Reaktoro  v2.6.0 A unified framework for modeling chemically reactive systems
Davies activity model

The Davies activity model for aqueous electrolyte solutions.

An instance of this class can be used to control how activity coefficients of ionic and neutral species, $$\gamma_i$$ and $$\gamma_n$$ respectively, as well as the activity of solvent water, $$a_\mathsf{H_2O(aq)}$$, are calculated using the Davies activity model.

The activity coefficients of ionics species are calculated using the following Davies equation[6]:

$\log\gamma_{i}=-AZ_{i}^{2}\left(\dfrac{\sqrt{I}}{1+\sqrt{I}}-b_{\mathrm{charged}}I\right),$

while the activity coefficients of neutral species are calculated using:

$\log\gamma_{n}=b_{\mathrm{neutral}}I$

In these equations, $$Z_i$$ is the electrical charge of the ionic species; $$b_{\mathrm{charged}}$$ is the Davies add-on parameter common to all charged species (default value is 0.3); $$b_{\mathrm{neutral}}$$ is the Davies add-on parameter common to all neutral species (default value is 0.1); $$I$$ is the ionic strength of the aqueous solution (in molality), calculated using:

$I=\frac{1}{2}\sum_{j}m_{j}Z_{j}^{2},$

with $$m_{j}$$ denoting the molality of the $$j$$th ion. The constant $$A$$ in the Davies model is calculated using (see Anderson and Crerar (1993)[1], page 439, and Langmuir (1997)[6], page 128):

$A=1.824829238\cdot10^{6}\rho_{\mathrm{H_{2}O}}^{1/2}(\epsilon_{\mathrm{H_{2}O}}T)^{-3/2},$

with $$A$$ in $$\mathrm{(mol/kg)^{-1/2}}$$. In these equations, $$T$$ is temperature (in K); $$\epsilon_{\mathrm{H_{2}O}}$$ is the dielectric constant of pure water (dimensionless), calculated using the Johnson and Norton (1991) model (see waterElectroPropsJohnsonNorton); and $$\rho_{\mathrm{H_{2}O}}$$ is the density of pure water (in $$\mathrm{g/cm^{3}}$$), calculated using either the equation of state of Haar–Gallagher–Kell (1984)[3] or the equation of state of Wagner and Pruss (2002)[11] (see waterThermoPropsHGK and waterThermoPropsWagnerPruss).

The activity of water is calculated using the following equation derived from the Gibbs-Duhem conditions for the species chemical potentials in the aqueous phase:

$\ln a_{w}=A\left[2\left(\frac{I+2\sqrt{I}}{1+\sqrt{I}}\right)-4\ln(1+\sqrt{I})-bI^{2}\right]M_{\mathrm{H_{2}O}}\ln10-\frac{1-x_{w}}{x_{w}}.$

In this equation, $$\mathrm{H_{2}O}=0.018015268$$ is the molar mass of water in kg/mol.