Numerical study on nonmonotonic fingering dynamics against flow rate for a reactive viscous fingering with Marangoni convection

When a displacing fluid is less viscous than a displaced one, the interface of two fluids gives a finger-like pattern in porous media. This phenomenon is called Saffman-Taylor instability or viscous fingering(VF). There have been many experimental studies on the VF that surfactants produced at the interface. A previous experimental study (Tsuzuki et al., Phys. Fluids, 31, 022102 (2019)) showed a nonmonotonic behavior of finger width against flow rate. At low flow rates, the fingers were thinner in the reactive system than those in the non-reactive system. At high flow rates, the non-reactive system and reactive system showed almost similar finger width patterns. However, at intermediate flow rates, the reactive system showed a more circular pattern than that in the non-reactive system, i.e. wider fingers in reactive system than in non-reactive system. Some simulation studies (Tsuzuki et al., Phys. Rev. Fluids, 4, 104003 (2019)) tried to reproduce the experimental results but failed. Therefore, in this study, we simulated such VF by producing surfactant at the interface with the Marangoni convection term. The numerical results have successfully shown the similar dynamics i.e. non-monotonic behavior against nondimensional number, which represents a flow rate.