Comment on "Note on the start-up of Couette flow for viscoelastic fluids" [Phys. Fluids 35, 113108 (2023)]

Abstract

I show that the initial conditions imposed by Balan [Phys. Fluids 35, 113108 (2023)] are incompatible with a nonzero retardation time, so that the problem solved is not impulsive start-up, but, as I prove exactly, the start-up of a plate ramped as $1-{\mathrm{e}}^{-t/{\lambda }_2}$ on the retardation timescale ${\lambda }_2$ (a material parameter, not a setting in a rheometer). Values digitized from that paper's viscoelastic figures fall on the ramped-plate solution, not on Tanner's start-up solution. The large negative wall normal stress reported for the corotational model is a grid-dependent artifact due to the same error in the initial data. An open-source code repository provides annotated notebooks reproducing every figure and number in this Comment.

4 pages, 1 figure. Comment on Phys. Fluids 35, 113108 (2023). v2: notation clarified; code repository updated to v1.1.0: https://doi.org/10.5281/zenodo.23005137