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 P{' e}clet number ${\rm Pe}$ on the efficiency of the chemical control of fingering. We show that the viscosity decreasing reaction has an increased stabilizing effect when ${\rm Pe}$ is decreased. On the contrary, fingering is more intense and the system more unstable when ${\rm Pe}$ is increased. The related reactive fingering patterns cover then respectively a smaller (larger) area than in the non-reactive equivalent. Depending on the value of the P{' e}clet number, a given chemical reaction may thus either enhance or suppress a fingering instability. This stabilization and destabilization at low and high ${\rm Pe}$ are shown to be related to the ${\rm Pe}$-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：

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Péclet数对反应性粘性指法的影响

流体动力粘性指法的不稳定性会受到简单的粘度变化类型的化学反应的影响 $\mathrm{一种}+乙\to C$，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，我们在此进行了这种反应性粘性指法的数值研究，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。特别地，我们分析了P {'e} clet数$ {\ rm Pe} $对指法化学控制效率的影响。我们表明，降低$ {\ rm Pe} $时，降低粘度的反应具有增强的稳定作用。相反，当$ {\ rm Pe} $时，指法更加激烈，系统更加不稳定增加。然后，相关的反应性指法图案分别覆盖比非反应性等效物更小的（更大）面积。根据P {e} clet数的值，给定的化学反应因此可以增强或抑制指状不稳定性。低和高$ {\ rm Pe} $时的这种稳定和去稳定作用与与$ {\ rm Pe} $的依赖特性有关，该特性取决于在互溶界面周围形成的最小粘度分布。化学反应。