Instabilities in Viscosity-Stratified Flow

Govindarajan, Rama; Sahu, Kirti Chandra

doi:10.1146/annurev-fluid-010313-141351

Cited by 211 publications

(122 citation statements)

References 131 publications

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“…Further, it is well known that when the less viscous fluid occupies the near wall region of the channel in a core-annular configuration, flow is stable in the context of single component flows. 31 In this study, the effects of wall-slip on the double-diffusive unstable mode in the configurations which are stable in the context of single component systems are investigated.…”

Section: B Base Statementioning

confidence: 99%

“…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%

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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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Section: B Base Statementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2014

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“…consist of one fluid in the core and the other fluid in the annular region of a pipe) have been extensively studied due to their relevance in many industrial applications, e.g transportation of crude oil in pipelines, polymer deposition and extrusion, food processing industries, etc (Homsy 1987;Selvam et al 2007;Govindarajan & Sahu 2014). Viscosity stratified flows can also be observed in natural phenomena, e.g.…”

Section: Introductionmentioning

confidence: 99%

“…displacement of a highly viscous fluid by a less viscous one in porous media (Mishra et al 2010;Swernath & Pushpavanam 2007), Hele-Shaw cell (Pritchard 2009), and in pressure-driven flow in a channel (Mishra et al 2012). A review of instabilities associated with DD effect in various flow configurations can be found in Govindarajan & Sahu (2014).…”

Section: Introductionmentioning

confidence: 99%

Double-diffusive instability in core–annular pipe flow

Sahu

2016

J. Fluid Mech.

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The instability in a pressure-driven core-annular flow of two miscible fluids having the same densities, but different viscosities in the presence of two scalars diffusing at different rates (double-diffusive effect) is investigated via linear stability analysis and axisymmetric direct numerical simulation. It is found that the double-diffusive flow in a cylindrical pipe exhibits strikingly different stability characteristics compared to the double-diffusive flow in a planar channel and the equivalent single-component flow (wherein viscosity stratification is achieved due to the variation of one scalar) in a cylindrical pipe. The flow which is stable in the context of single-component systems, now becomes unstable in the presence of two scalars diffusing at different rates. It is shown that increasing the diffusivity ratio enhances the instability. In contrast to the single fluid flow through a pipe (the Hagen-Poiseuille flow), the faster growing axisymmetric eigenmode is found to be more unstable than the corresponding corkscrew mode for the parameter values considered, for which the equivalent single-component flow is stable to both the axisymmtric and corkscrew modes. Unlike single-component flows of two miscible fluids in a cylindrical pipe, it is shown that the diffusivity and the radial location of the mixed layer have non-monotonic influences on the instability characteristics. An attempt is made to understand the underlying mechanism of this instability by conducting the energy budget and inviscid stability analyses. The investigation of linear instability due to the double-diffusive phenomenon is extended to the nonlinear regime via axisymmetric direct numerical simulations. It is found that in the nonlinear regime the flow becomes unstable in the presence of double-diffusive effect, which is consistent with the predictions of linear stability theory. A new type of instability pattern of an elliptical shape is observed in the nonlinear simulations in the presence of double-diffusive effect.

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“…The immiscible flows were described by Redapangu et al (2012Redapangu et al ( , 2013. The extensive review of instabilities in the above-mentioned systems is given in Govindarajan and Sahu (2014).…”

Section: Introductionmentioning

confidence: 99%

Capillary Model of Gravity Elution of High Viscosity Liquid from a Porous Bed with a Low-Viscosity Liquid

Błaszczyk

Sęk

2014

Transp Porous Med

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Modeling of the processes of elution from porous systems is essential importance for development of the removing oily contaminations from the soils and intensification of the oil recovery processes. In the paper, capillary model of gravitational elution of high viscosity substances from the porous medium by using low viscosity liquids was derived. This model allowed for the prediction of changes in time of such parameters like: level of bed saturation with oil, relative bed permeability, liquid flow rate, flow resistance, volume of eluted liquid during the process. When modeling, phenomena and the physical properties associated with the analyzed process, such as, for example, the effects of surface tension, fluids viscosity, specific size of the granular bed, initial oil saturation of bed, variable process driving force, and the flow of liquid through the preferential flow paths, were taken into account. This allowed for the more complete imaging of elution process. The model has been verified on the basis of the results of experimental studies. In addition, the discussion on the behavior of the model due to changes in values of various parameters was carried out.

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Instabilities in Viscosity-Stratified Flow

Cited by 211 publications

References 131 publications

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

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

Double-diffusive instability in core–annular pipe flow

Capillary Model of Gravity Elution of High Viscosity Liquid from a Porous Bed with a Low-Viscosity Liquid

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