Abstract:
When a less viscous miscible fluid displaces a more-viscous one under a pressure-driven
channel flow, unstable Kelvin–Helmholtz (K–H)-type billows are formed at the miscible
interface. In this paper, we investigate whether such instability can be induced by a
simple (A + B → C)-type chemical reaction. Here a miscible solution of one reactant A
is displacing another isoviscous reactant B and producing a more-viscous product C at
the reactive front. It is found that because of a local increase in viscosity gradient due
to the formation of more-viscous product C, K–H-type billows are formed at the A–C
interface. The changes in dynamical properties of such billows are examined by varying
the governing parameters such as the mobility ratio Rc, Damköhler number Da, Péclet
number Pe and Reynolds number Re. Interestingly, we have found that even at high reaction
rates (sufficiently large Da) for Rc = 1, the interface remains stable and for larger values of
Rc(= 3, 5) the K–H billows are observed. It is also noticed that a laminar horseshoe-type
vortex develops near the wall at the channel inlet where the less-viscous reactant pushes the
more-viscous product. We have computed numerically the onset time (ton) of instability
to understand the early-stage developments of the K–H billows. For different values of
Da, we have shown the unstable and stable time zones in the (ton–Rc) space. The bipartite
(ton–Rc) space also depicts the critical (Da-, Pe- and Re-dependent) Rc value for which
instability can be triggered in a finite desirable time. The delay in the onset of instability is
observed with increasing Pe. Further it is shown that ton can be linearly scaled with Pe to
have a modified onset time (t
∗
on), which establishes a proportionate dynamics with respect
to Pe in the early stages of the instability. Moreover, a reverse dependency of onset on
lower Rc values for higher Reynolds numbers is observed.
