# Mode: `MISCIBLE`

ΒΆ

The miscible mode applies to a mixture of water and proplyene glycol (PPG). In terms of molar density for the mixture \(\eta\) and mole fractions \(x_i\), \(i\)=1 (water), \(i\)=2 (PPG), the mass conservation equations have the form

with source/sink term \(Q_i\). It should be noted that the mass- and mole-fraction formulations of the conservation equations are not exactly equivalent. This is due to the diffusion term which gives an extra term when transformed from the mole-fraction to mass-fraction gradient.

The molar density \(\eta\) is related to the mass density by

and

It follows that

The second term on the right-hand side is ignored.

Simple equations of state are provided for density [g/cm:math:^3], viscosity [Pa s], and diffusivity [m:math:^2/s]. The density is a function of both composition are pressrue with the form

with the compressibility \(\beta(y_1)\) given by

and the mixture density at the reference pressure \(p_0\) taken as atmospheric pressure is given by

with mass fraction of water \(y_1\). The viscosity and diffusivity have the forms

and

The mass fraction is related to mole fraction according to

where the mean formula weight \(W\) is given by

with formula weights for water and proplyene glycol equal to \(W_{\rm H_2O}\) = 18.01534 and \(W_{\rm PPG}\) = 76.09 [kg/kmol].

Global mass conservation satisfies the relation

with

In terms of mass fractions and mass density