Experiments are carried out to explored the co-flows in a type of novel tapered rectanglar PMMA micro-channels. Variations of geometric parameter combinations bring great complexity to systematic descriptions of the co-flow behaviors. We find that the tapered co-flows are self-scaling processes. Based on theory of similitude, a self-similarity frame is buildup to reduce the complexity and dimension of the problem. Under such frame, universal scaling laws covering all the drop-detaching regimes (i.e., slug, dripping, thin jet) are derived, concisely and persuasively. The droplet length depends on the flow-rate-ratio and gives an exponential of nearly $1/2$, which is featured as a typical $\prime$Flow-Rate-Controlled-Flow$\prime$. The drop-detaching frequency depends on the two-phase capillary number and gives an exponential of nearly 3. Note that, these two formulas are valid in all the drop-detaching regimes over differed physical mechanisms. Moreover, the most astonishing thing is that, the former formula reproduce the scaling law of thin jet regime in straight circular co-flows, while the later one reproduce the scaling law of dripping regime in straight circular co-flows at the same time. Such highly consistency of scalings were rarely reported before. Furthermore, the clusters of the flow maps can be degenerated into one single flow diagram under our self-similarity frame. Such diagram can be divided naturally by machining learning into two parts, the Pan-dripping regime and the Pan-jetting regime, which are clear bordered at ${\mathit{We}}_d\approx 1$ and ${\mathit{Ca}}_c\approx 0.28$. These critical values are also consistent with the results in straight circular co-flows. This work can greatly facilitate the design and analysis method of devices for flow manipulation via simple formulas that catch the parameter range of liquid cells.

进行了实验以探索一种新型锥形矩形PMMA微通道中的共流。几何参数组合的变化给顺流行为的系统描述带来了极大的复杂性。我们发现锥形协同流是自缩放过程。基于相似性理论，建立自相似框架以降低问题的复杂性和维数。在这样的框架下，可以简洁而有说服力地推导出涵盖所有液滴分离状态（即段塞、滴落、细射流）的通用比例定律。液滴长度取决于流速比，并给出几乎为$1/2$, 这是一个典型的$\text{'}$流率控制流$\text{'}$. 液滴分离频率取决于两相毛细管数，指数接近 3。请注意，这两个公式在不同物理机制下的所有液滴分离方案中都有效。而且，最令人吃惊的是，前一个公式再现了直线循环顺流中薄射流状态的比例律，而后一个公式同时再现了直线循环顺流中滴水状态的比例律。这种高度一致性的尺度以前很少报道。此外，在我们的自相似框架下，流程图的集群可以退化为一个单一的流程图。这样的图可以通过加工学习自然地分为两部分，泛滴状态和泛喷射状态，它们的边界清晰${\mathit{我们}}_d\approx 1$和${\mathit{钙}}_C\approx 0.28$. 这些临界值也与直线循环协同流的结果一致。这项工作可以通过捕获液体细胞参数范围的简单公式，极大地促进流体操纵装置的设计和分析方法。