Cessation of flows of a viscoplastic medium in channels.

*(English. Russian original)*Zbl 1337.76001
Dokl. Phys. 55, No. 1, 39-42 (2010); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 430, No. 3, 326-329 (2010).

From the introduction: An important qualitative feature of the problems on the time-dependent motion of viscous-plastic media is the finiteness of the damping time of the motion in the absence of external forces. This is a distinction of kind from the corresponding flow of the viscous liquid, which damps exponentially for an infinitely long time. One of the most important problems of interest from both the theoretical and practical viewpoints is the flow in a channel. In this work, we carried out mathematical modeling of the cessation process for different transverse sections and investigated the evolution of rigid zones and the dependence of the stopping time on the internal parameters of the medium and cross-section geometry. We found a previously unknown qualitative feature, namely, the appearance of stagnant zones in the course of stopping, which completely or partially surround the boundary contour depending on the shape of the channel section.

##### MSC:

76A05 | Non-Newtonian fluids |

74C10 | Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity) |

76D99 | Incompressible viscous fluids |

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

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\textit{L. V. Muravlëva} and \textit{E. A. Muravlëva}, Dokl. Phys. 55, No. 1, 39--42 (2010; Zbl 1337.76001); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 430, No. 3, 326--329 (2010)

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