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- W4387323909 abstract "The motion of a freely rotating prolate spheroid in a simple shear flow of a dilute polymeric solution is examined in the limit of large particle aspect ratio, $kappa$. A regular perturbation expansion in the polymer concentration, $c$, a generalized reciprocal theorem, and slender body theory to represent the velocity field of a Newtonian fluid around the spheroid are used to obtain the $mathcal{O}(c)$ correction to the particle's orientational dynamics. The resulting dynamical system predicts a range of orientational behaviors qualitatively dependent upon $ccdot De$ ($De$ is the imposed shear rate times the polymer relaxation time) and $kappa$ and quantitatively on $c$. At a small but finite $ccdot De$, the particle spirals towards a limit cycle near the vorticity axis for all initial conditions. Upon increasing $kappa$, the limit cycle becomes smaller. Thus, ultimately the particle undergoes a periodic motion around and at a small angle from the vorticity axis. At moderate $ccdot De$, a particle starting near the flow-gradient plane departs it monotonically instead of spirally, as this plane (a limit cycle at smaller $ccdot De$) obtains a saddle and an unstable node. The former is close to the flow direction. Upon further increasing $ccdot De$, the saddle-node changes to a stable node. Therefore, depending upon the initial condition, a particle may either approach a periodic orbit near the vorticity axis or obtain a stable orientation near the flow direction. Upon further increasing $ccdot De$, the limit cycle near the vorticity axis vanishes, and the particle aligns with the flow direction for all starting orientations." @default.
- W4387323909 created "2023-10-04" @default.
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- W4387323909 date "2023-10-01" @default.
- W4387323909 modified "2023-10-14" @default.
- W4387323909 title "Rotation of a fiber in simple shear flow of a dilute polymer solution" @default.
- W4387323909 doi "https://doi.org/10.48550/arxiv.2310.00792" @default.
- W4387323909 hasPublicationYear "2023" @default.
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