electrolytes

Data and functions for calculating heat capacity, density, and viscosity of aqueous electrolyte solutions as given by 1.

References

1(1,2,3,4,5,6,7,8)

Laliberte, Marc. “A Model for Calculating the Heat Capacity of Aqueous Solutions, with Updated Density and Viscosity Data.” Journal of Chemical & Engineering Data 54, no. 6 (June 11, 2009): 1725-60. doi:10.1021/je8008123

thermosteam.properties.electrolytes.Laliberte_water_viscosity(T)[source]

Return the viscosity of a water (Pa*s) at arbitrary temperatures (K) using the form proposed by 1.

\[\mu_w = \frac{T - 27.15}{(0.05594T-25.27581)t + 2867.723}\]

Notes

Original source or pure water viscosity is not cited. No temperature range is given for this equation.

thermosteam.properties.electrolytes.Laliberte_partial_viscosity(T, w_w, v1, v2, v3, v4, v5, v6)[source]

Return the viscosity of a solute using the form proposed by 1

\[\mu_i = \frac{\exp\left( \frac{v_1(1-w_w)^{v_2}+v_3}{v_4 t +1}\right)} {v_5(1-w_w)^{v_6}+1}\]
Parameters
  • T (float) – Temperature of fluid [K]

  • w_w (float) – Weight fraction of water in the solution

  • v1-v6 (floats) – Function fit parameters

Returns

mu_i – Solute partial viscosity, Pa*s

Return type

float

Notes

Temperature range check is outside of this function. Check is performed using NaCl at 5 degC from the first value in 1’s spreadsheet.

Examples

>>> d =  Laliberte_Viscosity_ParametersDict['7647-14-5']
>>> Laliberte_viscosity_i(273.15+5, 1-0.005810, d["V1"], d["V2"], d["V3"], d["V4"], d["V5"], d["V6"] )
0.004254025533308794
thermosteam.properties.electrolytes.Laliberte_water_density(T)[source]

Return the density of water using the form proposed by 1. No parameters are needed, just a temperature.

\[\rho_w = \frac{\left\{\left([(-2.8054253\times 10^{-10}\cdot t + 1.0556302\times 10^{-7})t - 4.6170461\times 10^{-5}]t -0.0079870401\right)t + 16.945176 \right\}t + 999.83952} {1 + 0.01687985\cdot t}\]
Parameters

T (float) – Temperature of fluid [K]

Returns

rho_w – Water density, [kg/m^3]

Return type

float

Notes

Original source not cited No temperature range is used.

Examples

>>> Laliberte_density_w(298.15)
997.0448954179155
>>> Laliberte_density_w(273.15 + 50)
988.0362916114763
thermosteam.properties.electrolytes.Laliberte_partial_density(T, w_w, c0, c1, c2, c3, c4)[source]

Return the density of a solute using the form proposed by Laliberte 1.

\[\rho_{app,i} = \frac{(c_0[1-w_w]+c_1)\exp(10^{-6}[t+c_4]^2)} {(1-w_w) + c_2 + c_3 t}\]
Parameters
  • T (float) – Temperature of fluid [K]

  • w_w (float) – Weight fraction of water in the solution

  • c0-c4 (floats) – Function fit parameters

Returns

rho_i – Solute partial density, [kg/m^3]

Return type

float

Notes

Temperature range check is TODO

Examples

>>> d = Laliberte_Density_ParametersDict['7647-14-5']
>>> Laliberte_partial_density(273.15+0, 1-0.0037838838, d["C0"], d["C1"], d["C2"], d["C3"], d["C4"])
3761.8917585699983
thermosteam.properties.electrolytes.Laliberte_water_heat_capacity(T)[source]

Return the heat capacity of water using the interpolation proposed by 1.

\[Cp_w = Cp_1 + (Cp_2-Cp_1) \left( \frac{t-t_1}{t_2-t_1}\right) + \frac{(Cp_3 - 2Cp_2 + Cp_1)}{2}\left( \frac{t-t_1}{t_2-t_1}\right) \left( \frac{t-t_1}{t_2-t_1}-1\right)\]
Parameters

T (float) – Temperature of fluid [K]

Returns

Cp_w – Water heat capacity, [J/kg/K]

Return type

float

Notes

Units are Kelvin and J/kg/K. Original source not cited No temperature range is used. The original equation is not used, but rather a cubic scipy interpolation routine.

Examples

>>> Laliberte_heat_capacity_w(273.15+3.56)
4208.878020261102
thermosteam.properties.electrolytes.Laliberte_partial_heat_capacity(T, w_w, a1, a2, a3, a4, a5, a6)[source]

Return the heat capacity of a solute using the form proposed by 1

\[Cp_i = a_1 e^\alpha + a_5(1-w_w)^{a_6} \alpha = a_2 t + a_3 \exp(0.01t) + a_4(1-w_w)\]
Parameters
  • T (float) – Temperature of fluid [K]

  • w_w (float) – Weight fraction of water in the solution

  • a1-a6 (floats) – Function fit parameters

Returns

Cp_i – Solute partial heat capacity, [J/kg/K]

Return type

float

Notes

Units are Kelvin and J/kg/K. Temperature range check is TODO

Examples

>>> d = Laliberte_Heat_Capacity_ParametersDict['7647-14-5']
>>> Laliberte_heat_capacity_i(1.5+273.15, 1-0.00398447, d["A1"], d["A2"], d["A3"], d["A4"], d["A5"], d["A6"])
-2930.7353945880477