Condensation Tutorial: Radius Bin¶

Work in progress, probably split into multiple notebooks, need to find a model system to test this on

Condensation, is the first process where this framework we have been building up is applied. Here we need to account for the gas phase, and the particle phase. Then ensure that the partial pressures of species at the surface of the particle are equal to the partial pressure in the gas.

Core Concepts:

• Runnable: An abstract base class defining the interface for aerosol transformation processes.
  • Here and aerosol object is passed to the process, and the process is expected to modify the aerosol object in place, returning the modified object.
• MassCondensation: A concrete class implementing the RunnableProcess interface for the condensation process. Is an implementation of a Runnable process that adds mass to the aerosol object based on the partial pressures of the gas phase and the particle phase. Then removes the mass from the gas phase.

In [1]:

import numpy as np
import matplotlib.pyplot as plt

# particula imports
from particula import particles
from particula.gas import AtmosphereBuilder, VaporPressureFactory, GasSpeciesBuilder
from particula.aerosol import Aerosol
from particula.dynamics import MassCondensation
from particula.dynamics.condensation import CondensationIsothermal

import numpy as np import matplotlib.pyplot as plt # particula imports from particula import particles from particula.gas import AtmosphereBuilder, VaporPressureFactory, GasSpeciesBuilder from particula.aerosol import Aerosol from particula.dynamics import MassCondensation from particula.dynamics.condensation import CondensationIsothermal

Setup Aerosol¶

First we will repeat the aerosol object that we have been using in the previous notebooks. This object will be passed to the Runnable processes MassCondensation, and modified in place.

In [2]:

# Glycerol gas
molar_mass_glycerol = 92.09382e-3  # kg/mol
parameters_clausius = {
    "latent_heat": 71.5 * molar_mass_glycerol,
    "latent_heat_units": "kJ/kg",
    "temperature_initial": 125.5,
    "temperature_initial_units": "degC",
    "pressure_initial": 1,
    "pressure_initial_units": "mmHg",
}
vapor_pressure_strategy = VaporPressureFactory().get_strategy(
    "clausius_clapeyron", parameters_clausius
)

sat_concentration = vapor_pressure_strategy.saturation_concentration(
    molar_mass_glycerol, 298.15
)
print(f"Saturation concentration: {sat_concentration:.2e} kg/m^3")

sat_factor = 0.01  # 50% of saturation concentration
glycerol_gas = (
    GasSpeciesBuilder()
    .set_molar_mass(molar_mass_glycerol, "kg/mol")
    .set_vapor_pressure_strategy(vapor_pressure_strategy)
    .set_concentration(sat_concentration * sat_factor, "kg/m^3")
    .set_name("Glycerol")
    .set_condensable(True)
    .build()
)

atmosphere = (
    AtmosphereBuilder()
    .add_species(glycerol_gas)
    .set_temperature(25, temperature_units="degC")
    .set_pressure(1, pressure_units="atm")
    .build()
)

# Glycerol particle distribution
bins = np.logspace(-8, -5, 500)
lognormal_rep = (
    particles.PresetParticleRadiusBuilder()
    .set_mode(np.array([100]), "nm")
    .set_geometric_standard_deviation(np.array([1.3]))
    .set_number_concentration(np.array([1e4]), "1/cm^3")
    .set_density(1.26, "g/cm^3")
    .set_distribution_type("pmf")
    .set_radius_bins(bins, "m")
    .build()
)

aerosol = Aerosol(atmosphere=atmosphere, particles=lognormal_rep)

print(aerosol)

# Glycerol gas molar_mass_glycerol = 92.09382e-3 # kg/mol parameters_clausius = { "latent_heat": 71.5 * molar_mass_glycerol, "latent_heat_units": "kJ/kg", "temperature_initial": 125.5, "temperature_initial_units": "degC", "pressure_initial": 1, "pressure_initial_units": "mmHg", } vapor_pressure_strategy = VaporPressureFactory().get_strategy( "clausius_clapeyron", parameters_clausius ) sat_concentration = vapor_pressure_strategy.saturation_concentration( molar_mass_glycerol, 298.15 ) print(f"Saturation concentration: {sat_concentration:.2e} kg/m^3") sat_factor = 0.01 # 50% of saturation concentration glycerol_gas = ( GasSpeciesBuilder() .set_molar_mass(molar_mass_glycerol, "kg/mol") .set_vapor_pressure_strategy(vapor_pressure_strategy) .set_concentration(sat_concentration * sat_factor, "kg/m^3") .set_name("Glycerol") .set_condensable(True) .build() ) atmosphere = ( AtmosphereBuilder() .add_species(glycerol_gas) .set_temperature(25, temperature_units="degC") .set_pressure(1, pressure_units="atm") .build() ) # Glycerol particle distribution bins = np.logspace(-8, -5, 500) lognormal_rep = ( particles.PresetParticleRadiusBuilder() .set_mode(np.array([100]), "nm") .set_geometric_standard_deviation(np.array([1.3])) .set_number_concentration(np.array([1e4]), "1/cm^3") .set_density(1.26, "g/cm^3") .set_distribution_type("pmf") .set_radius_bins(bins, "m") .build() ) aerosol = Aerosol(atmosphere=atmosphere, particles=lognormal_rep) print(aerosol)

Saturation concentration: 2.54e-03 kg/m^3
Gas mixture at 298.15 K and 101325.0 Pa consisting of ['Glycerol']
[0]: Particle Representation:
	Strategy: RadiiBasedMovingBin
	Activity: ActivityIdealMass
	Surface: SurfaceStrategyVolume
	Mass Concentration: 7.194e-08 [kg/m^3]
	Number Concentration: 1.000e+10 [#/m^3]

Condensation Process (Isothermal)¶

In code this process is implemented as a Runnable process. This means that the process is expected to modify the aerosol object in place, returning the modified aerosol object. This is defined in Particle_processes.py as the MassCondensation class.

The MassCondensation class takes a CondensationStrategy object as an input. This object defines and evaluates the $dm_{i}/dt$ equation for the condensation process. More strategies can be added into the condensation.py file.

For now, let's just run it for a few time steps and see what happens.

Note: We have a moving bin particle representation, so we would expect all the bins to move.

In [3]:

# define the condensation process
condensation_isothermal = CondensationIsothermal(
    molar_mass=molar_mass_glycerol,
    diffusion_coefficient=2e-5,
    accommodation_coefficient=0.1,  #makes things go slower/faster
)
condensation_process = MassCondensation(condensation_strategy=condensation_isothermal)

# define the time array in seconds
time_step = 0.5
time_array = np.arange(0, 10, time_step)
total_mass = np.zeros_like(time_array)

# output arrays
aerosol_sim = []

rate = condensation_process.rate(aerosol)

# print(f"Inital rate: {rate[:5]}...")
# print(f"Initial rate shape: {rate.shape}")

fig, ax = plt.subplots(figsize=(8, 6))
ax.semilogx(aerosol.particles[0].get_radius()*1e9, aerosol.particles[0].concentration, label="Initial")
# singe step
aerosol = condensation_process.execute(aerosol, time_step)
ax.semilogx(aerosol.particles[0].get_radius()*1e9, aerosol.particles[0].concentration, label="After 1 step")
# second step
aerosol = condensation_process.execute(aerosol, time_step)
ax.semilogx(aerosol.particles[0].get_radius()*1e9, aerosol.particles[0].concentration, label="After 2 steps")
# 5th step
aerosol = condensation_process.execute(aerosol, time_step)
aerosol = condensation_process.execute(aerosol, time_step)
aerosol = condensation_process.execute(aerosol, time_step)
ax.semilogx(aerosol.particles[0].get_radius()*1e9, aerosol.particles[0].concentration, label="After 5 steps")
plt.legend()
ax.set_xlabel("Radius (nm)")
ax.set_ylabel("Concentration (1/m^3)")
plt.show()

# define the condensation process condensation_isothermal = CondensationIsothermal( molar_mass=molar_mass_glycerol, diffusion_coefficient=2e-5, accommodation_coefficient=0.1, #makes things go slower/faster ) condensation_process = MassCondensation(condensation_strategy=condensation_isothermal) # define the time array in seconds time_step = 0.5 time_array = np.arange(0, 10, time_step) total_mass = np.zeros_like(time_array) # output arrays aerosol_sim = [] rate = condensation_process.rate(aerosol) # print(f"Inital rate: {rate[:5]}...") # print(f"Initial rate shape: {rate.shape}") fig, ax = plt.subplots(figsize=(8, 6)) ax.semilogx(aerosol.particles[0].get_radius()*1e9, aerosol.particles[0].concentration, label="Initial") # singe step aerosol = condensation_process.execute(aerosol, time_step) ax.semilogx(aerosol.particles[0].get_radius()*1e9, aerosol.particles[0].concentration, label="After 1 step") # second step aerosol = condensation_process.execute(aerosol, time_step) ax.semilogx(aerosol.particles[0].get_radius()*1e9, aerosol.particles[0].concentration, label="After 2 steps") # 5th step aerosol = condensation_process.execute(aerosol, time_step) aerosol = condensation_process.execute(aerosol, time_step) aerosol = condensation_process.execute(aerosol, time_step) ax.semilogx(aerosol.particles[0].get_radius()*1e9, aerosol.particles[0].concentration, label="After 5 steps") plt.legend() ax.set_xlabel("Radius (nm)") ax.set_ylabel("Concentration (1/m^3)") plt.show()

Summary¶

We built out the condensation process, and the equations that define the process. We also defined the inputs and outputs of the process. Next we will build out coagulation and nucleation processes, to complete the aerosol dynamics framework.