"""
Handles the calculation of the diffusion coefficient of a binary gas
mixture.
"""
import numpy as np
import molmass as mm # pyright: ignore[reportMissingImports]
from typing import Protocol
from . import tools
[docs]
class required_attrs(Protocol):
P: float # Pressure in Pa
T: float # Temperature in K
reactant_gas: str # Molecular formula of reactant gas
carrier_gas: str # Molecular formula of carrier gas
## Physical Constants (Appendix B from Reid et al., 1987)
# Characteristic Lennard-Jones Lengths (Å)
sigmas: dict[str, float] = {
"Ar": 3.542,
"He": 2.551,
"Air": 3.711,
"Br2": 4.296,
"Cl2": 4.217,
"HBr": 3.353,
"HCl": 3.339,
"HI": 4.211,
"H2O": 2.641,
"I2": 5.160,
"NO": 3.492,
"N2": 3.798,
"O2": 3.467,
}
# Characteristic Lennard-Jones Energies (K)
e_ks: dict[str, float] = {
"Ar": 93.3,
"He": 10.22,
"Air": 78.6,
"Br2": 507.9,
"Cl2": 316.0,
"HBr": 449,
"HCl": 344.7,
"HI": 288.7,
"H2O": 809.1,
"I2": 474.2,
"NO": 116.7,
"N2": 71.4,
"O2": 106.7,
}
[docs]
def non_polar_Lennard_Jones_potential(e_k: float, T: float) -> float:
"""
Calculation of non-polar Lennard-Jones Potential for a binary gas
mixture. Formulas 11-3.4 to 11-3.6 in Reid et al., 1987
Args:
e_k (float): Lennard-Jones Energy (K).
T (float): Temperature in K.
Returns:
float: Non-polar Lennard Jones potential.
"""
T_star = T / e_k
return (
1.06036 / T_star**0.1561
+ 0.193 / np.exp(0.47635 * T_star)
+ 1.03587 / np.exp(1.52996 * T_star)
+ 1.76474 / np.exp(3.89411 * T_star)
)
[docs]
def binary_diffusion_coefficient(obj: required_attrs) -> float:
"""
Calculation of non-polar diffusion coefficient for a low pressure
binary gas mixture. Supported gases: Ar, He, Air, Br2, Cl2, HBr,
HCl, HI, H2O, I2, NO, N2, and O2. Formulas 11-3.1 to 11-3.2 in Reid
et al., 1987
Args:
object (required_attrs): Object with required attributes
(P in Pa, T in K, reactant_gas, carrier_gas).
Returns:
float: Diffusion coefficient for binary gas mixture (cm2 s-1)
"""
if (obj.reactant_gas not in sigmas.keys()) or (
obj.carrier_gas not in sigmas.keys()
):
raise ValueError(
f"Unsupported gas. Supported gases: {', '.join(sigmas.keys())}"
)
# Combined molar mass (g mol-1)
m1 = float(mm.Formula(obj.reactant_gas).mass) # pyright: ignore[reportUnknownArgumentType, reportUnknownMemberType]
m2 = float(mm.Formula(obj.carrier_gas).mass) # pyright: ignore[reportUnknownArgumentType, reportUnknownMemberType]
m: float = 2 / (1 / m1 + 1 / m2)
# Mean Lennard-Jones Length (Å)
mean_sigma = (sigmas[obj.reactant_gas] + sigmas[obj.carrier_gas]) / 2
# Mean Lennard-Jones Energy (K)
mean_e_k = (e_ks[obj.reactant_gas] * e_ks[obj.carrier_gas]) ** 0.5
# Diffusion Collision Integral (unitless)
Omega_D = non_polar_Lennard_Jones_potential(mean_e_k, obj.T)
return float(
0.00266
* obj.T**1.5
/ ((obj.P / tools.STANDARD_PRESSURE_Pa) * m**0.5 * mean_sigma**2 * Omega_D)
)
"""
Citations
Reid, R.C., Prausnitz, J.M., Poling, B.E., 1987. The Properties of Gases
and Liquids, 4th ed. McGraw-Hill, New York.
"""