Linear stability and energy growth of viscosity stratified flows

Malik, Satish V.; Hooper, A. P.

doi:10.1063/1.1834931

Cited by 41 publications

(37 citation statements)

References 11 publications

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“…The most recent work on the linear stability of neutrallybuoyant, core-annular flows was that of Sevlam et al [42]. These authors show that beyond a critical viscosity ratio, the flow is unstable even when the less viscous fluid is at the wall, in contrast to the case of immiscible lubricated pipelining [1] and to miscible channel flows [43], which are stable in this configuration. This study also shows that axisymmetric (corkscrew) modes are dominant if the more (less) viscous fluid is in the pipe core, and for large Schmidt numbers, relatively small Reynolds number and large wavenumbers.…”

Section: Introductionmentioning

confidence: 97%

“…1. The temporal stability analysis of three-layer flow in channel and pipe has been studied previously in the literature [28,43,[50][51][52]. As will be discussed in the following section, only half the channel will be considered in which the base state concentration, C, is characterized by the following steady concentration profile…”

Section: A Governing Equationsmentioning

confidence: 99%

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

Sahu¹,

Ding²,

Valluri³

et al. 2009

Physics of Fluids

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The stability of miscible two-fluid flow in a horizontal channel is examined. The flow dynamics are governed by the continuity and Navier-Stokes equations coupled to a convective-diffusion equation for the concentration of the more viscous fluid through a concentration-dependent viscosity.Our analysis of the flow in the linear regime delineates the presence of convective and absolute instabilities and identifies the vertical gradients of viscosity perturbations as the main destabilizing influence in agreement with previous work. Our transient numerical simulations demonstrate the development of complex dynamics in the nonlinear regime, characterized by roll-up phenomena and intense convective mixing; these become pronounced with increasing flow rate and viscosity ratio, as well as weak diffusion. *

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Section: Introductionmentioning

confidence: 97%

Section: A Governing Equationsmentioning

confidence: 99%

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

Sahu¹,

Ding²,

Valluri³

et al. 2009

Physics of Fluids

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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%

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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“…30 The instabilities which arise due to viscosity stratification in different geometries, such as in miscible channel flows and core-annular miscible flows are well documented in literature, and discussed in a recent review by Govindarajan and Sahu. 31 The articles relevant to the present study have examined flow system in a rigid channel (the linear stability analysis of SC systems; 11,22,[32][33][34][35][36] convective and absolute instabilities in SC systems 37 ). They have shown that the flow has a stabilising (destabilising) influence when the less (highly) viscous fluid occupies the near wall regions of the channel for low to moderate Schmidt numbers.…”

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 and energy growth of viscosity stratified flows

Cited by 41 publications

References 11 publications

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

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

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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