mean_free_path#
The mean free path is the average distance of a molecule between collisions with other molecules present in the medium. We use the kinetic theory of gases to calculate the mean free path in an ideal gas as
\[
\lambda = \frac{2 \mu / p}{(8 \, \mathrm{MW} / (\pi R T))^{1/2}}
\]
where \(\lambda\) is the mean free path, \(\mu\) is the dynamic viscosity, \(p\) is the pressure, \(\mathrm{MW}\) is the molecular weight, \(R\) is the gas constant, \(T\) is the temperature. As noted above, the user can provide an explicit value for \(\mu\) or it can be calculated using the above formula (that is, the user can provide the inputs to the above formula for \(\mu\)). At default conditions, \(\lambda\) is about 66.5 nm.
from particula.environment import Environment
print("mean free path is ", Environment().mean_free_path()) # will produce approx 66.5 nm
mean free path is 6.647984929145103e-08 meter
from particula.util import mean_free_path
help(mean_free_path)
Help on module particula.util.mean_free_path in particula.util:
NAME
particula.util.mean_free_path - calculating the mean free path of air
DESCRIPTION
The mean free path is the average distance
traveled by a molecule between collisions
with other molecules present in a medium (air).
The expeected mean free path of air is approx.
65 nm at 298 K and 101325 Pa.
FUNCTIONS
mfp(temperature=<Quantity(298.15, 'kelvin')>, pressure=<Quantity(101325, 'pascal')>, molecular_weight=<Quantity(0.0289644, 'kilogram / mole')>, dynamic_viscosity=None, gas_constant=<Quantity(8.31446261815324, 'kilogram * meter ** 2 / kelvin / mole / second ** 2')>, **kwargs)
Returns the mean free path of in air.
The mean free path is the average distance
traveled by a molecule between collisions
with other molecules present in a medium (air).
The expeected mean free path of air is approx.
65 nm at 298 K and 101325 Pa.
Examples:
```
>>> from particula import u
>>> from particula.util.mean_free_path import mfp
>>> # with no inputs, it defaults to 298 K and 101325 Pa
>>> mfp()
<Quantity(6.64373669e-08, 'meter')>
>>> # specifying a temperature of 300 K
>>> mfp(temperature=300*u.K).magnitude
6.700400687925813e-08
>>> # specifying 300 K and pressure of 1e5 Pa
>>> mfp(temperature=300*u.K, pressure=1e5*u.Pa)
<Quantity(6.789181e-08, 'meter')>
>>> mfp(
... temperature=300,
... pressure=1e5,
... molecular_weight=0.03
... )
<Quantity(6.67097062e-08, 'meter')>
>>> # specifying explicit value for dynamic viscosity
>>> mfp(dynamic_viscosity=1e-5)
<Quantity(3.61864151e-08, 'meter')>
>>> # specifying implicit value for dynamic viscosity
>>> mfp(
... temperature=300,
... reference_viscosity=1e-5,
... reference_temperature=273.15
... )
<Quantity(3.90466241e-08, 'meter')>
>>> # specifying a list of temperatures
>>> mfp(temperature=[200, 250, 300, 400]).m
array([3.93734886e-08, 5.29859655e-08, 6.70040069e-08, 9.57800224e-08])
>>> # specifying a list of pressures
>>> mfp(pressure=[1.0e5, 1.1e5, 1.2e5, 1.3e5]).m
array([6.73607078e-08, 6.12370071e-08, 5.61339232e-08, 5.18159291e-08])
>>> # specifying a list of pressures and temperatures
>>> mfp(temperature=[300,310], pressure=[1e5, 1.1e5])
<Quantity([6.78918100e-08 6.43354325e-08], 'meter')>
```
Args: (either # or $)
temperature (float) [K] (default: 298)
pressure (float) [Pa] (default: 101325)
molecular_weight (float) [kg/mol] (default: constants)
# dynamic_viscosity (float) [Pa*s] (default: util)
$ reference_viscosity (float) [Pa*s] (default: constants)
$ reference_temperature (float) [K] (default: constants)
Returns:
(float) [m]
Using particula.constants:
GAS_CONSTANT (float) [J/mol/K]
MOLECULAR_WEIGHT_AIR (float) [kg/mol]
REF_VISCOSITY_AIR_STP (float) [Pa*s]
REF_TEMPERATURE_STP (float) [K]
SUTHERLAND_CONSTANT (float) [K]
Notes:
dynamic_viscosity can be calculated independently via
particula.util.dynamic_viscosity.dyn_vis(**kwargs), but
if the value of dynamic_viscosity is provided directly,
it overrides the calculated value.
molecule_mean_free_path(molar_mass: Union[float, numpy.ndarray[Any, numpy.dtype[numpy.float64]]] = array(0.0289644), temperature: float = 298.15, pressure: float = 101325, dynamic_viscosity: Optional[float] = None) -> Union[float, numpy.ndarray[Any, numpy.dtype[numpy.float64]]]
Calculate the mean free path of a gas molecule in air based on the
temperature, pressure, and molar mass of the gas. The mean free path
is the average distance traveled by a molecule between collisions with
other molecules present in a medium (air).
Args:
-----
- molar_mass (Union[float, NDArray[np.float_]]): The molar mass
of the gas molecule [kg/mol]. Default is the molecular weight of air.
- temperature (float): The temperature of the gas [K]. Default is 298.15 K.
- pressure (float): The pressure of the gas [Pa]. Default is 101325 Pa.
- dynamic_viscosity (Optional[float]): The dynamic viscosity of the gas
[Pa*s]. If not provided, it will be calculated based on the temperature.
Returns:
--------
- Union[float, NDArray[np.float_]]: The mean free path of the gas molecule
in meters (m).
References:
----------
- https://en.wikipedia.org/wiki/Mean_free_path
DATA
GAS_CONSTANT = <Quantity(8.31446261815324, 'kilogram * meter ** 2 / ke...
MOLECULAR_WEIGHT_AIR = <Quantity(0.0289644, 'kilogram / mole')>
NDArray = numpy.ndarray[typing.Any, numpy.dtype[+_ScalarType_co]]
Optional = typing.Optional
Optional[X] is equivalent to Union[X, None].
Union = typing.Union
Union type; Union[X, Y] means either X or Y.
On Python 3.10 and higher, the | operator
can also be used to denote unions;
X | Y means the same thing to the type checker as Union[X, Y].
To define a union, use e.g. Union[int, str]. Details:
- The arguments must be types and there must be at least one.
- None as an argument is a special case and is replaced by
type(None).
- Unions of unions are flattened, e.g.::
assert Union[Union[int, str], float] == Union[int, str, float]
- Unions of a single argument vanish, e.g.::
assert Union[int] == int # The constructor actually returns int
- Redundant arguments are skipped, e.g.::
assert Union[int, str, int] == Union[int, str]
- When comparing unions, the argument order is ignored, e.g.::
assert Union[int, str] == Union[str, int]
- You cannot subclass or instantiate a union.
- You can use Optional[X] as a shorthand for Union[X, None].
u = <pint.registry.UnitRegistry object>
FILE
/opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/particula/util/mean_free_path.py
import inspect
print(inspect.getsource(mean_free_path))
""" calculating the mean free path of air
The mean free path is the average distance
traveled by a molecule between collisions
with other molecules present in a medium (air).
The expeected mean free path of air is approx.
65 nm at 298 K and 101325 Pa.
"""
from typing import Union, Optional
from numpy.typing import NDArray
import numpy as np
from particula import u
from particula.constants import (
GAS_CONSTANT, MOLECULAR_WEIGHT_AIR)
from particula.util.dynamic_viscosity import dyn_vis
from particula.util.input_handling import (in_gas_constant,
in_molecular_weight, in_pressure,
in_temperature, in_viscosity)
def mfp(
temperature=298.15 * u.K,
pressure=101325 * u.Pa,
molecular_weight=MOLECULAR_WEIGHT_AIR,
dynamic_viscosity=None,
gas_constant=GAS_CONSTANT,
**kwargs,
):
""" Returns the mean free path of in air.
The mean free path is the average distance
traveled by a molecule between collisions
with other molecules present in a medium (air).
The expeected mean free path of air is approx.
65 nm at 298 K and 101325 Pa.
Examples:
```
>>> from particula import u
>>> from particula.util.mean_free_path import mfp
>>> # with no inputs, it defaults to 298 K and 101325 Pa
>>> mfp()
<Quantity(6.64373669e-08, 'meter')>
>>> # specifying a temperature of 300 K
>>> mfp(temperature=300*u.K).magnitude
6.700400687925813e-08
>>> # specifying 300 K and pressure of 1e5 Pa
>>> mfp(temperature=300*u.K, pressure=1e5*u.Pa)
<Quantity(6.789181e-08, 'meter')>
>>> mfp(
... temperature=300,
... pressure=1e5,
... molecular_weight=0.03
... )
<Quantity(6.67097062e-08, 'meter')>
>>> # specifying explicit value for dynamic viscosity
>>> mfp(dynamic_viscosity=1e-5)
<Quantity(3.61864151e-08, 'meter')>
>>> # specifying implicit value for dynamic viscosity
>>> mfp(
... temperature=300,
... reference_viscosity=1e-5,
... reference_temperature=273.15
... )
<Quantity(3.90466241e-08, 'meter')>
>>> # specifying a list of temperatures
>>> mfp(temperature=[200, 250, 300, 400]).m
array([3.93734886e-08, 5.29859655e-08, 6.70040069e-08, 9.57800224e-08])
>>> # specifying a list of pressures
>>> mfp(pressure=[1.0e5, 1.1e5, 1.2e5, 1.3e5]).m
array([6.73607078e-08, 6.12370071e-08, 5.61339232e-08, 5.18159291e-08])
>>> # specifying a list of pressures and temperatures
>>> mfp(temperature=[300,310], pressure=[1e5, 1.1e5])
<Quantity([6.78918100e-08 6.43354325e-08], 'meter')>
```
Args: (either # or $)
temperature (float) [K] (default: 298)
pressure (float) [Pa] (default: 101325)
molecular_weight (float) [kg/mol] (default: constants)
# dynamic_viscosity (float) [Pa*s] (default: util)
$ reference_viscosity (float) [Pa*s] (default: constants)
$ reference_temperature (float) [K] (default: constants)
Returns:
(float) [m]
Using particula.constants:
GAS_CONSTANT (float) [J/mol/K]
MOLECULAR_WEIGHT_AIR (float) [kg/mol]
REF_VISCOSITY_AIR_STP (float) [Pa*s]
REF_TEMPERATURE_STP (float) [K]
SUTHERLAND_CONSTANT (float) [K]
Notes:
dynamic_viscosity can be calculated independently via
particula.util.dynamic_viscosity.dyn_vis(**kwargs), but
if the value of dynamic_viscosity is provided directly,
it overrides the calculated value.
"""
temp = in_temperature(temperature)
pres = in_pressure(pressure)
molec_wt = in_molecular_weight(molecular_weight)
if dynamic_viscosity is None:
dyn_vis_val = in_viscosity(
dyn_vis(temperature=temp, **kwargs)
)
else:
dyn_vis_val = in_viscosity(dynamic_viscosity)
gas_con = in_gas_constant(gas_constant)
return (
(2 * dyn_vis_val / pres) /
(8 * molec_wt / (np.pi * gas_con * temp))**0.5
).to_base_units()
def molecule_mean_free_path(
molar_mass: Union[
float, NDArray[np.float_]] = MOLECULAR_WEIGHT_AIR.m, # type: ignore
temperature: float = 298.15,
pressure: float = 101325,
dynamic_viscosity: Optional[float] = None,
) -> Union[float, NDArray[np.float_]]:
"""
Calculate the mean free path of a gas molecule in air based on the
temperature, pressure, and molar mass of the gas. The mean free path
is the average distance traveled by a molecule between collisions with
other molecules present in a medium (air).
Args:
-----
- molar_mass (Union[float, NDArray[np.float_]]): The molar mass
of the gas molecule [kg/mol]. Default is the molecular weight of air.
- temperature (float): The temperature of the gas [K]. Default is 298.15 K.
- pressure (float): The pressure of the gas [Pa]. Default is 101325 Pa.
- dynamic_viscosity (Optional[float]): The dynamic viscosity of the gas
[Pa*s]. If not provided, it will be calculated based on the temperature.
Returns:
--------
- Union[float, NDArray[np.float_]]: The mean free path of the gas molecule
in meters (m).
References:
----------
- https://en.wikipedia.org/wiki/Mean_free_path
"""
# check inputs are positive
if temperature <= 0:
raise ValueError("Temperature must be positive [Kelvin]")
if pressure <= 0:
raise ValueError("Pressure must be positive [Pascal]")
if np.any(molar_mass <= 0):
raise ValueError("Molar mass must be positive [kg/mol]")
if dynamic_viscosity is None:
dynamic_viscosity = dyn_vis(temperature) # type: ignore
dynamic_viscosity = float(dynamic_viscosity.m) # type: ignore
return np.array(
(2 * dynamic_viscosity / pressure)
/ (8 * molar_mass / (np.pi * GAS_CONSTANT.m * temperature))**0.5,
dtype=np.float_)