Diffusive Knudsen Module¶

Particula Index / Particula / Particles / Properties / Diffusive Knudsen Module

Auto-generated documentation for particula.particles.properties.diffusive_knudsen_module module.

get_diffusive_knudsen_number¶

Show source in diffusive_knudsen_module.py:13

Compute the diffusive Knudsen number for particle-particle interactions.

The diffusive Knudsen number (Kn_d) differs from the standard Knudsen number. It represents the ratio of the mean particle persistence distance to the effective Coulombic interaction scale. Mathematically:

Kn_d = [ √(k_B × T × μ_red) / f_red ] / [ (rᵢ + rⱼ) × (Γ_c / Γ_k) ]
- k_B is the Boltzmann constant (J/K).
- T is the temperature (K).
- μ_red is the reduced mass of particles (kg).
- f_red is the reduced friction factor (dimensionless).
- rᵢ + rⱼ is the sum of radii for the interacting particles (m).
- Γ_c is the continuum-limit Coulomb enhancement factor(dimensionless).
- Γ_k is the kinetic-limit Coulomb enhancement factor (dimensionless).

Arguments¶

particle_radius : Radius of the particle(s) in meters (m).
particle_mass : Mass of the particle(s) in kilograms (kg).
friction_factor : Friction factor(s) (dimensionless).
coulomb_potential_ratio : Coulomb potential ratio (dimensionless), zero if no charge.
temperature : Temperature of the system in Kelvin (K).

Returns¶

The diffusive Knudsen number, either a float or NDArray[np.float64].

Examples¶

Single Particle Example

import numpy as np
import particula as par
par.particles.get_diffusive_knudsen_number(
    particle_radius=1e-7,
    particle_mass=1e-17,
    friction_factor=0.8,
    coulomb_potential_ratio=0.3,
    temperature=300
)
# Output: 0.12...

Multiple Particles Example

import numpy as np
import particula as par
# Multiple particles example
radius_arr = np.array([1e-7, 2e-7])
mass_arr = np.array([1e-17, 2e-17])
friction_arr = np.array([0.8, 1.1])
potential_arr = np.array([0.3, 0.5])
par.particles.par.get_diffusive_knudsen_number(
    radius_arr, mass_arr, friction_arr, potential_arr
)
# Output: array([...])

References¶

Chahl, H. S., & Gopalakrishnan, R. (2019). "High potential, near free molecular regime Coulombic collisions in aerosols and dusty plasmas." Aerosol Science and Technology, 53(8), 933-957. https://doi.org/10.1080/02786826.2019.1614522
Gopalakrishnan, R., & Hogan, C. J. (2012). "Coulomb-influenced collisions in aerosols and dusty plasmas." Physical Review E, 85(2). https://doi.org/10.1103/PhysRevE.85.026410

Signature¶

@validate_inputs(
    {
        "particle_radius": "nonnegative",
        "particle_mass": "nonnegative",
        "friction_factor": "nonnegative",
    }
)
def get_diffusive_knudsen_number(
    particle_radius: Union[float, NDArray[np.float64]],
    particle_mass: Union[float, NDArray[np.float64]],
    friction_factor: Union[float, NDArray[np.float64]],
    coulomb_potential_ratio: Union[float, NDArray[np.float64]] = 0.0,
    temperature: float = 298.15,
) -> Union[float, NDArray[np.float64]]: ...