Reaction induced interfacial instability of miscible fluids in a channel

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.