Abstract:
The dynamics of A + B → C fronts is analysed numerically in a radial geometry. We
are interested to understand miscible fingering instabilities when the simple chemical
reaction changes the viscosity of the fluid locally and a non-monotonic viscosity
profile with a global maximum or minimum is formed. We consider viscosity-matched
reactants A and B generating a product C having different viscosity than the reactants.
Depending on the effect of C on the viscosity relative to the reactants, different
viscous fingering (VF) patterns are captured which are in good qualitative agreement
with the existing radial experiments. We have found that, for a given chemical reaction
rate, an unfavourable viscosity contrast is not always sufficient to trigger the instability.
For every fixed Péclet number (Pe), these effects of chemical reaction on VF are
summarized in the Damköhler number (Da) − the log-mobility ratio (Rc) parameter
space that exhibits a stable region separating two unstable regions corresponding to
the cases of more and less viscous product. Fixing Pe, we determine Da-dependent
critical log-mobility ratios R
+
c
and R
−
c
such that no VF is observable whenever
R
−
c 6 Rc 6 R
+
c
. The effect of geometry is observable on the onset of instability, where
we obtain significant differences from existing results in the rectilinear geometry.
