("=== Species Properties ===")
print("Species: water, ammonium sulfate")
print(f"Kappa values: {kappa_values}")
print(f"Densities: {densities} kg/m^3")
print(f"Molar masses: {molar_masses * 1e3} g/mol")

# Define species properties for water and ammonium sulfate # kappa=0 for water (not hygroscopic itself) # kappa=0.61 for ammonium sulfate (highly hygroscopic) kappa_values = np.array([0.0, 0.61]) densities = np.array([1000.0, 1770.0]) # kg/m^3 molar_masses = np.array([18.015e-3, 132.14e-3]) # kg/mol print("=== Species Properties ===") print("Species: water, ammonium sulfate") print(f"Kappa values: {kappa_values}") print(f"Densities: {densities} kg/m^3") print(f"Molar masses: {molar_masses * 1e3} g/mol")

2. Create Kappa Parameter Activity Strategy¶

In [ ]:

strategy = par.particles.ActivityKappaParameter(
    kappa=kappa_values,
    density=densities,
    molar_mass=molar_masses,
    water_index=0,
)

print(f"Strategy: {type(strategy).__name__}")

strategy = par.particles.ActivityKappaParameter( kappa=kappa_values, density=densities, molar_mass=molar_masses, water_index=0, ) print(f"Strategy: {type(strategy).__name__}")

3. Compute Activity at Different Water Contents¶

Vary the water mass fraction and observe how water activity changes.

In [ ]:

print("=== Kappa Parameter Activity ===")
print(f"Kappa values: {kappa_values}")
print("Species: water (kappa=0), ammonium sulfate (kappa=0.61)\n")

water_fractions = [0.3, 0.5, 0.7, 0.9]
for water_frac in water_fractions:
    # Mass concentrations (water fraction, salt fraction)
    mass = np.array([water_frac, 1.0 - water_frac]) * 1e-9  # kg/m^3
    activity = strategy.activity(mass_concentration=mass)
    print(f"Water mass fraction: {water_frac:.1f}")
    print(f"  Water activity: {activity[0]:.4f}")
    print(f"  Salt activity:  {activity[1]:.4f}\n")

print("=== Kappa Parameter Activity ===") print(f"Kappa values: {kappa_values}") print("Species: water (kappa=0), ammonium sulfate (kappa=0.61)\n") water_fractions = [0.3, 0.5, 0.7, 0.9] for water_frac in water_fractions: # Mass concentrations (water fraction, salt fraction) mass = np.array([water_frac, 1.0 - water_frac]) * 1e-9 # kg/m^3 activity = strategy.activity(mass_concentration=mass) print(f"Water mass fraction: {water_frac:.1f}") print(f" Water activity: {activity[0]:.4f}") print(f" Salt activity: {activity[1]:.4f}\n")

4. Effect of Kappa on Water Activity¶

Test how different kappa values affect water activity at a fixed composition (50% water by mass).

In [ ]:

print("=== Effect of Kappa on Water Activity ===")
print("(at 50% water by mass)\n")

# Test different kappa values
kappa_test_values = [0.0, 0.1, 0.3, 0.61, 1.0]
for kappa in kappa_test_values:
    test_strategy = par.particles.ActivityKappaParameter(
        kappa=np.array([0.0, kappa]),
        density=np.array([1000.0, 1500.0]),
        molar_mass=np.array([18.015e-3, 100.0e-3]),
        water_index=0,
    )
    mass = np.array([0.5, 0.5]) * 1e-9
    activity = test_strategy.activity(mass_concentration=mass)
    print(f"kappa={kappa:.2f}: water activity = {activity[0]:.4f}")

print("=== Effect of Kappa on Water Activity ===") print("(at 50% water by mass)\n") # Test different kappa values kappa_test_values = [0.0, 0.1, 0.3, 0.61, 1.0] for kappa in kappa_test_values: test_strategy = par.particles.ActivityKappaParameter( kappa=np.array([0.0, kappa]), density=np.array([1000.0, 1500.0]), molar_mass=np.array([18.015e-3, 100.0e-3]), water_index=0, ) mass = np.array([0.5, 0.5]) * 1e-9 activity = test_strategy.activity(mass_concentration=mass) print(f"kappa={kappa:.2f}: water activity = {activity[0]:.4f}")