Linear stability analysis and numerical simulation of miscible two-layer channel flow

Sahu, Kirti Chandra; Ding, Hang; Valluri, Prashant; Matar, Omar

doi:10.1063/1.3116285

Cited by 91 publications

(85 citation statements)

References 61 publications

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“…The numerical procedure and boundary conditions used to solve equations (2.7)-(2.10) are described in § 3. Note that, for the boundary conditions used here, when one of the log mobility ratios (either R f or R s ) is set to zero or δ = 1, the above equations (2.7)-(2.11) reduce to a single solute model, the flow dynamics of which has been discussed using a Navier-Stokes solver by Sahu et al (2009a). To have an idea of the order of magnitude of the log mobility ratios for real systems, we note that, if, for instance, the invading fluid is methanol (kinematic viscosity ν = 0.6704 cSt) and the displaced fluid is a mixture of ethylene glycol, acetone and methanol (ν = 0.5472 cSt) (Kalidas & Laddha 1964), we get R s = 3 and R f = −3.24.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

2012

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The pressure-driven miscible displacement of a less viscous fluid by a more viscous one in a horizontal channel is studied. This is a classically stable system if the more viscous solution is the displacing one. However, we show by numerical simulations based on the finite-volume approach that, in this system, double diffusive effects can be destabilizing. Such effects can appear if the fluid consists of a solvent containing two solutes both influencing the viscosity of the solution and diffusing at different rates. The continuity and Navier–Stokes equations coupled to two convection–diffusion equations for the evolution of the solute concentrations are solved. The viscosity is assumed to depend on the concentrations of both solutes, while density contrast is neglected. The results demonstrate the development of various instability patterns of the miscible ‘interface’ separating the fluids provided the two solutes diffuse at different rates. The intensity of the instability increases when increasing the diffusivity ratio between the faster-diffusing and the slower-diffusing solutes. This brings about fluid mixing and accelerates the displacement of the fluid originally filling the channel. The effects of varying dimensionless parameters, such as the Reynolds number and Schmidt number, on the development of the ‘interfacial’ instability pattern are also studied. The double diffusive instability appears after the moment when the invading fluid penetrates inside the channel. This is attributed to the presence of inertia in the problem.

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Section: Mathematical Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2012

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“…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.…”

Section: Introductionmentioning

confidence: 99%

“…3 The interface between the two fluids becomes unstable forming Yihtype instability for immiscible 4 and Kelvin-Helmholtz (KH) type instabilities and "roll-up" structures for miscible flows. A review of the phenomenon occurring in porous media (commonly known as viscous fingering) can be found in Ref.…”

Section: Introductionmentioning

confidence: 99%

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

2012

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The pressure-driven displacement of two immiscible fluids in an inclined channel in the presence of viscosity and density gradients is investigated using a multiphase lattice Boltzmann approach. The effects of viscosity ratio, Atwood number, Froude number, capillary number, and channel inclination are investigated through flow structures, front velocities, and fluid displacement rates. Our results indicate that increasing viscosity ratio between the fluids decreases the displacement rate. We observe that increasing the viscosity ratio has a non-monotonic effect on the velocity of the leading front; however, the velocity of the trailing edge decreases with increasing the viscosity ratio. The displacement rate of the thin-layers formed at the later times of the displacement process increases with increasing the angle of inclination because of the increase in the intensity of the interfacial instabilities. Our results also predict the front velocity of the lock-exchange flow of two immiscible fluids in the exchange flow dominated regime. A linear stability analysis has also been conducted in a three-layer system, and the results are consistent with those obtained by our lattice Boltzmann simulations.

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“…Sahu et al 37 showed that the above system becomes absolutely unstable for a certain range of parameters and have indicated the region of absolute and convective instabilities in the Reynolds number and viscosity ratio space. There are also several investigations 29,30,[38][39][40][41][42][43][44][45][46][47][48] not relevant to the present study (but worth mentioning in the present context) that deals with stability characteristics of viscosity stratified flows in rigid channels/pipes, involving the displacement of one fluid by another. The interesting features and the type of instabilities displayed by these flow systems with boundaries as either rigid walls or rigid circular pipes suggest that it is worth analyzing the analogous flow systems in configurations with velocity slip at the boundaries.…”

Section: Introductionmentioning

confidence: 99%

Double-diffusive two-fluid flow in a slippery channel: A linear stability analysis

2014

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The effect of velocity slip at the walls on the linear stability characteristics of two-fluid three-layer channel flow (the equivalent core-annular configuration in case of pipe) is investigated in the presence of double diffusive (DD) phenomenon. The fluids are miscible and consist of two solute species having different rates of diffusion. The fluids are assumed to be of the same density, but varying viscosity, which depends on the concentration of the solute species. It is found that the flow stabilizes when the less viscous fluid is present in the region adjacent to the slippery channel walls in the single-component (SC) system but becomes unstable at low Reynolds numbers in the presence of DD effect. As the mixed region of the fluids moves towards the channel walls, a new unstable mode (DD mode), distinct from the Tollman Schlichting (TS) mode, arises at Reynolds numbers smaller than the critical Reynolds number for the TS mode. We also found that this mode becomes more prominent when the mixed layer overlaps with the critical layer. It is shown that the slip parameter has nonmonotonic effect on the stability characteristics in this system. Through energy budget analysis, the dual role of slip is explained. The effect of slip is influenced by the location of mixed layer, the log-mobility ratio of the faster diffusing scalar, diffusivity, and the ratio of diffusion coefficients of the two species. Increasing the value of the slip parameter delays the first occurrence of the DD-mode. It is possible to achieve stabilization or destabilization by controlling the various physical parameters in the flow system. In the present study, we suggest an effective and realistic way to control three-layer miscible channel flow with viscosity stratification.

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Linear stability analysis and numerical simulation of miscible two-layer channel flow

Cited by 91 publications

References 61 publications

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

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

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

Double-diffusive two-fluid flow in a slippery channel: A linear stability analysis

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