On the detection, measurement, and characterization of slip-velocity in Couette-rheology involving viscoelastic liquids

Abstract

We present a robust calculation leading to experimentally convenient and accurate ways of detecting, measuring, and characterizing velocity-slippage in viscoelastic-fluids, unlike previous inaccurate Mooney-type techniques. Herein, the unsteady Navier-Stokes equation for viscoelastic-fluid is solved while highlighting the rheological ramification. Our results emphasize phase-lags amongst shear stresses and strains, key output used in differing slip-types. The viscoelastic fluid is non-aging and isothermal, and we obtain an exact solution of the non-trivial flow profile, without assuming a linear Couette profile as customarily used. Moreover, the Navier-type slip boundary condition is considered. This approach is similar to that done in our earlier paper [Azese, “Measurement and characterization of slippage and slip-law using a rigorous analysis in dynamics of oscillating rheometer: Newtonian fluid,” Phys. Fluids 30, 023103 (2018)] where instead it was a Newtonian fluid. Accordingly, the sample fluid is trapped in the Couette-gap, where one of them is stationary and the other is steadily oscillating with an amplitude Re (Reynolds-number) and angular speed Ω = Ro (Roshko number), thus Couette-rheometry. We showcase an alternative way to obtain a steady-periodic solution, matching the long-time solution obtained in our earlier paper. We obtain the unsteady solution for this viscoelastic case and also use the alternative method to obtain the steady-periodic version, later used in obtaining the velocity and stress at the walls. Interestingly, we note the influence of Re, Ro, and Wi (Weissenberg Number) on this analysis. The equations and plots presented evidently show the influence of the slip. We conclude with reverse algorithms, Fourier-transform, Lissajous-figures, and Mooney-like procedures, capable of reproducing the slip-parameters, leading to a systematic measurement-and-characterization of the slip, useful in the calibration of rheological devices.