论文标题
垂直管道中流动的旋转微生物悬浮液的分叉和稳定性
Bifurcation and stability of downflowing gyrotactic micro-organism suspensions in a vertical pipe
论文作者
论文摘要
In the experiment that first demonstrated gyrotactic behaviour of bottom-heavy swimming microalgae (e.g. Chlamydomonas), Kessler (Nature, vol. 313, 1985, pp. 218-220) showed that a beam-like structure, often referred to as a gyrotactic plume, would spontaneously appear from a suspension of gyrotactic swimmers in a downflowing pipe.这样的羽流很容易形成叶片。这项工作将Gyrotactic Plume作为稳定的平行基本状态，随后将其分解为Blips作为不稳定，采用广义泰勒分散（GTD）理论和Fokker-Planck模型进行比较。解决基本状态后，发现稳定的羽流解决方案会经历复杂的分叉。当没有净流量时，除固定均匀悬浮液以外的羽状结构的非平凡溶液是由于平均细胞浓度的跨临界分叉而导致的。当规定了净下降时，就会存在尖端分叉。此外，存在一个临界浓度，其中中心的细胞浓度会吹出GTD模型。随后使用稳定羽流溶液的稳定性分析表明，Fokker-Planck模型与实验观察到的情况不一致，因为它可以预测在高浓度的高浓度下轴对称BLIP的稳定，并在低流速下首次非轴对称模式的稳定。
In the experiment that first demonstrated gyrotactic behaviour of bottom-heavy swimming microalgae (e.g. Chlamydomonas), Kessler (Nature, vol. 313, 1985, pp. 218-220) showed that a beam-like structure, often referred to as a gyrotactic plume, would spontaneously appear from a suspension of gyrotactic swimmers in a downflowing pipe. Such a plume is prone to an instability to form blips. This work models the gyrotactic plume as a steady parallel basic state and its subsequent breakdown into blips as an instability, employing both the Generalised Taylor Dispersion (GTD) theory and the Fokker-Planck model for comparison. Upon solving for the basic state, it is discovered that the steady plume solution undergoes sophisticated bifurcations. When there is no net flow, there exists a non-trivial solution of the plume structure other than the stationary uniform suspension, stemming from a transcritical bifurcation with the average cell concentration. When a net downflow is prescribed, there exists a cusp bifurcation. Furthermore, there is a critical concentration, at which the cell concentration at the centre would blow up for the GTD model. The subsequent stability analysis using the steady plume solution shows that the Fokker-Planck model is inconsistent with what was experimentally observed, as it predicts stabilisation of axisymmetric blips at high concentration of the plume and destabilisation of the first non-axisymmetric mode at low flow rates.
