Non-equilibrium Thermodynamics Modeling of Concentrated Polymer Blends
M. Dressler [1], B.J. Edwards [2]

[1] ETH Zurich, Switzerland, [2] Department of Chemical Engineering, UT Knoxville, U.S.A.

Abstract: In the third workshop of non-equilibrium Thermodynamics we proposed a non--equilibrium Thermodynamics model for dilute polymer blends (disperse phase volume fraction φ < 0.1) with a droplet morphology [1]. In the fourth workshop we applied this model to analyze microstructure--rheology relationships in simple viscometric flows [2]. Our contribution in the fifth workshop is about non--equilibrium Thermodynamics of more concentrated polymer blends (disperse phase volume fraction φ > 0.1) with a droplet morphology. In these systems we expect significant droplet--droplet interactions, lyotropic isotropic--nematic phase transitions of oriented droplets, distortion elasticity, and a pronounced effect of droplet inertia on the flow behavior. To give a physically satisfactory description of these phenomena, we chose as the thermodynamic variables a second rank conformation tensor for the matrix phase, a droplet shape tensor for the disperse phase, and a droplet orientation tensor. For these thermodynamic variables we derive Poisson and dissipation brackets. We use the bracket formalism of non--equilibrium Thermodynamics to derive a thermodynamically consistent conformation tensor theory for concentrated polymer blends. We discuss this set of flow equations and we compare it with our earlier theories for dilute polymer blends with a droplet morphology.

[1] M. Dressler and B. J. Edwards, Rheology of polymer blends with matrix-phase viscoelasticity and a narrow droplet size distribution, J. Non-Newtonian Fluid Mech. 120 (2004) 189-205.
[2] M. Dressler, B. J. Edwards, E. J. Windhab, An examination of droplet deformation and break-up between concentrically rotating cylinders, J. Non-Newtonian Fluid Mech. 152 (2008) 86-100.