Acoustic detection of pressure-induced phase separation spinodals in polymer solutions

Abstract

Acoustic detection of pressure-induced spinodal phase separation is predicted using an integrated compressible polymer solution thermodynamic-multi transport model and by calculating sound speed and attenuation under pressure conditions that gradually approach the pressure-induced (PIPS) phase separation conditions from the stable state. The integrated model consists of the thermodynamic pressure–concentration phase diagram computed using the Sanchez–Lacombe equation of state (polyethylene–hexane solution), momentum, mass and heat transport equations, and rheological constitutive equations for Newtonian and non-Newtonian fluids. The linearized model results in two coupled density-polymer concentration wave equations that describe the propagation of acoustic waves. Solving the set of equation leads to a six order polynomial that generalizes the Kirchhoff–Langevin biquadratic equation for an ideal single component gas, and that gives an expression for the attenuation and the phase velocity. For the Newtonian fluid, the behavior of the acoustic parameters, attenuation and phase velocity, is analyzed as a function of PIPS proximity and found to be sensitive at low frequency only. On the other hand for non-Newtonian fluids viscoelastic relaxation leads to pressure sensitivity of acoustic properties at all frequencies and hence providing a robust method to detect PIPS. The results provide new insights on the coupling between acoustics and phase separation thermodynamics as well as provide useful scaling pressure-attenuation-speed relations of utility to polymer processing.