Eur. Phys. J. E 6, 79-89 (2001)
A minimal model for vorticity and gradient banding in complex fluids
J.L. Goveas1 and P.D. Olmsted21 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
jlgoveas@rice.edu
p.d.olmsted@leeds.ac.uk
(Received 1 April 2001 and Received in final form 16 June 2001)
Abstract
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
