Drop breakup dynamics of dilute polymer solutions: Effect of molecular weight, concentration, and viscosity

The large extensional viscosity of dilute polymer solutions has been shown to dramatically delay the breakup of jets into drops. For low shear viscosity solutions, the jet breakup is initially governed by a balance of inertial and capillary stresses before transitioning to a balance of viscoelastic and capillary stresses at later times. This transition occurs at a critical time when the radius decay dynamics shift from a 2/3 power law to an exponential decay as the increasing deformation rate imposed on the fluid filament results in large molecular deformations and rapid crossover into the elasto-capillary regime. By experimental fits of the elasto-capillary thinning diameter data, a relaxation time of less than 100 μs has been successfully measured. In this paper, we show that, with a better understanding of the transition from the inertia-capillary to the elasto-capillary breakup regime, relaxation times close to 10 μs can be measured with the relaxation time resolution limited only by the frame rate and spatial resolution of the high speed camera. In this paper, the dynamics of drop formation and pinch-off are presented using dripping onto substrate capillary breakup extensional rheometry (CaBER-DoS) for a series of dilute solutions of polyethylene oxide (PEO) in water and in a viscosified water and glycerin mixture. Four different molecular weights between 100 k and 1 M g/mol were studied with varying solution viscosities between 1 and 22 mPa s and at concentrations between 0.004 and 0.5 times the overlap concentration, c*. The dependence of the relaxation time and extensional viscosity on these varying parameters was studied and compared to the predictions of dilute solution theory while simultaneously searching for the lower limit in solution elasticity that can be detected. For PEO in water, this limit was found to be a fluid with a relaxation time of roughly 20 μs. These results confirm that CaBER-DoS can be a powerful technique characterizing the rheology of a notoriously difficult material to quantify, namely, low viscosity inkjet printer inks.