IPR, UMR CNRS 6251, Campus Beaulieu, Université Rennes 1, 35042 Rennes, France.
Phys Rev Lett. 2010 Oct 8;105(15):154501. doi: 10.1103/PhysRevLett.105.154501. Epub 2010 Oct 5.
The binary path selection of droplets reaching a T junction is regulated by time-delayed feedback and nonlinear couplings. Such mechanisms result in complex dynamics of droplet partitioning: numerous discrete bifurcations between periodic regimes are observed. We introduce a model based on an approximation that makes this problem tractable. This allows us to derive analytical formulae that predict the occurrence of the bifurcations between consecutive regimes, establish selection rules for the period of a regime, and describe the evolutions of the period and complexity of droplet pattern in a cycle with the key parameters of the system. We discuss the validity and limitations of our model which describes semiquantitatively both numerical simulations and microfluidic experiments.
液滴到达 T 形交叉口时的二进制路径选择受时滞反馈和非线性耦合的调节。这些机制导致液滴分配的复杂动力学：观察到许多周期性状态之间的离散分岔。我们引入了一种基于近似的模型，使这个问题变得可行。这使我们能够推导出分析公式，预测连续状态之间分岔的发生，为状态的周期建立选择规则，并描述在系统的关键参数下，一个周期内的周期和液滴图案复杂性的演变。我们讨论了我们的模型的有效性和局限性，该模型对数值模拟和微流控实验进行了半定量描述。
