The hydrodynamic viscous fingering instability can be influenced by a simple viscosity-changing chemical reaction of type $A+B\to C$, when a solution of reactant $A$ is injected into a solution of $B$ and a product $C$ of different viscosity is formed by reaction. We investigate here numerically such reactive viscous fingering in the case of a reaction decreasing the viscosity to define the optimal conditions on the chemical and hydrodynamic parameters for controlling fingering. In particular, we analyze the influence of the Péclet number, $\mathrm{Pe}$, on the efficiency of the chemical control of fingering. We show that the viscosity-decreasing reaction has an increased stabilizing effect when $\mathrm{Pe}$ is decreased. On the contrary, fingering is more intense and the system more unstable when $\mathrm{Pe}$ is increased. The related reactive fingering patterns cover then respectively a smaller (larger) area than in the nonreactive equivalent. Depending on the value of the Péclet number, a given chemical reaction may thus either enhance or suppress a fingering instability. This stabilization and destabilization at low and high $\mathrm{Pe}$ are shown to be related to the $\mathrm{Pe}$-dependent characteristics of a minimum in the viscosity profile that develops around the miscible interface thanks to the effect of the chemical reaction.

中文翻译：

---

Péclet数对反应性粘性指法的影响

流体动力粘滞指法的不稳定性会受到以下类型的简单变粘度化学反应的影响 $\mathrm{一种}+乙\to C$，当反应物溶液 $\mathrm{一种}$ 被注入到 $乙$ 和一个产品 $C$通过反应形成不同粘度的。在反应降低粘度的情况下，我们在此进行了数值研究，研究了这种反应性粘性指法，以定义用于控制指法的化学和流体动力学参数的最佳条件。特别是，我们分析了佩克利数的影响，$\mathrm{PE}$，关于指法化学控制的效率。我们表明，当降低粘度时，当增加粘度时，稳定作用增加。$\mathrm{PE}$减少。相反，在以下情况下，指法更激烈，系统更不稳定$\mathrm{PE}$增加。然后，相关的反应性指法图案分别覆盖比非反应性等效物更小的（更大）面积。因此，取决于佩克利特数的值，给定的化学反应可能会增强或抑制指法的不稳定性。在高低处的这种稳定和不稳定$\mathrm{PE}$ 显示与 $\mathrm{PE}$由于化学反应的影响，在可混溶界面周围形成的最小粘度分布相关特性。