"Stretched Polymer Physics, Elasticity, and Extensional Rheology: Influence of Charge, Flexibility and Extensibility"
Stringiness, stickiness and dispensing behavior of complex fluids is often assessed qualitatively by stretching a liquid bridge between two surfaces (say thumb and forefinger), and observing the pinch-off time. The handy tactile test involves complex free-surface flows including the formation of columnar neck that undergoes spontaneous capillary-driven instability, thinning and pinch-off. Liquid transfer and drop formation/deposition processes associated with printing, spraying, atomization and coating flows involve similar neck formation, thinning and pinch-off. For simple (Newtonian and inelastic) fluids, a complex interplay of capillary, inertial and viscous stresses determines the neck thinning dynamics. In rheologically complex fluids, extra elastic stresses as well as non-Newtonian shear and extensional viscosities dramatically alter the pinchoff dynamics. Stream-wise velocity gradients that arise within the thinning columnar neck create an extensional flow field, and many complex fluids exhibit a much larger resistance to elongational flows than Newtonian fluids with similar shear viscosity. Characterization of extensional viscosity, extensional relaxation time and finite extensibility effects, as well as macromolecular properties that determine pinch-off dynamics are beyond capabilities of conventional shear and extensional rheology techniques in which free surface flows are absent. Here we show that dripping-onto-substrate (DoS) rheometry protocols we developed recently can be used for measuring extensional viscosity and extensional relaxation time of polymeric complex fluids, including low viscosity printing inks and polymer solutions that are beyond the measurable range of commercially-available capillary break-up extensional rheometer (CaBER). Using DoS rheometry protocols that involve visualization and analysis of capillary-driven thinning and pinch-off dynamics of a columnar neck formed between a nozzle and a sessile drop, we characterize the pinch-off dynamics and extensional rheology of solutions of three model polyelectrolytes poly(sodium 4-styrenesulfonate) (NaPSS), poly(acrylic acid) (PAA) and sodium carboxymethylcellulose (NaCMC) in different solvents and salt concentrations. Unlike shear relaxation time that decreases with increase in concentration in the unentangled, semidilute solutions, the extensional relaxation time of salt-free PAA solutions increases with an exponent of 1/2, and the entangled semidilute solutions also exhibit a stronger concentration dependence of 3/2. In contrast, the extensional relaxation time is not measurable for the unentangled, semidilute aqueous NaPSS solutions, though entangled NaPSS solutions show concentration-dependent values. We analyze the shear and extensional rheology response for all three olyelectrolytes as a function of solvent and salt concentration, and elucidate the influence of both electrostatic and hydrodynamic stretching of macromolecules on stickiness, printability, jettability and overall
processability.
