Free surface oscillation driven by rotating stirrer

IF 1.8 4区物理与天体物理 Q4 CHEMISTRY, PHYSICAL

The European Physical Journal E Pub Date : 2024-04-13 DOI:10.1140/epje/s10189-024-00420-z

Tomoaki Watamura, Reiji Iwata, Kazuyasu Sugiyama

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Abstract

To gain insights into the mechanisms of free surface oscillation in a rotating mixing container, we observe the free surface deformation and measure the torque acting on the bar. The container was half-filled with liquids. Periodic surface oscillation occurs. At the rotational speed where the amplitude of the oscillation reaches its maximum, the time-averaged torque also takes the local maximum values. To account for the sloshing mechanism, an equation of motion is derived using the Lagrangian mechanics; we found that the sloshing occurs when the collision frequency of bar on the surface is consistent with the natural frequency of the system and the damping coefficient is sufficiently smaller than unity. The time-averaged torque increases when the sloshing becomes violent. We conclude that the hydrodynamics of oscillation is successfully modeled using point-mass mechanics, and thus we can reasonably capture the rotation speed at which violent oscillation occurs.

Free surface deformation driven by the rotating arm in the cylindrical container which is half-filled with liquids

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由旋转搅拌器驱动的自由表面摆动

摘要为了深入了解旋转混合容器中自由表面振荡的机理，我们观察了自由表面的变形并测量了作用在杆上的扭矩。容器中装有一半液体。表面发生周期性振荡。在振荡振幅达到最大值的转速处，时间平均扭矩也达到局部最大值。我们发现，当棒材在表面的碰撞频率与系统的固有频率一致，且阻尼系数足够小于 1 时，就会发生荡动。当荡动变得剧烈时，时间平均扭矩会增加。我们得出结论，利用点质量力学成功地模拟了振荡的流体力学，因此我们可以合理地捕捉到发生剧烈振荡时的旋转速度。图解摘要在装有一半液体的圆柱形容器中，旋转臂驱动自由表面变形

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来源期刊

The European Physical Journal E CHEMISTRY, PHYSICAL-MATERIALS SCIENCE, MULTIDISCIPLINARY

CiteScore

2.60

自引率

5.60%

发文量

审稿时长

3 months

期刊介绍： EPJ E publishes papers describing advances in the understanding of physical aspects of Soft, Liquid and Living Systems. Soft matter is a generic term for a large group of condensed, often heterogeneous systems -- often also called complex fluids -- that display a large response to weak external perturbations and that possess properties governed by slow internal dynamics. Flowing matter refers to all systems that can actually flow, from simple to multiphase liquids, from foams to granular matter. Living matter concerns the new physics that emerges from novel insights into the properties and behaviours of living systems. Furthermore, it aims at developing new concepts and quantitative approaches for the study of biological phenomena. Approaches from soft matter physics and statistical physics play a key role in this research. The journal includes reports of experimental, computational and theoretical studies and appeals to the broad interdisciplinary communities including physics, chemistry, biology, mathematics and materials science.