On driving a viscous fluid out of a tube

Cox, Brian

doi:10.1017/s0022112062001081

Cited by 171 publications

(116 citation statements)

References 2 publications

(2 reference statements)

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“…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. [24][25][26][27][28] In neutrallybuoyant core-annular pipe flows, d'Olce et al 29 observed axisymmetric "pearl" and "mushroom" patterns at high Schmidt number.…”

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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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 interface between the two fluids becomes unstable, forming Kelvin-Helmholtz (KH) instabilities and 'roll-up' structures (Joseph et al 1997;Sahu et al 2009a,b). Experimental studies in miscible core-annular flows (Taylor 1961;Cox 1962;Chen & Meiburg 1996;Petitjeans & Maxworthy 1996;Kuang, Maxworthy & Petitjeans 2003) have focused on analysing the thickness of the more viscous fluid layer left on the pipe walls and the speed of the propagating 'finger' tip. The development of different instability patterns, like axisymmetric 'corkscrew' patterns, in miscible flows has also been investigated (Lajeunesse et al 1997(Lajeunesse et al , 1999Scoffoni, Lajeunesse & Homsy 2001;Cao et al 2003;Gabard & Hulin 2003).…”

Section: Introductionmentioning

confidence: 99%

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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“…Other studies involving channel flows have demonstrated the destabilising effect of diffusion for continuous but rapidly varying viscosity stratification [30]. In the case of core-annular miscible flows, some experimental studies have focused on determining the thickness of the more viscous fluid left on the pipe walls following its displacement by a less viscous fluid and on measuring the tip speed of the propagating 'finger' of the latter [31][32][33][34][35][36]. Others works have examined the development of 'interfacial' axisymmetric and "corkscrew" patterns that accompany these flows [2,[37][38][39][40].…”

Section: Introductionmentioning

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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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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On driving a viscous fluid out of a tube

Cited by 171 publications

References 2 publications

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

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

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

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

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