Equilibrium distribution of water in the two-phase system supercritical carbon dioxide-textile

When natural fibres are dyed in supercritical carbon dioxide, the addition of a small amount of water increases coloration. For a process design it is important to know how much water has to be added to obtain a desired humidity of both textile and carbon dioxide. In this work a thermodynamic model is proposed to calculate the distribution of water over the textile phase and the supercritical phase as a function of pressure and temperature. The phase equilibrium is described with Raoult's law for non-ideal fluids. The absorbed water in the textile is a condensed phase and is modelled here as a non-ideal liquid, using the NRTL-equation. The non-ideality of the supercritical phase is described by a solubility enhancement factor, a new equation derived from statistical thermodynamics. Although the model is applied to cotton, viscose, silk and wool, it can be used for all water absorbing textiles.