API Reference

Main Classes

flowtube.CoatedWallReactor(FT_ID, FT_length, ...)

flowtube.BoatReactor(FT_ID, FT_length, ...)

Modules

flowtube.tools

Constants and unit conversions.

flowtube.viscosity_density

Handles the calculation of the viscosity and density of a variety of pure gases.

flowtube.diffusion_coef

Handles the calculation of the diffusion coefficient of a binary gas mixture.

flowtube.flow_calc

Conversion functions for flow rates and concentrations in flowtube package.

flowtube.kinetics

Kinetics calculations for flow tube experiments.

Detailed Documentation

flowtube - A Python package for transport and diffusion calculations in cylindrical flow reactors.

This package provides tools and utilities for flow reactor analysis including coated wall reactor (CWR), boat reactor, viscosity/density, and binary diffusion coefficients calculations for atmospheric chemistry research.

class flowtube.CoatedWallReactor(FT_ID, FT_length, injector_ID, injector_OD, reactant_gas, carrier_gas, reactant_MR, insert_ID=0, insert_length=0)[source]

Bases: object

Parameters:

  • FT_ID (float)

  • FT_length (float)

  • injector_ID (float)

  • injector_OD (float)

  • reactant_gas (str)

  • carrier_gas (str)

  • reactant_MR (float)

  • insert_ID (float)

  • insert_length (float)

__init__(FT_ID, FT_length, injector_ID, injector_OD, reactant_gas, carrier_gas, reactant_MR, insert_ID=0, insert_length=0)[source]

Handles calculations relevant to flow rate, flow diagnostics, transport, and uptake for a coated wall reactor. By default assumes no insert and a fully coated flow tube. To calculate terms for a fully-coated cylindrical insert or for a partially coated flow tube, simply pass values for the insert length and ID.

Parameters:

  • 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).

  • carrier_gas (str) – Molecular formula of carrier gas (supported: Ar, He, N2, O2).

  • reactant_MR (float) – Reactant mixing ratio (mol mol-1).

  • insert_ID (float, optional) – Inner diameter (cm) of insert.

  • insert_length (float, optional) – Length (cm) of insert.

Returns:

None

Return type:

None

calculate_gamma(concentrations, exposure, exposure_units)[source]

Fits the observed loss to the boat to a first order kinetic model to extract the uptake coefficient.

Parameters:

  • 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:

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

Return type:

float

carrier_flow(radial_delta_T=1, axial_delta_T=1, disp=True)[source]

Performs and displays carrier gas transport calculations.

Parameters:

  • delta_T_radial (float) – Radial temperature gradient (K).

  • delta_T_axial (float) – Axial temperature gradient (K).

  • disp (bool) – Display calculated values.

  • radial_delta_T (float)

  • axial_delta_T (float)

Returns:

None

flows(reactant_FR, reactant_carrier_FR, carrier_FR, disp=True)[source]

Calculates Flow Tube flows.

Parameters:

  • 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.

Return type:

None

Returns:

None

initialize(reactant_FR, reactant_carrier_FR, carrier_FR, P, P_units, T, reactant_diffusion_rate=nan, radial_delta_T=1, axial_delta_T=1, disp=True)[source]

Sets experimental conditions and calls calculation functions for numerous flow and diffusion parameters.

Parameters:

  • 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) – 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.

Return type:

None

Returns:

None

reactant_diffusion(reactant_diffusion_rate=nan, disp=True)[source]

Performs and displays reactant diffusion calculations.

Parameters:

  • reactant_diffusion_rate (float) – Reactant diffusion rate (cm2 s-1).

  • disp (bool) – Display calculated calculated values.

Return type:

None

Returns:

None

reactant_uptake(hypothetical_gamma, gamma_wall=5e-06, disp=True)[source]

Calculates reactant uptake to coated wall or insert and loss to flow tube walls.

Parameters:

  • 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., J. Mass Spectrom., 2021).

  • disp (bool) – Display calculated values.

Return type:

None

Returns:

None.

class flowtube.BoatReactor(FT_ID, FT_length, injector_ID, injector_OD, reactant_gas, carrier_gas, reactant_MR, boat_width, boat_height, boat_length, boat_wall_thickness)[source]

Bases: object

Parameters:

  • 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)

__init__(FT_ID, FT_length, injector_ID, injector_OD, reactant_gas, carrier_gas, reactant_MR, boat_width, boat_height, boat_length, boat_wall_thickness)[source]

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.

Parameters:

  • 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

Return type:

None

calculate_gamma(concentrations, exposure, exposure_units)[source]

Fits the observed loss to the boat to a first order kinetic model to extract the uptake coefficient.

Parameters:

  • 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:

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

Return type:

float

carrier_flow(radial_delta_T=1, axial_delta_T=1, disp=True)[source]

Performs and displays carrier gas transport calculations.

Parameters:

  • delta_T_radial (float) – Radial temperature gradient (K).

  • delta_T_axial (float) – Axial temperature gradient (K).

  • disp (bool) – Display calculated values.

  • radial_delta_T (float)

  • axial_delta_T (float)

Returns:

None

flows(reactant_FR, reactant_carrier_FR, carrier_FR, disp=True)[source]

Calculates Flow Tube flows.

Parameters:

  • 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.

Return type:

None

Returns:

None

initialize(reactant_FR, reactant_carrier_FR, carrier_FR, P, P_units, T, reactant_diffusion_rate=nan, radial_delta_T=1, axial_delta_T=1, disp=True)[source]

Sets experimental conditions and calls calculation functions for numerous flow and diffusion parameters.

Parameters:

  • 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.

Return type:

None

Returns:

None

reactant_diffusion(reactant_diffusion_rate=nan, disp=True)[source]

Performs and displays reactant diffusion calculations.

Parameters:

  • reactant_diffusion_rate (float) – Reactant diffusion rate (cm2 s-1).

  • disp (bool) – Display calculated calculated values.

Return type:

None

Returns:

None

reactant_uptake(hypothetical_gamma, gamma_wall=5e-06, disp=True)[source]

Calculates reactant uptake to the boat and loss to flow tube walls.

Parameters:

  • 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.

Return type:

None

Returns:

None

CoatedWallReactor

class flowtube.CoatedWallReactor(FT_ID, FT_length, injector_ID, injector_OD, reactant_gas, carrier_gas, reactant_MR, insert_ID=0, insert_length=0)[source]

Bases: object

Parameters:

  • FT_ID (float)

  • FT_length (float)

  • injector_ID (float)

  • injector_OD (float)

  • reactant_gas (str)

  • carrier_gas (str)

  • reactant_MR (float)

  • insert_ID (float)

  • insert_length (float)

__init__(FT_ID, FT_length, injector_ID, injector_OD, reactant_gas, carrier_gas, reactant_MR, insert_ID=0, insert_length=0)[source]

Handles calculations relevant to flow rate, flow diagnostics, transport, and uptake for a coated wall reactor. By default assumes no insert and a fully coated flow tube. To calculate terms for a fully-coated cylindrical insert or for a partially coated flow tube, simply pass values for the insert length and ID.

Parameters:

  • 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).

  • carrier_gas (str) – Molecular formula of carrier gas (supported: Ar, He, N2, O2).

  • reactant_MR (float) – Reactant mixing ratio (mol mol-1).

  • insert_ID (float, optional) – Inner diameter (cm) of insert.

  • insert_length (float, optional) – Length (cm) of insert.

Returns:

None

Return type:

None

initialize(reactant_FR, reactant_carrier_FR, carrier_FR, P, P_units, T, reactant_diffusion_rate=nan, radial_delta_T=1, axial_delta_T=1, disp=True)[source]

Sets experimental conditions and calls calculation functions for numerous flow and diffusion parameters.

Parameters:

  • 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) – 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.

Return type:

None

Returns:

None

flows(reactant_FR, reactant_carrier_FR, carrier_FR, disp=True)[source]

Calculates Flow Tube flows.

Parameters:

  • 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.

Return type:

None

Returns:

None

carrier_flow(radial_delta_T=1, axial_delta_T=1, disp=True)[source]

Performs and displays carrier gas transport calculations.

Parameters:

  • delta_T_radial (float) – Radial temperature gradient (K).

  • delta_T_axial (float) – Axial temperature gradient (K).

  • disp (bool) – Display calculated values.

  • radial_delta_T (float)

  • axial_delta_T (float)

Returns:

None

reactant_diffusion(reactant_diffusion_rate=nan, disp=True)[source]

Performs and displays reactant diffusion calculations.

Parameters:

  • reactant_diffusion_rate (float) – Reactant diffusion rate (cm2 s-1).

  • disp (bool) – Display calculated calculated values.

Return type:

None

Returns:

None

reactant_uptake(hypothetical_gamma, gamma_wall=5e-06, disp=True)[source]

Calculates reactant uptake to coated wall or insert and loss to flow tube walls.

Parameters:

  • 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., J. Mass Spectrom., 2021).

  • disp (bool) – Display calculated values.

Return type:

None

Returns:

None.

calculate_gamma(concentrations, exposure, exposure_units)[source]

Fits the observed loss to the boat to a first order kinetic model to extract the uptake coefficient.

Parameters:

  • 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:

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

Return type:

float

BoatReactor

class flowtube.BoatReactor(FT_ID, FT_length, injector_ID, injector_OD, reactant_gas, carrier_gas, reactant_MR, boat_width, boat_height, boat_length, boat_wall_thickness)[source]

Bases: object

Parameters:

  • 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)

__init__(FT_ID, FT_length, injector_ID, injector_OD, reactant_gas, carrier_gas, reactant_MR, boat_width, boat_height, boat_length, boat_wall_thickness)[source]

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.

Parameters:

  • 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

Return type:

None

initialize(reactant_FR, reactant_carrier_FR, carrier_FR, P, P_units, T, reactant_diffusion_rate=nan, radial_delta_T=1, axial_delta_T=1, disp=True)[source]

Sets experimental conditions and calls calculation functions for numerous flow and diffusion parameters.

Parameters:

  • 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.

Return type:

None

Returns:

None

flows(reactant_FR, reactant_carrier_FR, carrier_FR, disp=True)[source]

Calculates Flow Tube flows.

Parameters:

  • 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.

Return type:

None

Returns:

None

carrier_flow(radial_delta_T=1, axial_delta_T=1, disp=True)[source]

Performs and displays carrier gas transport calculations.

Parameters:

  • delta_T_radial (float) – Radial temperature gradient (K).

  • delta_T_axial (float) – Axial temperature gradient (K).

  • disp (bool) – Display calculated values.

  • radial_delta_T (float)

  • axial_delta_T (float)

Returns:

None

reactant_diffusion(reactant_diffusion_rate=nan, disp=True)[source]

Performs and displays reactant diffusion calculations.

Parameters:

  • reactant_diffusion_rate (float) – Reactant diffusion rate (cm2 s-1).

  • disp (bool) – Display calculated calculated values.

Return type:

None

Returns:

None

reactant_uptake(hypothetical_gamma, gamma_wall=5e-06, disp=True)[source]

Calculates reactant uptake to the boat and loss to flow tube walls.

Parameters:

  • 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.

Return type:

None

Returns:

None

calculate_gamma(concentrations, exposure, exposure_units)[source]

Fits the observed loss to the boat to a first order kinetic model to extract the uptake coefficient.

Parameters:

  • 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:

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

Return type:

float

Utility Modules

Constants and unit conversions.

flowtube.tools.T_in_K(T)[source]

Convert celcius to Kelvin.

Parameters:

T (float) – Temperature in Celcius.

Returns:

Temperature in Kelvin.

Return type:

float

flowtube.tools.P_in_Pa(P, units)[source]

Convert pressure to Pa.

Parameters:

  • P (float) – Pressure.

  • units (float) – Supported pressure units: Torr, bar, mbar, or hPa.

Returns:

Pressure in Pa.

Return type:

float

flowtube.tools.cross_sectional_area(diameter)[source]

Calculate cross sectional area.

Parameters:

diameter (float) – Diameter.

Returns:

Cross sectional area.

Return type:

float

flowtube.tools.partial_cylinder_area(height, width)[source]

Calculate the cross-sectional area and perimeter of a partial cylinder (“boat”) given its height and width. Assumes the partial cylinder is a segment of a circle with given width as chord length and that the height is less than the diameter of the circle. Calculations based on: https://mathworld.wolfram.com/CircularSegment.html and https://www.vcalc.com/wiki/KurtHeckman/Circle-area-of-an-arc-segment-h.

Parameters:

  • height (float) – Height of the segment (cm).

  • width (float) – Chord length of the segment (cm).

Returns:

Outer perimeter (cm). float: Cross-sectional area (cm^2).

Return type:

float

flowtube.tools.table(title, var_names, var, var_fmts, units)[source]

Print a formatted table of variables.

Parameters:

  • title (str) – Title of the table.

  • var_names (list) – List of variable names.

  • var (list) – Variable values.

  • var_fmts (list) – List of formats for each variable.

  • units (list) – List of units for each variable.

Return type:

None

Returns:

None

Conversion functions for flow rates and concentrations in flowtube package.

class flowtube.flow_calc.basic_attrs(*args, **kwargs)[source]
P: float
T: float
__init__(*args, **kwargs)
class flowtube.flow_calc.carrier_attrs(*args, **kwargs)[source]
carrier_dynamic_viscosity: float
carrier_density: float
P: float
T: float
class flowtube.flow_calc.full_attrs(*args, **kwargs)[source]
reactant_diffusion_rate: float
reactant_molec_velocity: float
carrier_dynamic_viscosity: float
carrier_density: float
P: float
T: float
flowtube.flow_calc.sccm_to_ccm(obj, FR)[source]

Convert sccm to cm3 per min.

Parameters:

  • obj (basic_attrs) – Object with basic attributes (P in Pa, T in K).

  • FR (float) – Flow rate in sccm.

Returns:

Flow rate in cm3 min-1

Return type:

float

flowtube.flow_calc.ccm_to_sccm(obj, FR)[source]

Convert cm3 per min to sccm

Parameters:

  • obj (basic_attrs) – Object with basic attributes (P in Pa, T in K).

  • FR (float) – Flow rate in cm3 min-1.

Returns:

Flow rate to sccm.

Return type:

float

flowtube.flow_calc.sccm_to_velocity(obj, FR, diameter)[source]

Calculate flow velocity.

Parameters:

  • obj (basic_attrs) – Object with basic attributes (P in Pa, T in K).

  • FR (float) – Flow rate in sccm.

  • diameter (float) – Diameter in cm.

Returns:

Flow velocity in cm s-1.

Return type:

float

flowtube.flow_calc.MR_to_molec(obj, conc)[source]

Convert mixing ratio in ppb to molecules cm-3.

Parameters:

  • obj (basic_attrs) – Object with basic attributes (P in Pa, T in K).

  • conc (float) – Mixing ratio (ppb - mol mol-1).

Returns:

Concentration in molec. cm-3.

Return type:

float

flowtube.flow_calc.molec_velocity(obj, molar_mass)[source]

Calculate thermal molecular velocity. Formula matched to values from Knopf et al., Anal. Chem., 2015

Parameters:

  • obj (basic_attrs) – Object with basic attributes (P in Pa, T in K).

  • molar_mass (float) – Molar mass of the gas (g mol-1).

Returns:

Thermal molecular velocity in cm s-1.

Return type:

float

flowtube.flow_calc.reynolds_number(obj, FR, diameter)[source]

Calculate Reynolds number for a gas flowing through a cylinder.

Parameters:

  • obj (carrier_attrs) – Object with full attributes (P in Pa, T in K, carrier_dynamic_viscosity in kg m-1 s-1, carrier_density in kg m-3).

  • FR (float) – Total flow rate in sccm.

  • diameter (float) – Diameter of the cylinder (cm).

Returns:

Reynolds number.

Return type:

float

flowtube.flow_calc.reynolds_number_irregular(obj, cross_sectional_area, wetted_perimeter, FR)[source]

Calculate Reynolds number for a gas flowing through a cylinder. Formula 6-14 from Holman and Bhattacharyya 2011.

Parameters:

  • obj (carrier_attrs) – Object with full attributes (P in Pa, T in K, carrier_dynamic_viscosity in kg m-1 s-1, carrier_density in kg m-3).

  • cross_sectional_area (float) – Cross sectional area of the flow passage (cm2).

  • wetted_perimeter (float) – Wetted perimeter of the flow passage (cm).

  • FR (float) – Total flow rate in sccm.

Returns:

Reynolds number.

Return type:

float

flowtube.flow_calc.conductance(obj, diameter, length)[source]

Calculate conductance through cylinder - eq. 3.17 from Moore et al., 2009.

Parameters:

  • obj (carrier_attrs) – Object with full attributes (P in Pa, T in K, carrier_dynamic_viscosity in kg m-1 s-1, carrier_density in kg m-3).

  • diameter (float) – Inner diameter (cm).

  • length (float) – Length (cm).

Returns:

Conductance in L s-1.

Return type:

float

flowtube.flow_calc.pressure_gradient(obj, conductance, FR)[source]

Calculate pressure gradient - eqs. 3.9 & 3.10 from Moore et al., 2009.

Parameters:

  • obj (basic_attrs) – Object with basic attributes (P in Pa, T in K).

  • conductance (float) – Conductance in L s-1.

  • flow_rate (float) – Flow rate in sccm.

  • FR (float)

Returns:

Pressure gradient ratio.

Return type:

float

flowtube.flow_calc.buoyancy_parameters(obj, delta_T, distance, Re)[source]

Calculate buoyancy parameters.

Parameters:

  • obj (carrier_attrs) – Object with full attributes (P in Pa, T in K, carrier_dynamic_viscosity in kg m-1 s-1, carrier_density in kg m-3).

  • delta_T (float) – Temperature difference (K).

  • distance (float) – Distance over which the temperature difference is measured (cm) (typically axial or radial).

  • Re (float) – Reynolds number of the flow tube.

Returns:

Buoyancy parameter (>1 indicates the flow being driven by

buoyancy).

Return type:

float

flowtube.flow_calc.length_to_laminar(diameter, Re)[source]

Entrance length (cm) - length to achieve laminar profile - Bird et al., 2002, page 52. Note that the scalar term can vary depending on the source. Keyser, 1994 gives a value of 0.0565 for 99% attainment of parabolic profile while Hanson and Kosciuch, 2003 provide a value of 0.05 for 95% attainment. Using an exponential fit of the values, it seems that the 0.035 figure that Bird et al., 2002 gives is for a 85% attainment. Choose whichever value is most appropriate for your purposes.

Parameters:

  • diameter (float) – Diameter of the cylinder (cm).

  • Re (float) – Reynolds number of the flow tube.

Returns:

Length to laminar profile (cm).

Return type:

float

flowtube.flow_calc.mixing_time(obj, diameter)[source]

Calculate mixing time (s) - Hanson and Lovejoy, Geophys. Res. Lett., 1994.

Parameters:

  • obj (full_attrs) – Object with full attributes (P in Pa, T in K, reactant_diffusion_rate in cm2 s-1, carrier_dynamic_viscosity in kg m-1 s-1, carrier_density in kg m-3).

  • diameter (float) – Diameter of the cylinder (cm).

Returns:

Mixing time in seconds.

Return type:

float

flowtube.flow_calc.N_eff_Shw(obj, length, FR)[source]

Calculate the effective Sherwood number - eq. 11 from Knopf et al., 2015.

Parameters:

  • obj (full_attrs) – Object with full attributes (P in Pa, T in K, reactant_diffusion_rate in cm2 s-1, carrier_dynamic_viscosity in kg m-1 s-1, carrier_density in kg m-3).

  • length (float) – Length of the flow tube (cm).

  • FR (float) – Total flow rate in cm3 min-1.

Returns:

Effective Sherwood number.

Return type:

float

flowtube.flow_calc.Kn(mean_free_path, char_length)[source]

Calculate Knudsen number - eq. 8 from Knopf et al., 2015.

Parameters:

  • mean_free_path (float) – Mean free path of the reactant (cm).

  • char_length (float) – Characteristic length: diameter of cylinder for a coated wall reactor (cm).

Returns:

Knudsen number.

Return type:

float

Kinetics calculations for flow tube experiments.

flowtube.kinetics.diffusion_limited_rate_constant(obj, N_eff_Shw, diameter)[source]

Calculate diffusion limited rate constant (s-1) - eq. 10 from Knopf et al., 2015.

Parameters:

  • obj (full_attrs) – Object with full attributes (P in Pa, T in K, reactant_diffusion_rate in cm2 s-1, carrier_dynamic_viscosity in kg m-1 s-1, carrier_density in kg m-3).

  • N_eff_Shw (float) – Effective Sherwood number.

  • diameter (float) – Diameter of the cylinder (cm).

Returns:

Diffusion limited rate constant (s-1).

Return type:

float

flowtube.kinetics.diffusion_limited_uptake_coefficient(obj, diameter, k_diff)[source]

Calculate diffusion limited effective uptake coefficient - eq. 19 from Knopf et al., 2015.

Parameters:

  • obj (full_attrs) – Object with full attributes (P in Pa, T in K, reactant_diffusion_rate in cm2 s-1, carrier_dynamic_viscosity in kg m-1 s-1, carrier_density in kg m-3).

  • diameter (float) – Diameter of the cylinder (cm).

  • k_diff (float) – Diffusion limited rate constant (s-1).

Returns:

Diffusion limited effective uptake coefficient (cm s-1).

Return type:

float

flowtube.kinetics.correction_factor(N_eff_Shw, Kn, gamma)[source]

Calculate correction factor for uptake coefficient - eq. 20 from Knopf et al., 2015.

Parameters:

  • N_eff_Shw (float) – Effective Sherwood number (unitless).

  • Kn (float) – Knudsen number (unitless).

  • hypothetical_gamma (float) – Hypothetical uptake coefficient (unitless).

  • gamma (ndarray[tuple[Any, ...], dtype[float64]] | float)

Returns:

Correction factor (unitless).

Return type:

float

flowtube.kinetics.observed_loss_rate(obj, diameter, gamma_eff)[source]

Calculate observed loss rate (s-1) - eq. 19 from Knopf et al., 2015.

Parameters:

  • obj (full_attrs) – Object with full attributes (P in Pa, T in K, reactant_diffusion_rate in cm2 s-1, carrier_dynamic_viscosity in kg m-1 s-1, carrier_density in kg m-3).

  • diameter (float) – Diameter of the cylinder (cm).

  • gamma_eff (float) – Effective uptake coefficient (unitless).

Returns:

Observed loss rate (s-1).

Return type:

float

flowtube.kinetics.cylinder_loss(obj, diameter, N_eff_Shw, Kn, gamma, time)[source]

Calculate penetration (unitless) - eq. 21 from Knopf et al., 2015.

Parameters:

  • obj (full_attrs) – Object with full attributes (P in Pa, T in K, reactant_diffusion_rate in cm2 s-1, carrier_dynamic_viscosity in kg m-1 s-1, carrier_density in kg m-3).

  • time (float) – Residence time in cylinder (s).

  • diameter (float)

  • N_eff_Shw (float)

  • Kn (float)

  • gamma (ndarray[tuple[Any, ...], dtype[float64]] | float)

Returns:

Penetration - fraction of initial reactant after passing

through cylinder (unitless).

Return type:

float

flowtube.kinetics.gamma_from_k(obj, k, diameter)[source]

Calculate effective uptake coefficient from rate constant.

Parameters:

  • obj (full_attrs) – Object with full attributes (P in Pa, T in K, reactant_diffusion_rate in cm2 s-1, carrier_dynamic_viscosity in kg m-1 s-1, carrier_density in kg m-3).

  • k (float) – Rate constant (s-1).

  • diameter (float) – Diameter of the cylinder (cm).

Returns:

Effective uptake coefficient (unitless).

Return type:

float

flowtube.kinetics.fit_first_order_kinetics(obj, concentrations, exposure, exposure_units)[source]

Fits the observed loss to a first order kinetic model to extract the uptake coefficient.

Parameters:

  • obj (full_attrs) – Object with full attributes (P in Pa, T in K, reactant_diffusion_rate in cm2 s-1, carrier_dynamic_viscosity in kg m-1 s-1, carrier_density in kg m-3).

  • concentrations (NDArray[np.float64]) – Array of observed concentrations (unitless).

  • exposure (NDArray[np.float64]) – Array of exposures (s or cm).

  • exposure_units (str) – Units of exposure (“s”, “sec”, “second”, “seconds”, “cm”, “centimeter”, “centimeters”).

Returns:

Tuple containing the

slope, intercept, r-value, p-value, and standard error of the regression.

Return type:

tuple[float, float, float, float, float]

Handles the calculation of the diffusion coefficient of a binary gas mixture.

class flowtube.diffusion_coef.required_attrs(*args, **kwargs)[source]
P: float
T: float
reactant_gas: str
carrier_gas: str
__init__(*args, **kwargs)
flowtube.diffusion_coef.non_polar_Lennard_Jones_potential(e_k, T)[source]

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

Parameters:

  • e_k (float) – Lennard-Jones Energy (K).

  • T (float) – Temperature in K.

Returns:

Non-polar Lennard Jones potential.

Return type:

float

flowtube.diffusion_coef.binary_diffusion_coefficient(obj)[source]

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

Parameters:
Returns:

Diffusion coefficient for binary gas mixture (cm2 s-1)

Return type:

float

Handles the calculation of the viscosity and density of a variety of pure gases.

class flowtube.viscosity_density.basic_attrs(*args, **kwargs)[source]
P: float
T: float
__init__(*args, **kwargs)
flowtube.viscosity_density.real_density(obj, gas)[source]

Calculates the real density of a gas using van der Waal’s equation of state.

Parameters:

  • obj (basic_attrs) – Object with basic attributes (P in Pa, T in K).

  • gas (str) – Molecular formula of gas (supported: Ar, He, N2, O2).

Returns:

Real density of gas in kg m-3.

Return type:

float

flowtube.viscosity_density.dynamic_viscosity(obj, gas)[source]

Estimate absolute/dynamic viscosity of pure gases using the corresponding states method from Reid et al., 1987.

Parameters:

  • obj (basic_attrs) – Object with basic attributes (P in Pa, T in K).

  • gas (str) – Molecular formula of gas (supported: Ar, He, N2, O2).

Returns:

Gas viscosity (kg m-1 s-1).

Return type:

float