Ion–particle coagulation¶

The problem here: positive particles (1 to 9 charges) of radius 3 nm colliding with a negative ion of radius 0.45 nm.

Several coagulation approximations:

• hard shpere
• gh2012: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.85.026410
• gk2008: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.78.046402
• dy2007: https://aip.scitation.org/doi/10.1063/1.2713719
• cg2019: https://www.tandfonline.com/doi/suppl/10.1080/02786826.2019.1614522
• lf2013: https://www.tandfonline.com/doi/full/10.1080/02786826.2013.783684

In [1]:

try:
    import particula, matplotlib
except ImportError:
    print("Setting up computational environment...")
    %pip install -U particula -qqq
    %pip install matplotlib -qqq

import numpy as np
from matplotlib import pyplot as plt
from particula import particle, u
from particula.util.lf2013_coagulation import lf2013_coag_full

try: import particula, matplotlib except ImportError: print("Setting up computational environment...") %pip install -U particula -qqq %pip install matplotlib -qqq import numpy as np from matplotlib import pyplot as plt from particula import particle, u from particula.util.lf2013_coagulation import lf2013_coag_full

In [2]:

approx = ["hardsphere", "gk2008", "gh2012", "dy2007", "cg2019"]
for i in range(len(approx)):
    shared_dict = {
        "temperature": 278,
        "coagulation_approximation": approx[i]
    }
    positive_particles = [
        particle.Particle(
            **shared_dict,
            particle_radius=3e-9,
            particle_charge=i,
            particle_density=1700,
        ) for i in range(1, 10)
    ]
    negative_ion = particle.Particle(
        **shared_dict,
        particle_radius=0.45e-9,
        particle_charge=-1,
        particle_density=1860,
    )
    coags = [
        negative_ion.coagulation(particle)
        for particle in positive_particles
    ]
    coags_ccps_mags = [
        coags[index].to("cc/s").m
        for index in range(0, 9)
    ]
    plt.semilogy(range(1,10), np.array(coags_ccps_mags).squeeze(), label=approx[i]);
   


ret = np.nan_to_num(lf2013_coag_full(
        ion_type="air",
        particle_type="conductive",
        temperature_val=298.15,
        pressure_val=101325,
        charge_vals=np.arange(1, 10),
        radius_vals=3e-9,)[0], 0)  # [0] returns negative, [1] returns positive ions
plt.semilogy(range(1,10),  np.array(ret*1e6).squeeze(), label="lf2013");
plt.ylim([1e-7, 1e-4]); plt.ylabel("Attachment coefficient, cc/s"); plt.legend(); plt.xlabel("# charges");

approx = ["hardsphere", "gk2008", "gh2012", "dy2007", "cg2019"] for i in range(len(approx)): shared_dict = { "temperature": 278, "coagulation_approximation": approx[i] } positive_particles = [ particle.Particle( **shared_dict, particle_radius=3e-9, particle_charge=i, particle_density=1700, ) for i in range(1, 10) ] negative_ion = particle.Particle( **shared_dict, particle_radius=0.45e-9, particle_charge=-1, particle_density=1860, ) coags = [ negative_ion.coagulation(particle) for particle in positive_particles ] coags_ccps_mags = [ coags[index].to("cc/s").m for index in range(0, 9) ] plt.semilogy(range(1,10), np.array(coags_ccps_mags).squeeze(), label=approx[i]); ret = np.nan_to_num(lf2013_coag_full( ion_type="air", particle_type="conductive", temperature_val=298.15, pressure_val=101325, charge_vals=np.arange(1, 10), radius_vals=3e-9,)[0], 0) # [0] returns negative, [1] returns positive ions plt.semilogy(range(1,10), np.array(ret*1e6).squeeze(), label="lf2013"); plt.ylim([1e-7, 1e-4]); plt.ylabel("Attachment coefficient, cc/s"); plt.legend(); plt.xlabel("# charges");