  The present study proposes a novel and simple rheo-optical technique to
investigate the relation between the rheology of complex fluids and their
internal structural deformation under uniaxial extensional flow. The macroscale
results of viscoelasticity from rheological measurements and microscale results
of birefringence from optical measurements are combined to evaluate the
microstructural deformation and orientation state inside the fluids under
extensional stress. The proposed technique combines a liquid dripping method
with a high-speed polarization camera to measure the extensional stress and
flow-induced birefringence field simultaneously. In the liquid dripping method,
temporal evolution images of the liquid filament diameter for fluids dripping
from a nozzle are measured to obtain the extensional stress loading on the
liquid filament. These images are captured with a high-speed polarization
camera connected to a micro polarization element alley, enabling high-speed
imaging of the birefringent field. Worm-like micellar solutions of
cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal) with
varying concentrations of CTAB and NaSal are employed as the measurement
targets. Consequently, we successfully visualized temporally developing images
of the birefringence field of uniaxially extending worm-like micellar solutions
induced by the orientation of micelles toward the extensional direction.
Furthermore, the proposed technique supports investigating the conditions for
establishing the stress-optical rule, which is the linear relation between
stress and birefringence for complex fluids. The stress-optical coefficient, a
proportionality constant indicating the sensitivity of birefringence to stress,
is analyzed from these measurements. The stress-optical coefficient under
uniaxial extensional flow is confirmed to be comparable to that under shear
flow.
