Second order virial coefficients from phase diagrams

The prediction of phase separation is essential to understand and control the properties of food systems. In this work, an existing theoretical model for describing phase separation between binary mixtures of hydrocolloids, using a virial approach up to second order, is extended with several new analytical expressions. These new expressions allow one to determine the three virial coefficients directly from three characteristics of the phase diagram, where the critical point plays a pivotal role and allows one to predict the complete phase diagram. The advantage of this approach is that experimental techniques, like membrane osmometry or static light scattering, to directly measure virial coefficients can be, in principle, avoided. It was found that just the location of the critical point is sufficient to determine two of the three virial coefficients, when one of the virial coefficients is known. When, in addition to the critical point, one other characteristic of the phase diagram is known with sufficient accuracy, like the slope of the tie-lines near or far away from the critical point, all three virial coefficients can be determined from the phase diagram. Using this approach, three virial coefficients for aqueous mixtures of dextran and polyethylene oxide were determined and compared to the ones obtained from membrane osmometry.