Stability analysis of finitely extensible viscoelastic subdiffusive flows

The current paper deals with temporal stability analysis of viscoelastic, subdiffusive plane Poiseuille flow by considering Fractional Upper Convected Maxwell (FUCM) model. The analysis employs Finitely Extensible Nonlinear Elastic-Pterlin (FENE-P) model, with the aim of identifying regions where topological transitions occur at the advancing flow interface. A direct correspondence between the power-law exponent, α (0<α<1) in viscoelastic models and the fractional time derivatives, in the continuum non-linear stress constitutive equation, is demonstrated. Graphical analyses are presented specifically for the monomer diffusion in Rouse chain melts and Zimm chain solutions which corresponds to α=1/2 and 2/3, respectively, followed by a detailed discussion of the generalized results. Temporal stability regions are classified by identifying highly energetic and dominant modes, selected based on quantization theory, thereby emphasizing the model's ability to analytically capture the onset and evolution of flow instabilities as observed in experimental studies of subdiffusive flows. The results indicate that a decrease in the value of fractional derivative reduces the magnitude of the most unstable mode and shifts its peak toward lower Reynolds numbers, thereby enhancing temporal stability. Reducing the polymer length also contributes to increased stability while greater elasticity intensifies the most unstable mode, leading to stronger temporal instabilities in viscoelastic subdiffusive media.