(535c) Mechanistic Constitutive Model for Wormlike Micelle Solutions with Flow-Induced Structure Formation
AIChE Annual Meeting
2017
2017 Annual Meeting
Engineering Sciences and Fundamentals
Complex Fluids: Self & Directed Assembly
Wednesday, November 1, 2017 - 1:00pm to 1:15pm
We present a tensor constitutive model for predicting stress and flow-induced
structure formation in dilute wormlike micellar solutions. The micellar
solution is treated as a dilute suspension of rigid Brownian rods whose length
varies dynamically. Consistent with the mechanism presented by Turner and
Cates [J. Phys.:Condens. Matter 4, 3719 (1992)], flow-induced alignment of
the rods is assumed to promote increase of rod length that corresponds to the
formation of flow-induced structures observed in experiments. At very high
deformation rate, hydrodynamic stresses causes the rod length to decrease.
These mechanisms are implemented in a phenomenological equation governing the
evolution of rod length, with the number density of rods appropriately
modified to ensure conservation of surfactant mass. The model leads first to
an increase in both shear and extensional viscosity as deformation rate
increases and then to a decrease at higher rates. If the rate constant for
flow-induced rod growth is sufficiently large, the model predicts a
multivalued relation between stress and deformation rate in both shear and
uniaxial extension. Predictions for shear and extensional flow at steady
state are in reasonable agreement with experimental results. The model is
simple enough to serve as a tractable constitutive relation for computational fluid dynamics studies.
structure formation in dilute wormlike micellar solutions. The micellar
solution is treated as a dilute suspension of rigid Brownian rods whose length
varies dynamically. Consistent with the mechanism presented by Turner and
Cates [J. Phys.:Condens. Matter 4, 3719 (1992)], flow-induced alignment of
the rods is assumed to promote increase of rod length that corresponds to the
formation of flow-induced structures observed in experiments. At very high
deformation rate, hydrodynamic stresses causes the rod length to decrease.
These mechanisms are implemented in a phenomenological equation governing the
evolution of rod length, with the number density of rods appropriately
modified to ensure conservation of surfactant mass. The model leads first to
an increase in both shear and extensional viscosity as deformation rate
increases and then to a decrease at higher rates. If the rate constant for
flow-induced rod growth is sufficiently large, the model predicts a
multivalued relation between stress and deformation rate in both shear and
uniaxial extension. Predictions for shear and extensional flow at steady
state are in reasonable agreement with experimental results. The model is
simple enough to serve as a tractable constitutive relation for computational fluid dynamics studies.