[Paper Review] Simultaneous measurement of extensional stress and flow birefringence field for uniaxially extending worm-like micellar solutions

Masakazu Muto, Tatsuya Yoshino+1 more|arXiv (Cornell University)|Apr 26, 2024

Surfactants and Colloidal SystemsChemistry3 citations

TL;DR

This study presents a novel rheo-optical technique combining a liquid dripping method with a high-speed polarization camera to simultaneously measure extensional stress and flow birefringence in uniaxially extending worm-like micellar solutions. The method enables real-time visualization of micelle orientation and confirms a linear stress-optical rule with a stress-optical coefficient comparable under both extensional and shear flows.

ABSTRACT

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.

Motivation & Objective

• To develop a simple, high-resolution rheo-optical technique for simultaneously measuring macroscopic extensional stress and microscopic flow birefringence in complex fluids.
• To investigate the structural deformation and orientation state of worm-like micelles under uniaxial extensional flow.
• To validate the stress-optical rule in uniaxial extensional flow by measuring the stress-optical coefficient.
• To examine the dependence of the stress-optical coefficient on micelle concentration in CTAB/NaSal solutions.

Proposed method

• A liquid dripping method is used to generate uniaxial extensional flow in worm-like micellar solutions by dripping from a nozzle.
• High-speed imaging of the liquid filament's diameter evolution captures temporal extensional stress loading.
• A high-speed polarization camera with a micro-polarization element array enables real-time, high-spatial-resolution imaging of the flow-induced birefringence field.
• Phase retardation and orientation angle are extracted from polarization images using line profiles of light intensity at the filament's minimum radius to avoid curvature-induced scattering.
• The stress-optical coefficient is calculated from the linear relationship between measured extensional stress and birefringence (δn = C(σ∥ − σ⊥)).
• Solutions with varying CTAB and NaSal concentrations are tested to examine concentration dependence of the stress-optical coefficient.

Figure 1: Birefringence induced by a change in the orientation state of worm-like micelles under stress loading. Without stress loading, the worm-like micelles in the solutions have random orientations in the coil state; thus, flow-induced birefringence does not occur. When applying stress to the so

Experimental results

Research questions

• RQ1 Can extensional stress and flow birefringence be simultaneously measured in uniaxially extending worm-like micellar solutions with high temporal and spatial resolution?
• RQ2 Does the stress-optical rule hold under uniaxial extensional flow, and what is the value of the stress-optical coefficient in this regime?
• RQ3 How does the stress-optical coefficient of CTAB/NaSal solutions compare between uniaxial extensional and shear flows?
• RQ4 How does the stress-optical coefficient depend on the concentration of worm-like micelles in the solution?

Key findings

• The proposed technique successfully visualized the temporally evolving birefringence field of uniaxially extending worm-like micellar solutions, revealing micelle orientation along the extensional direction.
• A linear relationship was observed between extensional stress and birefringence, confirming the validity of the stress-optical rule under uniaxial extensional flow.
• The stress-optical coefficient under uniaxial extensional flow was found to be comparable in magnitude to that under shear flow, indicating consistent sensitivity of birefringence to stress across flow types.
• The stress-optical coefficient of CTAB/NaSal solutions varied with CTAB concentration, indicating a dependence on the total amount of worm-like micelles in the solution.
• Filament break-up time increased with higher CTAB/NaSal concentrations, correlating with enhanced structural integrity and prolonged stress loading.
• The analysis area was optimized per magnification to ensure accurate measurement by selecting regions with constant light intensity profiles, minimizing curvature-induced errors.

Figure 2: Conditions of index ellipsoids under (a) shear and (b) uniaxial extensional flows. Here, the major axis ( $n_{\perp}$ ) and minor axis ( $n_{\parallel}$ ) of refractive indices in the index ellipsoid correspond to $n_{y}$ and $n_{x}$ , respectively. $x,y,z$ denote the coordinate system bas