Title: Emergent oscillations and chaos in non-compliant microfluidic networks Show Chinese title

Title: 非顺应性微流控网络中的自发振荡和混沌现象

Abstract: Incompressible fluids in microfluidic networks with non-rigid channels can exhibit flow rate oscillations analogous to electric current oscillations in RLC circuits. This is due to the elastic deformation of channel walls that can store and release fluid, as electric capacitors can store and release electric charges. This property is quantified through the compliance of the system, defined as the volume change relative to the pressure change. In systems with rigid walls and incompressible fluid, compliance vanishes and no oscillations can occur through this mechanism. Here, we show that not only oscillations but also chaos can emerge in the flow-rate dynamics of non-compliant microfluidic networks with incompressible fluid. Notably, these dynamics emerge spontaneously, even under time-independent driving pressures. The underlying mechanism is governed by the effect of fluid inertia, which becomes relevant at moderate Reynolds numbers observed in microfluidic systems exhibiting complex flow patterns. The results are established using a combination of direct numerical simulations and a reduced model derived from modal analysis. This approach enables us to determine the onset of oscillations, the associated bifurcations, the oscillation frequencies and amplitudes, and their dependence on the driving pressures. These findings can inspire novel studies and applications of previously unexplored oscillatory and chaotic regimes in non-compliant microfluidic systems. Show Chinese abstract

Abstract: 不可压缩流体在具有非刚性通道的微流控网络中可以表现出流量振荡，类似于RLC电路中的电流振荡。这是由于通道壁的弹性变形能够储存和释放流体，就像电容器可以储存和释放电荷一样。这一特性通过系统的顺应性来量化，定义为体积变化与压力变化的比值。在具有刚性壁和不可压缩流体的系统中，顺应性消失且不会通过这种机制发生振荡。在这里，我们展示了不仅振荡而且混沌可以在具有不可压缩流体的非顺应性微流控网络的流量动力学中出现。值得注意的是，即使在时间无关的驱动压力下，这些动力学也会自发出现。潜在的机制是由流体惯性的影响所支配的，在微流控系统中观察到的表现出复杂流动模式的中等雷诺数下，流体惯性变得相关。研究结果是通过直接数值模拟和从模态分析推导出的简化模型相结合的方法建立的。这种方法使我们能够确定振荡的发生、相关的分岔、振荡频率和幅度及其对驱动压力的依赖性。这些发现可以启发对以前未探索的振荡和混沌状态的新研究和应用。