This paper proposes a theoretical framework to analyze the long-term stability of affine solutions in viscoelastic flows governed by Oldroyd-B models. It introduces a perturbation analysis, unifying linear and nonlinear stability, and establishes conditions for asymptotic stability.
Key findings
Affine solutions provide analytical benchmarks for viscoelastic fluid dynamics.
Stability characteristics of affine solutions are poorly understood, especially at high Weissenberg numbers.
A novel perturbation analysis decomposes stress tensor into affine and non-affine components.
The approach connects Hadamard ill-posedness with physical instability mechanisms.
Identifies key dimensionless parameters governing stability transitions.
Limitations & open questions
The study focuses on Oldroyd-B models and may not generalize to all viscoelastic fluids.
The analysis primarily addresses theoretical aspects with computational validation needed for broader applicability.