Abstract:
Viscous fingering or Saffman–Taylor instability shows fingering interfacial patterns when
a more mobile fluid displaces a less mobile one in porous media. The effective interfacial
tension (EIT) is like capillary force, acting at the miscible interface on time scales shorter
than interface relaxation. It has been numerically reported so far that the fingers are
wider with EIT compared with those without EIT. A recent experiment observed finger
widening with increasing flow rate in a miscible system with EIT, which is not observed in
classical immiscible and miscible systems. In this study, we have numerically investigated
the effect of Pe (which corresponds to the injection flow rates in the experiment)
on miscible viscous fingering with/without EIT. We have shown that the fingers are
monotonically thinner with an increase in Pe in the system without EIT, while finger
widening with increasing Pe is observed in the system with EIT. Furthermore, we have also
examined a one-dimensional underlying concentration profile and EIT profile by using a
one-dimensional diffusion–convection model because EIT is proportional to the squared
concentration gradient. We have then shown that the concentration gradient is steeper
and, thus, the EIT is larger as Pe is larger. Therefore, this is the first numerical study
that can theoretically verify finger widening with increasing flow rate, which occurs only
in a miscible system with EIT to the extent of our targeting EIT values, and explain the
mechanism by one-dimensional analysis.
