import numpy as np
import molmass as mm
from numpy.typing import NDArray
import warnings
from . import tools, diffusion_coef, viscosity_density, flow_calc, kinetics
[docs]
class BoatReactor:
[docs]
def __init__(
self,
FT_ID: float,
FT_length: float,
injector_ID: float,
injector_OD: float,
reactant_gas: str,
carrier_gas: str,
reactant_MR: float,
boat_width: float,
boat_height: float,
boat_length: float,
boat_wall_thickness: float,
) -> None:
"""
Handles calculations relevant to flow rate, flow diagnostics,
transport, and uptake for a boat reactor (partial cylinder (less
than half) inside of a cylinder). Since there is no diffusion
correction for the boat reactor geometry, the assumption is that
gas-phase diffusion is negligible. Assumes that the boat reactor
is filled to the brim with a liquid. The injector is assumed to
be above the boat reactor at all times. All calculations are for
over the boat.
Args:
FT_ID (float): Inner diameter (cm) of flow tube.
FT_length (float): Length (cm) of flow tube.
injector_ID (float): Inner diameter (cm) of reactant
injector.
injector_OD (float): Outer diameter (cm) of reactant
injector.
reactant_gas (str): Molecular formula of reactant gas
(supported Ar, He, Air, Br2, Cl2, HBr, HCl, HI, H2O, I2,
NO, N2, and O2 or other if manually inputting the
diffusion coefficient).
carrier_gas (str): Molecular formula of carrier gas
(supported: Ar, He, N2, O2).
reactant_MR (float): Reactant mixing ratio (mol mol-1).
boat_width (float): Width (cm) of boat reactor.
boat_height (float): Height (cm) of boat reactor.
boat_length (float): Length (cm) of boat reactor.
boat_wall_thickness (float): Wall thickness (cm).
Returns:
None
"""
### Check for valid inputs ###
# Check if the gases are supported
if reactant_gas not in diffusion_coef.sigmas.keys():
# Validate molecular formulas using molarmass
try:
mm.Formula(reactant_gas).mass # raises on invalid formula
except Exception:
raise ValueError(
f"Invalid reactant gas molecular formula: {reactant_gas}. "
f"Supported gases: {', '.join(diffusion_coef.sigmas.keys())}, or "
f"other if manually inputting diffusion coefficient"
)
if carrier_gas not in viscosity_density.a.keys():
raise ValueError(
f"Unsupported carrier gas. "
f"Supported gases: {', '.join(viscosity_density.a.keys())}"
)
# Check physicality of insert dimensions
if (
boat_length < 0
or boat_height < 0
or boat_width < 0
or boat_wall_thickness < 0
):
raise ValueError("Boat dimensions must be positive")
elif boat_height > FT_ID or boat_width > FT_ID:
raise ValueError("Boat width or height cannot be larger than flow tube ID")
elif boat_length > FT_length:
raise ValueError("Boat length cannot be larger than flow tube length")
# Check physicality of injector dimensions
if injector_ID < 0 or injector_OD < 0:
raise ValueError("Injector ID and OD must be positive")
elif injector_ID > FT_ID:
raise ValueError("Injector ID cannot be larger than flow tube ID")
elif injector_OD > FT_ID:
raise ValueError("Injector OD cannot be larger than flow tube ID")
elif injector_ID > injector_OD:
raise ValueError("Injector ID cannot be larger than injector OD")
elif injector_ID == 0 or injector_OD == 0:
raise ValueError("Injector dimensions must be non-zero")
# Check mixing ratio
if reactant_MR < 0 or reactant_MR > 1:
raise ValueError("Reactant mixing ratio must be between 0 and 1")
# Initialize variables
self.FT_ID = FT_ID
self.FT_length = FT_length
self.injector_ID = injector_ID
self.injector_OD = injector_OD
self.reactant_gas = reactant_gas
self.carrier_gas = carrier_gas
self.reactant_MR = reactant_MR
self.boat_height = boat_height
self.boat_width = boat_width
self.boat_length = boat_length
self.boat_wall_thickness = boat_wall_thickness
[docs]
def initialize(
self,
reactant_FR: float,
reactant_carrier_FR: float,
carrier_FR: float,
P: float,
P_units: str,
T: float,
reactant_diffusion_rate: float = np.nan,
radial_delta_T: float = 1,
axial_delta_T: float = 1,
disp: bool = True,
) -> None:
"""
Sets experimental conditions and calls calculation functions for
numerous flow and diffusion parameters.
Args:
reactant_FR (float): Reactant flow rate (sccm).
reactant_carrier_FR (float): Carrier flow rate (sccm) used
to dilute the reactant.
carrier_FR (float): Carrier flow rate (sccm) typically
injected near the start of the flow tube.
P (float): Pressure.
P_units (str): Pressure units.
T (float): Temperature (C).
reactant_diffusion_rate (float, optional): Reactant
diffusion rate (cm2 s-1).
radial_delta_T (float): Radial temperature gradient (K)
(default = 1 K).
axial_delta_T (float): Axial temperature gradient (K)
(default = 1 K).
disp (bool): Display calculated calculated values.
Returns:
None
"""
### Check for valid inputs ###
# Check if flow rates are positive
if reactant_FR < 0 or reactant_carrier_FR < 0 or carrier_FR < 0:
raise ValueError("Flow rates must be positive")
# Check for non-zero flow
if (reactant_FR <= 0) + (reactant_carrier_FR < 0) + (carrier_FR < 0):
raise ValueError("Reactant flow rate must be positive and non-zero")
if reactant_carrier_FR < 0 and carrier_FR < 0:
raise ValueError(" Flow rates must be positive or zero")
# Check if the pressure units are supported
if P_units not in tools.P_CF.keys():
raise ValueError(
f"Unsupported pressure units. "
f"Supported units: {', '.join(tools.P_CF.keys())}"
)
elif P < 0:
raise ValueError("Pressure must be positive")
# Check if the temperature & temperature gradients are valid numbers
if T < -273.15:
raise ValueError("Temperature must be above absolute zero (-273.15 C)")
if radial_delta_T < 0 or axial_delta_T < 0:
raise ValueError("Temperature gradients must be positive")
self.P = tools.P_in_Pa(P, P_units)
self.T = tools.T_in_K(T)
self.flows(
reactant_FR,
reactant_carrier_FR,
carrier_FR,
disp=disp,
)
self.carrier_flow(
radial_delta_T=radial_delta_T,
axial_delta_T=axial_delta_T,
disp=disp,
)
self.reactant_diffusion(
reactant_diffusion_rate=reactant_diffusion_rate,
disp=disp,
)
[docs]
def flows(
self,
reactant_FR: float,
reactant_carrier_FR: float,
carrier_FR: float,
disp: bool = True,
) -> None:
"""Calculates Flow Tube flows.
Args:
reactant_FR (float): Reactant flow rate (sccm).
reactant_carrier_FR (float): Carrier flow rate (sccm) used
to dilute the reactant.
carrier_FR (float): Carrier flow rate (sccm) typically
injected near the start of the flow tube.
disp (bool): Display calculated calculated values.
Returns:
None
"""
# Check if the flow rates are positive
if reactant_FR < 0 or reactant_carrier_FR < 0 or carrier_FR < 0:
raise ValueError("Flow rates must be positive")
# Lists for displaying values
var_names: list[str] = []
var: list[float] = []
var_fmts: list[str] = []
units: list[str] = []
# Flow Rate Setpoints
var_names += ["Reactant Flow Rate"]
var += [reactant_FR]
var_fmts += [".2f"]
units += ["sccm"]
var_names += ["Reactant Carrier Flow Rate"]
var += [reactant_carrier_FR]
var_fmts += [".1f"]
units += ["sccm"]
# Total Flow Rates
total_reactant_FR = reactant_FR + reactant_carrier_FR
self.total_FR = reactant_FR + reactant_carrier_FR + carrier_FR
var_names += ["Total Reactant Flow Rate"]
var += [total_reactant_FR]
var_fmts += [".1f"]
units += ["sccm"]
# Total Reactant Flow Velocity
total_reactant_flow_velocity = flow_calc.sccm_to_velocity(
self, total_reactant_FR, self.injector_ID
)
# Calculate the cross-sectional area of the boat reactor and flow tube
self.boat_perimeter, self.boat_cross_section = tools.partial_cylinder_area(
self.boat_height, self.boat_width
)
self.net_cross_section = (
tools.cross_sectional_area(self.FT_ID) - self.boat_cross_section
)
# Minimum Carrier Flow Velocity & Rate
# - to prevent effect mentioned in Li et al., ACP, 2020
min_carrier_flow_velocity = total_reactant_flow_velocity * 1.33
min_carrier_FR = flow_calc.ccm_to_sccm(
self,
min_carrier_flow_velocity
* (self.net_cross_section - tools.cross_sectional_area(self.injector_OD))
* 60,
)
var_names += ["Minimum Carrier Flow Rate"]
var += [min_carrier_FR]
var_fmts += [".1f"]
units += ["sccm"]
if carrier_FR < min_carrier_FR:
warnings.warn(
"Carrier flow rate is below the minimum. "
"This may affect the flow profile in the flow tube."
)
# More Flow Rates
var_names += ["Carrier Flow Rate"]
var += [carrier_FR]
var_fmts += [".1f"]
units += ["sccm"]
var_names += ["Total Flow Rate"]
var += [self.total_FR]
var_fmts += [".1f"]
units += ["sccm"]
# Reactant Concentrations (ppb)
injector_conc = reactant_FR / total_reactant_FR * self.reactant_MR * 1e9
FT_conc = reactant_FR / self.total_FR * self.reactant_MR * 1e9
FT_conc_molec = flow_calc.MR_to_molec(self, FT_conc)
var_names += [f"Injector {self.reactant_gas} Concentration"]
var += [injector_conc]
var_fmts += [".3g"]
units += ["ppb"]
var_names += [f"Flow Tube {self.reactant_gas} Concentration"]
var += [FT_conc]
var_fmts += [".3g"]
units += ["ppb"]
var_names += [f"Flow Tube {self.reactant_gas} Concentration"]
var += [FT_conc_molec]
var_fmts += [".2e"]
units += ["molec. cm-3"]
# Total Flow Velocity over the boat
self.flow_velocity = (
flow_calc.sccm_to_ccm(self, self.total_FR) / self.net_cross_section / 60
)
var_names += ["Flow Velocity Over Boat"]
var += [self.flow_velocity]
var_fmts += [".3g"]
units += ["cm s-1"]
# Residence Time over the boat
self.residence_time = (
self.boat_length - self.boat_wall_thickness * 2
) / self.flow_velocity
var_names += ["Residence Time Over Boat"]
var += [self.residence_time]
var_fmts += [".3g"]
units += ["s"]
### Display Values ###
if disp:
tools.table(
"Flow Setpoints and Conditions",
var_names,
var,
var_fmts,
units,
)
[docs]
def carrier_flow(
self,
radial_delta_T: float = 1,
axial_delta_T: float = 1,
disp: bool = True,
):
"""Performs and displays carrier gas transport calculations.
Args:
delta_T_radial (float): Radial temperature gradient (K).
delta_T_axial (float): Axial temperature gradient (K).
disp (bool): Display calculated values.
Returns:
None
"""
# Lists for displaying values
var_names: list[str] = []
var: list[float] = []
var_fmts: list[str] = []
units: list[str] = []
# Carrier Gas Dynamic Viscosity (kg m-1 s-1)
self.carrier_dynamic_viscosity = viscosity_density.dynamic_viscosity(
self, self.carrier_gas
)
var_names += ["Carrier Gas Dynamic Viscosity"]
var += [self.carrier_dynamic_viscosity]
var_fmts += [".2e"]
units += ["kg m-1 s-1"]
# Carrier Gas Density (kg m-3)
self.carrier_density = viscosity_density.real_density(self, self.carrier_gas)
var_names += ["Carrier Gas Density"]
var += [self.carrier_density]
var_fmts += [".3g"]
units += ["kg m-3"]
# Reynolds Number - considers the boat as floating in the flow and thus this
# should be taken as an upper limit.
self.Re = flow_calc.reynolds_number_irregular(
self,
cross_sectional_area=self.net_cross_section,
wetted_perimeter=self.boat_perimeter,
FR=self.total_FR,
)
var_names += ["Reynolds Number Over Boat (upper limit)"]
var += [self.Re]
var_fmts += [".0f"]
units += ["unitless"]
if self.Re > 1800:
warnings.warn("Re > 1800. Flow in flow tube may not be laminar")
# Entrance length (cm) - see flow_calc.py for details
length_to_laminar = flow_calc.length_to_laminar(self.FT_ID, self.Re)
var_names += ["Entrance length Over Boat (upper limit)"]
var += [length_to_laminar]
var_fmts += [".1f"]
units += ["cm"]
# Pressure Gradient (%) - see flow_calc.py for details
equivalent_diameter = np.sqrt(self.net_cross_section / np.pi)
boat_conductance = flow_calc.conductance(
self, equivalent_diameter, self.boat_length
)
FT_conductance = flow_calc.conductance(
self, self.FT_ID, self.FT_length - self.boat_length
)
total_conductance = 1 / (1 / boat_conductance + 1 / FT_conductance)
FT_pressure_gradient = flow_calc.pressure_gradient(
self, total_conductance, self.total_FR
)
var_names += ["Flow Tube Pressure Gradient (approx.)"]
var += [FT_pressure_gradient * 100]
var_fmts += [".2f"]
units += ["%"]
# Buoyancy Parameters - see flow_calc.py for details
radial_buoyancy = flow_calc.buoyancy_parameters(
self, radial_delta_T, self.FT_ID, self.Re
)
axial_buoyancy = flow_calc.buoyancy_parameters(
self, axial_delta_T, self.FT_length, self.Re
)
var_names += [f"Radial Buoyancy Parameter (ΔT={radial_delta_T:.1f} C)"]
var += [radial_buoyancy]
var_fmts += [".2f"]
units += ["unitless"]
var_names += [f"Axial Buoyancy Parameter (ΔT={axial_delta_T:.1f} C)"]
var += [axial_buoyancy]
var_fmts += [".2f"]
units += ["unitless"]
if radial_buoyancy > 1:
warnings.warn(
"Radial buoyancy parameter > 1. "
"Flow may be affected by buoyancy effects"
)
if axial_buoyancy > 1:
warnings.warn(
"Axial buoyancy parameter > 1. Flow may be affected by buoyancy effects"
)
### Display Values ###
if disp:
tools.table(
"Fluid Dynamics of Carrier Gas",
var_names,
var,
var_fmts,
units,
)
[docs]
def reactant_diffusion(
self,
reactant_diffusion_rate: float = np.nan,
disp: bool = True,
) -> None:
"""Performs and displays reactant diffusion calculations.
Args:
reactant_diffusion_rate (float): Reactant diffusion rate (cm2 s-1).
disp (bool): Display calculated calculated values.
Returns:
None
"""
# Lists for displaying values
var_names: list[str] = []
var: list[float] = []
var_fmts: list[str] = []
units: list[str] = []
# Reactant Diffusion Rate (cm2 s-1)
if self.reactant_gas not in diffusion_coef.sigmas.keys():
if isinstance(reactant_diffusion_rate, (float, np.floating)):
if np.isnan(reactant_diffusion_rate):
raise ValueError(
f"Must input reactant diffusion rate for {self.reactant_gas}"
)
else:
raise TypeError("Reactant diffusion rate must be a number")
self.reactant_diffusion_rate = reactant_diffusion_rate
var_names += ["Manually Inputted Reactant Diffusion Rate"]
else:
self.reactant_diffusion_rate = diffusion_coef.binary_diffusion_coefficient(
self
)
var_names += ["Reactant Diffusion Rate"]
var += [self.reactant_diffusion_rate]
var_fmts += [".3g"]
units += ["cm2 s-1"]
# Thermal Molecular Velocity (cm s-1) - see flow_calc.py for details
self.reactant_molec_velocity = flow_calc.molec_velocity(
self, float(mm.Formula(self.reactant_gas).mass)
)
# Reactant Mean Free Path (cm) - Fuchs and Sutugin, 1971
reactant_mean_free_path = (
3 * self.reactant_diffusion_rate / self.reactant_molec_velocity
)
# Flow Tube Advection Rate (cm2 s-1)
# - eq. 1 from Knopf et al., Anal. Chem., 2015
# - should be smaller than over the boat, take this as a lower limit.
advection_rate = self.flow_velocity * self.FT_ID
var_names += ["Flow Tube Advection Rate (lower limit for boat)"]
var += [advection_rate]
var_fmts += [".3g"]
units += ["cm2 s-1"]
# Flow Tube Peclet Number - if > 10 then axial diffusion is negligible
# - eq. 1 from Knopf et al., Anal. Chem., 2015
# - should be smaller than over the boat, take this as a lower limit.
Pe = advection_rate / self.reactant_diffusion_rate
var_names += ["Flow Tube Peclet Number (lower limit for boat)"]
var += [Pe]
var_fmts += [".4g"]
units += ["unitless"]
if Pe < 10:
warnings.warn("Pe < 10. Axial diffusion is non-negligible")
# Mixing Time (s) - see flow_calc.py for details
# - should be larger than over the boat, take this as an upper limit.
mixing_time = flow_calc.mixing_time(self, self.FT_ID)
var_names += ["Flow Tube Mixing Time (upper limit for boat)"]
var += [mixing_time]
var_fmts += [".2g"]
units += ["s"]
# Mixing Length (cm)
# - should be larger than over the boat, take this as an upper limit.
mixing_length = self.flow_velocity * mixing_time
var_names += ["Flow Tube Mixing Length (upper limit for boat)"]
var += [mixing_length]
var_fmts += [".2g"]
units += ["cm"]
# Effective Sherwood Number (unitless)
# Note: the boat geometry is not considered and thus this value
# should be used as a limiting case
self.N_eff_Shw_FT = flow_calc.N_eff_Shw(self, self.FT_length, self.total_FR)
# Knudsen Number for reactant-wall/insert interaction
# Note: the boat geometry is not considered and thus this value
# should be used as a limiting case
self.Kn_FT = flow_calc.Kn(reactant_mean_free_path, self.FT_ID)
### Display Values ###
if disp:
tools.table(
"Reactant Diffusion Parameters",
var_names,
var,
var_fmts,
units,
)
[docs]
def reactant_uptake(
self,
hypothetical_gamma: NDArray[np.float64] | float,
gamma_wall: float = 5e-6,
disp: bool = True,
) -> None:
"""
Calculates reactant uptake to the boat and loss to flow tube
walls.
Args:
hypothetical_gamma (float or numpy.ndarray): Hypothetical
uptake coefficient to calculate diffusion correction
factor.
gamma_wall (float): Wall uptake coefficient (default: 5e-6
for halocarbon wax coating - Ivanov et al., 2021).
disp (bool): Display calculated values.
Returns:
None
"""
### Check for valid inputs ###
# Check if hypothetical_gamma is between 0 and 1
if np.min(hypothetical_gamma) < 0 or np.max(hypothetical_gamma) > 1: # pyright: ignore[reportUnknownMemberType]
raise ValueError("Hypothetical gamma must be between 0 and 1")
# Check if gamma_wall is between 0 and 1
if gamma_wall < 0 or gamma_wall > 1:
raise ValueError("Wall uptake coefficient must be between 0 and 1")
# Lists for displaying values
var_names: list[str] = []
var: list[NDArray[np.float64] | float] = []
var_fmts: list[str] = []
units: list[str] = []
# Boat surface area and volume
liquid_width = self.boat_width - self.boat_wall_thickness * 2
liquid_length = self.boat_length - self.boat_wall_thickness * 2
liquid_height = self.boat_height - self.boat_wall_thickness
liquid_surface_area = liquid_width * liquid_length
_, liquid_cross_section = tools.partial_cylinder_area(
liquid_height,
liquid_width,
)
liquid_volume = liquid_cross_section * liquid_length
var_names += ["Boat Surface Area", "Boat Volume"]
var += [liquid_surface_area, liquid_volume]
var_fmts += [".1f", ".1f"]
units += ["cm2", "cm3"]
# Diffusion Correction - see kinetics.py for details
diff_corr = 1 - kinetics.correction_factor(
self.N_eff_Shw_FT, self.Kn_FT, hypothetical_gamma
)
if diff_corr > 0.05:
warnings.warn(
"Diffusion correction is > 5%. "
"Negligible diffusion may no longer be a valid assumption"
)
var_names += [
"Flow Tube Wall Diffusion Correction "
"\n(must be small to neglect for boat reactor)"
]
var += [diff_corr * 100]
var_fmts += [".1f"]
units += ["%"]
# Geometric correction for boat geometry – Hanson and Ravishankara, 1993
cylinder_SA_V_ratio = 4 / self.FT_ID
actual_SA_V_ratio = liquid_surface_area / (
self.net_cross_section * liquid_length
)
self.geometric_correction = cylinder_SA_V_ratio / actual_SA_V_ratio
var_names += ["Boat geometry correction factor"]
var += [self.geometric_correction]
var_fmts += [".2f"]
units += ["unitless"]
# Corrected Loss Rate (s-1)
# - see kinetics.py and Hanson and Ravishankara, 1993 for details
self.k = (
kinetics.observed_loss_rate(self, self.FT_ID, hypothetical_gamma)
/ self.geometric_correction
)
var_names += ["Loss Rate"]
var += [self.k]
var_fmts += [".3g"]
units += ["s-1"]
# Uptake to boat (fraction) - first order kinetics
self.uptake = 1 - np.exp(-self.k * self.residence_time / 4)
var_names += ["Loss to Boat - 1/4 Length"]
var += [self.uptake * 100]
var_fmts += [".1f"]
units += ["%"]
# Reactant Wall Loss (fraction)
# - calculated as if there is no boat, take as an upper limit
reactant_wall_loss = kinetics.cylinder_loss(
self,
self.FT_ID,
self.N_eff_Shw_FT,
self.Kn_FT,
gamma_wall,
self.residence_time,
)
var_names += ["Estimated Wall Loss (upper limit)"]
var += [reactant_wall_loss * 100]
var_fmts += [".2g"]
units += ["%"]
### Display Values ###
if disp and not isinstance(var, np.ndarray):
tools.table(
"Reactant Uptake",
var_names,
var, # pyright: ignore[reportArgumentType]
var_fmts,
units,
)
[docs]
def calculate_gamma(
self,
concentrations: NDArray[np.float64],
exposure: NDArray[np.float64],
exposure_units: str,
) -> tuple[float, float, float, tuple[float, float]]:
"""
Fits the observed loss to the boat to a first order kinetic
model to extract the uptake coefficient.
Args:
concentrations (numpy.ndarray): Reactant concentrations
(arbitrary units).
exposure (numpy.ndarray): Reactant exposure (s or cm).
exposure_units (str): Units of exposure (s or cm).
Returns:
float: k, first order loss rate (s-1).
float: r_value, correlation coefficient of the fit.
float: gamma, uptake coefficient.
tuple[float, float]: 95% confidence interval for gamma
"""
# Check for geometric correction and apply
# (see geometric_correction in reactant_uptake)
if not hasattr(self, "geometric_correction"):
raise RuntimeError("Must call reactant_uptake() before calculate_gamma()")
else:
diameter = self.FT_ID * self.geometric_correction
# Fit data to first order kinetics
slope, _, r_value, _, std_err = kinetics.fit_first_order_kinetics(
obj=self,
concentrations=concentrations,
exposure=exposure,
exposure_units=exposure_units,
)
k = -slope
# Calculate gamma and confidence intervals
gamma = kinetics.gamma_from_k(
self,
k=k,
diameter=diameter,
)
gamma_upper = kinetics.gamma_from_k(
self,
k=k + std_err * 1.96,
diameter=diameter,
)
gamma_lower = kinetics.gamma_from_k(
self,
k=k - std_err * 1.96,
diameter=diameter,
)
return k, r_value, gamma, (gamma_lower, gamma_upper)
"""
Citations:
Knopf, D.A., Pöschl, U., Shiraiwa, M., 2015. Radial Diffusion and
Penetration of Gas Molecules and Aerosol Particles through Laminar Flow
Reactors, Denuders, and Sampling Tubes. Anal. Chem. 87, 3746–3754.
https://doi.org/10.1021/ac5042395
Hanson, D.R., Ravishankara, A.R., 1993. Uptake of hydrochloric acid and
hypochlorous acid onto sulfuric acid: solubilities, diffusivities, and
reaction. J. Phys. Chem. 97, 12309–12319.
https://doi.org/10.1021/j100149a035
Fuchs, N.A., Sutugin, A.G., 1971. HIGH-DISPERSED AEROSOLS, in: Hidy,
G.M., Brock, J.R. (Eds.), Topics in Current Aerosol Research,
International Reviews in Aerosol Physics and Chemistry. Pergamon, p. 1.
https://doi.org/10.1016/B978-0-08-016674-2.50006-6
Ivanov, A.V., Molina, M.J., Park, J., 2021. Experimental study on HCl
uptake by MgCl2 and sea salt under humid conditions. J Mass Spectrom 56,
e4601. https://doi.org/10.1002/jms.4601
Tang, M.J., Cox, R.A., Kalberer, M., 2014. Compilation and evaluation of
gas phase diffusion coefficients of reactive trace gases in the
atmosphere: volume 1. Inorganic compounds. Atmos. Chem. Phys. 14,
9233–9247. https://doi.org/10.5194/acp-14-9233-2014
"""