Reduced modelling and global instability of finite-Reynolds-number flow in compliant rectangular channels
Reduced modelling and global instability of finite-Reynolds-number flow in compliant rectangular channels
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DOI：
10.1017/jfm.2022.802
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发表时间：
2022-02
影响因子：
3.7
通讯作者：
Xiaojia Wang;I. Christov
中科院分区：
文献类型：
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作者：
Xiaojia Wang;I. Christov
摘要实验表明，柔性微通道中的流动在比刚性管道中的相应流动低得多的雷诺数下会变得不稳定。因此，有人建议，壁的弹性顺应性，可以利用对新的模式的微尺度混合。虽然以前的研究主要集中在局部不稳定性引起的流体-结构相互作用（FSI）在系统中，我们推导出一个一维（1-D）模型来研究FSI的整体不稳定性的影响。建议的1-D FSI模型是专门为长，浅的矩形微通道与可变形的顶壁，类似的实验。超越通常的润滑流动分析，在这些几何形状，我们包括有限的流体惯性和耦合的减少流量方程到一个新的减少1-D壁变形方程。虽然与以前的实验进行定量比较是困难的，所提出的模型的行为显示，定性，与实验观察，并捕捉几个关键的影响。具体地说，我们找到了1-D FSI模型的膨胀基态对无穷小扰动线性不稳定的临界条件。临界雷诺数的预测与实验观察。不稳定模式是高度振荡的，频率接近壁的固有频率，这表明所观察到的不稳定性是共振现象。此外，在从未变形的初始状态启动期间，FSI可以触发自持振荡。我们的建模框架可以应用到其他微流体系统在不同的操作条件下具有类似的几何尺度分离。
Abstract Experiments have shown that flow in compliant microchannels can become unstable at a much lower Reynolds number than the corresponding flow in a rigid conduit. Therefore, it has been suggested that the wall's elastic compliance can be exploited towards new modalities of microscale mixing. While previous studies mainly focused on the local instability induced by the fluid–structure interactions (FSIs) in the system, we derive a one-dimensional (1-D) model to study the FSI's effect on the global instability. The proposed 1-D FSI model is tailored to long, shallow rectangular microchannels with a deformable top wall, similar to the experiments. Going beyond the usual lubrication flows analysed in these geometries, we include finite fluid inertia and couple the reduced flow equations to a novel reduced 1-D wall deformation equation. Although a quantitative comparison with previous experiments is difficult, the behaviours of the proposed model show, qualitatively, agreement with the experimental observations, and capture several key effects. Specifically, we find the critical conditions under which the inflated base state of the 1-D FSI model is linearly unstable to infinitesimal perturbations. The critical Reynolds numbers predicted are in agreement with experimental observations. The unstable modes are highly oscillatory, with frequencies close to the natural frequency of the wall, suggesting that the observed instabilities are resonance phenomena. Furthermore, during the start-up from an undeformed initial state, self-sustained oscillations can be triggered by FSI. Our modelling framework can be applied to other microfluidic systems with similar geometric scale separation under different operating conditions.