Influence of a chemical reaction on viscous fingering: Effect of the injection flow rate

TL;DR

This study numerically examines how a viscosity-changing chemical reaction influences viscous fingering during fluid injection, revealing that lower Peclet numbers stabilize the system while higher ones promote instability, depending on flow conditions.

Contribution

It demonstrates how a viscosity decreasing chemical reaction can control viscous fingering by analyzing the effects of injection flow rate and Peclet number on pattern stability.

Findings

Lower Peclet numbers stabilize fingering patterns.

Higher Peclet numbers increase fingering instability.

Chemical reactions can either suppress or enhance fingering depending on flow conditions.

Abstract

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.