Equilibria Partitioning Example¶

Demonstrates using LiquidVaporPartitioningStrategy for computing gas-particle equilibrium concentrations.

What This Example Shows¶

• Creating a liquid-vapor partitioning strategy
• Solving for equilibrium with organic species
• Interpreting the equilibrium results
• Observing the effect of relative humidity on partitioning

In [ ]:

import numpy as np
import particula as par

import numpy as np import particula as par

1. Define Organic Species Properties¶

Set up three organic species with different volatilities (C* values). Lower C* means less volatile and more tendency to partition to the particle phase.

In [ ]:

# Three species with different volatilities (C* values)
c_star_j_dry = np.array([1e-6, 1e-4, 1e-2])  # saturation concentrations
concentration_organic = np.array([1.0, 5.0, 10.0])  # ug/m^3
molar_mass = np.array([200.0, 200.0, 200.0])  # g/mol
o2c_ratio = np.array([0.2, 0.3, 0.5])  # O:C ratios
density = np.array([1200.0, 1200.0, 1200.0])  # kg/m^3

print("=== Organic Species Properties ===")
print(f"C* (dry): {c_star_j_dry}")
print(f"Total concentration: {concentration_organic} ug/m^3")
print(f"O:C ratios: {o2c_ratio}")

# Three species with different volatilities (C* values) c_star_j_dry = np.array([1e-6, 1e-4, 1e-2]) # saturation concentrations concentration_organic = np.array([1.0, 5.0, 10.0]) # ug/m^3 molar_mass = np.array([200.0, 200.0, 200.0]) # g/mol o2c_ratio = np.array([0.2, 0.3, 0.5]) # O:C ratios density = np.array([1200.0, 1200.0, 1200.0]) # kg/m^3 print("=== Organic Species Properties ===") print(f"C* (dry): {c_star_j_dry}") print(f"Total concentration: {concentration_organic} ug/m^3") print(f"O:C ratios: {o2c_ratio}")

2. Create Partitioning Strategy at 75% RH¶

Water activity corresponds to relative humidity for aerosol systems.

In [ ]:

strategy = par.equilibria.LiquidVaporPartitioningStrategy(
    water_activity=0.75,  # 75% relative humidity
)

print(f"Strategy: {type(strategy).__name__}")
print(f"Water activity (RH): {strategy.water_activity * 100:.0f}%")

strategy = par.equilibria.LiquidVaporPartitioningStrategy( water_activity=0.75, # 75% relative humidity ) print(f"Strategy: {type(strategy).__name__}") print(f"Water activity (RH): {strategy.water_activity * 100:.0f}%")

3. Solve for Equilibrium¶

In [ ]:

result = strategy.solve(
    c_star_j_dry=c_star_j_dry,
    concentration_organic_matter=concentration_organic,
    molar_mass=molar_mass,
    oxygen2carbon=o2c_ratio,
    density=density,
)

print("Equilibrium solved successfully!")

result = strategy.solve( c_star_j_dry=c_star_j_dry, concentration_organic_matter=concentration_organic, molar_mass=molar_mass, oxygen2carbon=o2c_ratio, density=density, ) print("Equilibrium solved successfully!")

4. Print Equilibrium Results¶

The result contains partition coefficients (fraction in condensed phase), phase concentrations, and water content.

In [ ]:

print("=== Liquid-Vapor Partitioning ===")
print(f"Water activity (RH): {strategy.water_activity * 100:.0f}%\n")

print("Input organic species:")
print(f"  C* (dry): {c_star_j_dry}")
print(f"  Total concentration: {concentration_organic} ug/m^3")
print(f"  O:C ratios: {o2c_ratio}")

print("\n=== Equilibrium Results ===")
print(f"Partition coefficients: {result.partition_coefficients}")
print("  (fraction in condensed phase)")

print("\nAlpha phase (water-rich):")
print(f"  Species concentrations: {result.alpha_phase.species_concentrations}")
print(
    "  Water concentration: "
    f"{result.alpha_phase.water_concentration:.2f} ug/m^3"
)
print(
    "  Total concentration: "
    f"{result.alpha_phase.total_concentration:.2f} ug/m^3"
)

if result.beta_phase is not None:
    print("\nBeta phase (organic-rich):")
    print(
        f"  Species concentrations: {result.beta_phase.species_concentrations}"
    )
    print(
        "  Water concentration: "
        f"{result.beta_phase.water_concentration:.2f} ug/m^3"
    )

print(
    f"\nWater content: alpha={result.water_content[0]:.2f}, "
    f"beta={result.water_content[1]:.2f} ug/m^3"
)
print(f"Optimization error: {result.error:.2e}")

print("=== Liquid-Vapor Partitioning ===") print(f"Water activity (RH): {strategy.water_activity * 100:.0f}%\n") print("Input organic species:") print(f" C* (dry): {c_star_j_dry}") print(f" Total concentration: {concentration_organic} ug/m^3") print(f" O:C ratios: {o2c_ratio}") print("\n=== Equilibrium Results ===") print(f"Partition coefficients: {result.partition_coefficients}") print(" (fraction in condensed phase)") print("\nAlpha phase (water-rich):") print(f" Species concentrations: {result.alpha_phase.species_concentrations}") print( " Water concentration: " f"{result.alpha_phase.water_concentration:.2f} ug/m^3" ) print( " Total concentration: " f"{result.alpha_phase.total_concentration:.2f} ug/m^3" ) if result.beta_phase is not None: print("\nBeta phase (organic-rich):") print( f" Species concentrations: {result.beta_phase.species_concentrations}" ) print( " Water concentration: " f"{result.beta_phase.water_concentration:.2f} ug/m^3" ) print( f"\nWater content: alpha={result.water_content[0]:.2f}, " f"beta={result.water_content[1]:.2f} ug/m^3" ) print(f"Optimization error: {result.error:.2e}")

5. Effect of RH on Partitioning¶

As relative humidity increases, more water is absorbed and partitioning changes.

In [ ]:

print("=== Effect of RH on Partitioning ===\n")
rh_values = [0.3, 0.5, 0.75, 0.9]
for rh in rh_values:
    strat = par.equilibria.LiquidVaporPartitioningStrategy(
        water_activity=rh,
    )
    res = strat.solve(
        c_star_j_dry=c_star_j_dry,
        concentration_organic_matter=concentration_organic,
        molar_mass=molar_mass,
        oxygen2carbon=o2c_ratio,
        density=density,
    )
    mean_partition = np.mean(res.partition_coefficients)
    print(
        f"RH={rh * 100:.0f}%: mean partition coeff = {mean_partition:.4f}, "
        f"water = {res.alpha_phase.water_concentration:.2f} ug/m^3"
    )

print("=== Effect of RH on Partitioning ===\n") rh_values = [0.3, 0.5, 0.75, 0.9] for rh in rh_values: strat = par.equilibria.LiquidVaporPartitioningStrategy( water_activity=rh, ) res = strat.solve( c_star_j_dry=c_star_j_dry, concentration_organic_matter=concentration_organic, molar_mass=molar_mass, oxygen2carbon=o2c_ratio, density=density, ) mean_partition = np.mean(res.partition_coefficients) print( f"RH={rh * 100:.0f}%: mean partition coeff = {mean_partition:.4f}, " f"water = {res.alpha_phase.water_concentration:.2f} ug/m^3" )