This work considers the displacement of a resident fluid in a radial Hele-Shaw cell by an invading low viscosity fluid driven by time-dependent injection rates. Finger formation in the circular interface through a sequence of bifurcations may be minimized by the optimal choice of a time-dependent injection rate. Approximate solutions of fluid equations predict how bifurcations can be suppressed or strongly reduced. Based on a computational fluid-dynamic approach, the magnitude of the fluctuations of invading interface is numerically evaluated, leading to the identification of the optimal parameter choice for any injection rate family. The combination of two time-dependent injection rates is investigated, where one decreases as a power-law and the second increases linearly. Results for a well tuned change between the two regimes reduce the injection time as compared to those based on a single rate whole process, with similar or reduced effects on interface fluctuations.

中文翻译：

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径向 Hele-Shaw 单元中粘性指的优化控制

这项工作考虑了由随时间变化的注入速率驱动的侵入低粘度流体对径向 Hele-Shaw 单元中的驻留流体的置换。通过一系列分叉在圆形界面中形成的指状物可以通过最佳选择与时间相关的注入速率来最小化。流体方程的近似解可以预测如何抑制或强烈减少分岔。基于计算流体动力学方法，对侵入界面的波动幅度进行数值评估，从而确定任何注入速率系列的最佳参数选择。研究了两种与时间相关的喷射率的组合，其中一个随着幂律而减小，第二个线性增加。