Stability of miscible core–annular flows with viscosity stratification

Abstract

The linear stability of variable viscosity, miscible core–annular flows is investigated. Consistent with pipe flow of a single fluid, the flow is stable at any Reynolds number when the magnitude of the viscosity ratio is less than a critical value. This is in contrast to the immiscible case without interfacial tension, which is unstable at any viscosity ratio. Beyond the critical value of the viscosity ratio, the flow can be unstable even when the more viscous fluid is in the core. This is in contrast to plane channel flows with finite interface thickness, which are always stabilized relative to single fluid flow when the less viscous fluid is in contact with the wall. If the more viscous fluid occupies the core, the axisymmetric mode usually dominates over the corkscrew mode. It is demonstrated that, for a less viscous core, the corkscrew mode is inviscidly unstable, whereas the axisymmetric mode is unstable for small Reynolds numbers at high Schmidt numbers. For the parameters under consideration, the switchover occurs at an intermediate Schmidt number of about 500. The occurrence of inviscid instability for the corkscrew mode is shown to be consistent with the Rayleigh criterion for pipe flows. In some parameter ranges, the miscible flow is seen to be more unstable than its immiscible counterpart, and the physical reasons for this behaviour are discussed.A detailed parametric study shows that increasing the interface thickness has a uniformly stabilizing effect. The flow is least stable when the interface between the two fluids is located at approximately 0.6 times the tube radius. Unlike for channel flow, there is no sudden change in the stability with radial location of the interface. The instability originates mainly in the less viscous fluid, close to the interface.

Double diffusive effects on pressure-driven miscible displacement flows in a channel

“…This is known to be a stable situation in core-annular types of flow (Sahu & Govindarajan 2011). Unlike for δ = 1, when δ = 5 and 10, the viscosity is maximum near the wall regions, which, in the context of core-annular flow, is an unstable situation, as discussed in Selvam et al (2007) and Sahu & Govindarajan (2011). Close inspection also reveals that increasing δ increases the viscosity near the wall regions, and thus has a destabilizing effect.…”

“…In the food processing industries cleaning involves the removal of a highly viscous fluid by water. The stability of this type of two-phase flow in a channel or pipe has been widely investigated both theoretically (Ranganathan & Govindarajan 2001;Selvam et al 2007;Sahu et al 2009a; and experimentally (Hickox 1971;Hu & Joseph 1989;Joseph & Renardy 1992;Joseph et al 1997). Linear stability analyses of displacement flows in porous media (Saffman & Taylor 1958;Chouke, Van Meurs & Van Der Pol 1959;Tan & Homsy 1986) explain that, if the displacing fluid is less viscous than the displaced one, the interface separating them becomes unstable and a fingering pattern develops at the interface.…”

A study of pressure-driven displacement flow of two immiscible liquids using a multiphase lattice Boltzmann approach

“…In pressure-driven two-layer/core-annular flows, several authors have conducted linear stability analyses by considering the fluids to be immiscible 4,[6][7][8] and miscible. 3,[9][10][11][12] This problem was also studied by many researchers experimentally 13,14 and numerically. [15][16][17][18] In miscible core-annular flows, the thickness of the more viscous fluid layer left on the pipe walls and the speed of the propagating "finger" were experimentally investigated by many authors [19][20][21][22][23] and the axisymmetric and "corkscrew" patterns were found.…”

“…On the other hand, miscible flows are associated with diffusion. Selvam et al 10 compared the stability of immiscible flows (with zero surface tension) with miscible flows and found that miscible flows are stable for any Reynolds number when the viscosity ratio is less than a critical value, unlike the immiscible flows with zero surface tension, which can be unstable for any Reynolds number for any arbitrarily small viscosity gradient. Also in miscible flows, the width of the interfacial region increases with time even when the diffusion coefficient is very small (this rate is proportional to the inverse of Peclet number), which in turn stabilizes the flow (see Refs.…”

“…40,42 We have conducted a systematic parametric study to investigate the effects of viscosity ratio, Atwood number, Froude number, and surface tension. As Selvam et al 10 found that in core-annular flows beyond a critical viscosity ratio, the flow is unstable even when the less viscous fluid is at the wall, we investigated what will happen when a high viscous fluid displaces a less viscous one (a classically stable system) at high viscosity ratio. The effects of angle of inclination on the flow dynamics are also investigated, which have not been studied earlier in the context of immiscible fluids.…”