Stretching vs. Shearing
While shear flow slides fluid layers past each other, extensional flow stretches material elements along one direction and compresses them along others. This seemingly simple difference has profound consequences for polymer solutions: in shear, flexible chains tumble and partially align but remain largely coiled; in extension, chains are pulled from both ends and can unravel dramatically. The result is extensional viscosities that can exceed shear viscosities by factors of 1000 or more — a phenomenon with enormous implications for processing.
The Coil-Stretch Transition
De Gennes predicted that at a critical strain rate, polymer chains would undergo an abrupt conformational change from random coils to nearly fully extended states. This coil-stretch transition occurs when the Weissenberg number Wi = λ_r × ε̇ exceeds approximately 0.5 — the extensional deformation rate overwhelms the chain's relaxation. The simulation visualizes this transition as a sharp rise in extensional viscosity and an animated representation of chain conformation.
Filament Thinning
One of the most elegant ways to measure extensional properties is the capillary breakup extensional rheometer (CaBER). A fluid bridge is stretched between two plates, and the midpoint diameter is tracked as the filament thins under capillary pressure. For polymer solutions, the filament thins exponentially rather than linearly, with a time constant equal to three times the relaxation time. This simulation shows the filament profile and diameter evolution in real time as you adjust polymer parameters.
Processing Impact
Extensional flow dominates many industrial processes: converging flows into fiber-spinning dies, inflation of polymer film bubbles, atomization of inkjet droplets, and turbulent drag reduction in pipelines. The strain-hardening behavior of polymer solutions prevents filament breakup during fiber spinning (producing uniform fibers) and suppresses droplet formation during spraying. Understanding and controlling extensional rheology is essential for designing processes that exploit — or avoid — these dramatic viscoelastic effects.