  The hydrodynamic viscous fingering instability can be influenced by a simple
viscosity changing chemical reaction of type A+B --> C, when a solution of
reactant A is injected into a solution of B and a product C of different
viscosity is formed. 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 injection flow rate
or equivalently of the Peclet number (Pe) of the problem on the efficiency of
the chemical control of fingering. We show that the viscosity decreasing
reaction has an increased stabilizing effect when Pe is decreased. On the
contrary, fingering is more intense and the system more unstable when 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 flow rate, a given chemical reaction may thus either enhance or
suppress a fingering instability. This stabilization and destabilization at low
and high Pe are shown to be related to the Pe-dependent characteristics of a
minimum in the viscosity profile that develops around the miscible interface
thanks to the effect of the chemical reaction.
