2026-05-31T14:57:30Zhttps://riuma.uma.es/rest/oai/request

oai:riuma.uma.es:10630/358942026-02-03T11:27:52Zcom_10630_2254col_10630_37953

Three dimensional viscoelastic instabilities in a four-roll mill geometry at the Stokes limit. Gutiérrez-Castillo, Paloma Kagel, Adam Thomases, Becca Stokes, Teorema de Three-dimensional numerical simulations of viscoelastic fluids in the Stokes limit with a four-roll mill background force (extended to the third dimension). Both the Oldroyd-B model and FENE-P model of viscoelastic fluids were used. Different temporal behaviors were observed depending on the Weissenberg number (non-dimensional relaxation time), model, and initial conditions. Temporal dynamics evolve on long time scales and simulations were accelerated by using a Graphics Processing Unit (GPU). Previously, parameter explorations and long-time simulations in 3D were prohibitively expensive. For small Weissenberg number, all the solutions are constant in the third dimension, displaying strictly two-dimensional temporal evolutions. However, for sufficiently large Weissenberg number, three-dimensional instabilities were observed, creating complex temporal behaviors. In some of the cases, the instability that first emerges is two-dimensional (in the x; y plane), and then the solution develops an instability in the z-direction whereas in others the z instability comes first. Using a linear perturbation from a steady two-dimensional background solution, extended to three dimensions as constant in the third dimension, it is demonstrated that there is a linear instability for sufficiently large Weissenberg number, and possible mechanisms for this instability are discussed. 2025-01-07T12:18:25Z 2025-01-07T12:18:25Z 2025-01-07T12:18:25Z 2020 journal article P. Gutierrez-Castillo, A. Kagel and B. Thomases. Three dimensional viscoelastic instabilities in a four- roll mill geometry at the Stokes limit., Physics of Fluids, Vol.32, Issue 2, 2020. https://hdl.handle.net/10630/35894 10.1063/1.5134927 eng open access American Institute of Physics