In the present paper, we provide evidence of the vital impact of inertia on the flow in microfluidic networks, which is disclosed by the appearance of nonlinear velocity–pressure coupling. The experiments and numerical analysis of microfluidic junctions within the range of moderate Reynolds number (1 < Re < 250) revealed that inertial effects are of high relevance when Re > 10. Thus, our results estimate the applicability limit of the linear relationship between the flow rate and pressure drop in channels, commonly described by the so-called hydraulic resistance. Herein, we show that neglecting the nonlinear in their nature inertial effects can make such linear resistance-based approximation mistaken for the network operating beyond Re < 10. In the course of our research, we investigated the distribution of flows in connections of three channels in two flow modes. In the splitting mode, the flow from a common channel divides between two outputs, while in the merging mode, streams from two channels join together in a common duct. We tested a wide range of junction geometries characterized by parameters such as: (1) the angle between bifurcating channels (45°, 90°, 135° and 180°); (2) angle of the common channel relative to bifurcating channels (varied within the available range); (3) ratio of lengths of bifurcating channels (up to 8). The research revealed that the inertial effects strongly depend on angles between the channels. Additionally, we observed substantial differences between the distributions of flows in the splitting and merging modes in the same geometries, which reflects the non-reversibility of the motion of an inertial fluid. The promising aspect of our research is that for some combinations of both lengths and angles of the channels, the inertial contributions balance each other in such a way that the equations recover their linear character. In such an optimal configuration, the dependence on Reynolds number can be effectively mitigated.

在本文中，我们提供了惯性对微流体网络中流动的重要影响的证据，非线性速度-压力耦合的出现揭示了这一点。在中等雷诺数（1 <Re <250）范围内的微流体连接的实验和数值分析表明，当Re> 10时，惯性效应具有很高的相关性。因此，我们的结果估计了流体之间线性关系的适用极限速率和通道中的压降，通常用所谓的水力阻力来描述。在这里，我们表明，忽略非线性本质上的惯性效应会使基于线性电阻的近似误认为是在Re <10以外的网络中工作。在我们的研究过程中，我们研究了两种流动模式下三个通道连接处的流动分布。在分流模式下，来自公共通道的流量在两个输出之间分配，而在合并模式下，来自两个通道的流在公共管道中汇聚在一起。我们测试了各种以参数为特征的结几何形状：（1）分叉通道之间的角度（45°，90°，135°和180°）；（2）公共通道相对于分叉通道的角度（在可用范围内变化）；（3）分叉通道的长度之比（最大为8）。研究表明，惯性效应很大程度上取决于通道之间的角度。此外，我们观察到在相同几何形状的分裂和合并模式下，流量分布之间存在实质性差异，这反映了惯性流体运动的不可逆性。我们研究的有希望的方面是，对于通道长度和角度的某些组合，惯性贡献相互平衡，以使方程式恢复其线性特征。在这样的最佳配置中，可以有效地减轻对雷诺数的依赖性。