Unstable Flow and Non-Monotonic Constitutive Equation of Transient   Networks
  We have measured the nonlinear rheological response of a model transient network over a large range of steady shear rates. The system is built up from an oil in water droplet microemulsion into which a telechelic polymer is incorporated. The phase behaviour is characterized which comprises a liquid-gas phase separation and a percolation threshold. The rheological measurements are performed in the one phase region above the percolation line. Shear thinning is observed for all samples, leading in most cases to an unstable stress response at intermediate shear rates. We built up a very simple mean field model which involves the reduction of the residence time of the stickers in the droplets due to the chain tensions at high shear. The computed constitutive equation is non-monotonic with a range where the stress is a decreasing function of the rate, a feature that indeed makes homogeneous flows unstable. The computed the flow curves compare well to the experiments. 
Eric Michel (GDPC), Jacqueline Appell (GDPC), Francois Molino (GDPC),   Jean Kieffer (GDPC), Gregoire Porte (GDPC)