Micro-scale extensional rheometry using hyperbolic converging/diverging channels and jet breakup

Understanding the elongational rheology of dilute polymer solutions plays an important role in many biological and industrial applications ranging from microfluidic lab-on-a-chip diagnostics to phenomena such as fuel atomization and combustion. Making quantitative measurements of the extensional viscosity for dilute viscoelastic fluids is a long-standing challenge and it motivates developments in microfluidic fabrication techniques and high speed/strobe imaging of millifluidic capillary phenomena in order to develop new classes of instruments. In this paper, we study the elongational rheology of a family of dilute polymeric solutions in two devices: first, steady pressure-driven flow through a hyperbolic microfluidic contraction/expansion and, second, the capillary driven breakup of a thin filament formed from a small diameter jet ( D j ∼ O ( 100 μ m ) ). The small length scale of the device allows very large deformation rates to be achieved. Our results show that in certain limits of low viscosity and elasticity, jet breakup studies offer significant advantages over the hyperbolic channel measurements despite the more complex implementation. Using our results, together with scaling estimates of the competing viscous, elastic, inertial and capillary timescales that control the dynamics, we construct a dimensionless map or nomogram summarizing the operating space for each instrument.