Eur. Phys. J. E 6, 79-89 (2001)
A minimal model for vorticity and gradient banding in complex fluidsJ.L. Goveas1 and P.D. Olmsted2
1 Department of Chemical Engineering, MS 362 Rice University, 6100 Main Street, Houston, TX 77005, USA
2 Polymer IRC and Department of Physics & Astronomy, University of Leeds, Leeds LS2 9LT, UK
(Received 1 April 2001 and Received in final form 16 June 2001)
A general phenomenological reaction-diffusion model for flow-induced phase transitions in complex fluids is presented. The model consists of an equation of motion for a nonconserved composition variable, coupled to a Newtonian stress relation for the reactant and product species. Multivalued reaction terms allow for different homogeneous phases to coexist with each other, resulting in banded composition and shear rate profiles. The one-dimensional equation of motion is evolved from a random initial state to its final steady state. We find that the system chooses banded states over homogeneous states, depending on the shape of the stress constitutive curve and the magnitude of the diffusion coefficient. Banding in the flow gradient direction under shear rate control is observed for shear-thinning transitions, while banding in the vorticity direction under stress control is observed for shear-thickening transitions.
47.20.Ft - Instability of shear flows.
47.20.Hw - Fluid dynamics: Morphological instability; phase changes.
05.45.-a - Nonlinear dynamics and nonlinear dynamic systems.
05.70.Ln - Nonequilibrium and irreversible thermodynamics.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001