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Diffusion Coefficient

Particula Index / Particula / Particles / Properties / Diffusion Coefficient

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

get_diffusion_coefficient

Show source in diffusion_coefficient.py:22

Calculate the diffusion coefficient of a particle based on temperature and aerodynamic mobility.

The diffusion coefficient (D) can be computed using:

  • D = k_B T × B
    • D is the diffusion coefficient in m²/s,
    • k_B is the Boltzmann constant in J/K,
    • T is the temperature in Kelvin,
    • B is the aerodynamic mobility in m²/s.

Arguments

  • temperature : Temperature in Kelvin (K).
  • aerodynamic_mobility : Aerodynamic mobility in m²/s.
  • boltzmann_constant : Boltzmann constant in J/K.

Returns

  • The diffusion coefficient of the particle in m²/s.

Examples

Example
import particula as par
par.particles.get_diffusion_coefficient(
    temperature=300.0, aerodynamic_mobility=1.0e-8
)
# Output: ...

References

  • Einstein, A. (1905). "On the movement of small particles suspended in stationary liquids required by the molecular-kinetic theory of heat." Annalen der Physik, 17(8), 549–560.
  • "Stokes-Einstein equation," Wikipedia, https://en.wikipedia.org/wiki/Stokes%E2%80%93Einstein_equation

Signature

@validate_inputs({"temperature": "positive", "aerodynamic_mobility": "nonnegative"})
def get_diffusion_coefficient(
    temperature: Union[float, NDArray[np.float64]],
    aerodynamic_mobility: Union[float, NDArray[np.float64]],
    boltzmann_constant: float = BOLTZMANN_CONSTANT,
) -> Union[float, NDArray[np.float64]]: ...

See also

get_diffusion_coefficient_via_system_state

Show source in diffusion_coefficient.py:72

Calculate the diffusion coefficient from system state parameters.

This function determines the diffusion coefficient (D) of a particle by: 1. Computing gas properties (dynamic viscosity, mean free path), 2. Determining particle slip correction and aerodynamic mobility, 3. Calling get_diffusion_coefficient() to get D.

Arguments

  • particle_radius : Particle radius in meters (m).
  • temperature : System temperature in Kelvin (K).
  • pressure : System pressure in Pascals (Pa).

Returns

  • The diffusion coefficient of the particle in m²/s.

Examples

Example
import particula as par
par.particles.get_diffusion_coefficient_via_system_state(
    particle_radius=1.0e-7,
    temperature=298.15,
    pressure=101325
)
# Output: ...

References

  • Millikan, R. A. (1923). "On the elementary electrical charge and the Avogadro constant." Physical Review, 2(2), 109–143. [check]
  • "Mass Diffusion," Wikipedia, https://en.wikipedia.org/wiki/Diffusion#Mass_diffusion

Signature

def get_diffusion_coefficient_via_system_state(
    particle_radius: Union[float, NDArray[np.float64]],
    temperature: float,
    pressure: float,
) -> Union[float, NDArray[np.float64]]: ...