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
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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.
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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
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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
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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
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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
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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