CaBER vs ROJER - Different time scales for the thinning of a weakly elastic jet

In this paper, we demonstrate that the capillary thinning dynamics of a weakly viscoelastic jet follow a different timescale than a liquid bridge of the same fluid between two stationary surfaces for similar geometrical scales. The thinning in the latter case observed with capillary breakup extensional rheometry (or CaBER) follows a well established scaling of the radius with time for an elasto-capillary (EC) balance of R ∼ exp (- t / 3 λ). However, for the thinning of the filaments between droplets in a jet, it was so far just assumed that the same scaling law holds. In this paper, we experimentally demonstrate that the jet thinning in a Rayleigh-Ohnesorge jetting extensional rheometer (or ROJER) follows a different scaling of R ∼ exp (- t / 2 λ). This is demonstrated by a direct comparison of the thinning dynamics of weakly viscoelastic (O h < 0.01) aqueous solutions of polyethylene oxide in the two experimental setups, covering a wide range of jetting velocities or Weber numbers of 1-70. We demonstrate outgoing from a momentum balance that includes inertia and elasticity that this difference in scaling is due to a constant axial tension in the jet arising from the constant creation rate of new surface at the nozzle. Numerical simulations using the FENE-P model support this theory and demonstrate that in the exponential thinning regime of the jet the elastic stresses are indeed balanced by the axial tension (rather than by capillary pressure as in the EC balance regime of the CaBER experiment). It is readily shown from the reduced stress balance that this axial-elastic balance regime in the ROJER experiment leads to a faster exponential thinning, following the new scaling of R ∼ exp (- t / 2 λ) that was experimentally observed. Furthermore, we observe both in experiment and simulation that a jet thinning does not exhibit a self-similar structure of the corner region where the thinning filament connects to the drop as it is generally observed for a filament with an axial tension decaying with the filament radius as in the CaBER. The resulting difference of 50% in extensional relaxation time λ extracted from ROJER experiments might require one to revisit previously reported ROJER experiments and is required for the correct evaluation of future jetting rheometry experiments.