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Lattice Boltzmann simulation reveals supercritical bifurcation in flow mode transitions of power-law fluids in the four-roll mill by Yu, Yuan; Jiang, Xiao; Gu, Qingqing; Lin, Chuandong; Zhu, Qingyong; Yuan, Hai-zhuan is a scholarly article available to read on EtoBox.

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The four-roll mill has been traditionally viewed as a device generating simple extensional flow with a central stagnation point. Our systematic investigation using a two-relaxation-time regularized lattice Boltzmann (TRT-RLB) model reveals unexpected richness in the flow physics, identifying two previously unreported supercritical bifurcation modes: a quadrifoliate vortex mode featuring four symmetrical counter-rotating vortices, and a dumbbell-shaped quad-vortex mode where vortices detach from but remain symmetric about the stagnation point. The numerical framework, representing the first successful extension of TRT-RLB method to power-law fluid dynamics, enables comprehensive mapping of flow characteristics across Reynolds numbers ($1 \leq Re \leq 50$), power-law indices ($0.7 \leq n \leq 1.3$), and geometric configurations. The transition from quadrifoliate vortex mode exhibits distinct pathways depending on the power-law index: at relatively small $n$, the flow undergoes a direct supercritical bifurcation to simple extensional flow, while at relatively large $n$, it evolves through an intermediate dumbbell-shaped state. Among geometric parameters, the roller radius $r$ emerges

Author

Yu, Yuan; Jiang, Xiao; Gu, Qingqing; Lin, Chuandong; Zhu, Qingyong; Yuan, Hai-zhuan

Published

2025

Language

EN