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)^[12] (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.