Flexible non-Brownian filament in intensified shear flow

The behavior of a three-dimensional, non-Brownian flexible filament in a low Reynolds number shear flow was investigated through theoretical and numerical analyses. In the phase plane with Reynolds number Re∈[0.03,8] and flow intensity Z∈[800,35 000], four primary motion modes of the filament were identified: rigid, C-buckling, U-turn, and S-turn. By employing the principle of symmetry, a theoretical model was developed to explain the S-turn mode, and we discovered that the critical flow strength for the transition from U-turn to S-turn was approximately Zc=4900. Our numerical simulations confirmed this transition value. In a system devoid of thermal fluctuations, it was observed that the mode transitions of microscale filament precisely corresponded to the abrupt scale rate changes in the non-Newtonian behavior of the macroscopic solution. Although the polymer stress under different modes has distinct underlying causes, they can all be predicted by the generalized Hooke's law.