Instability of Poiseuille flow of two immiscible liquids with different viscosities in a channel

Than, P.; Rosso, Fábio; Joseph, Daniel D.

doi:10.1016/0020-7225(87)90005-x

Cited by 24 publications

(15 citation statements)

References 11 publications

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“…The velocity profiles are given in tables 2 and 3; c µ = µ L /µ G indicates the viscosity contrast and d the relative gas layer thickness (d = δ/h or d = δ/R) where h is the channel height (Couette and one-sided channel flow) or half-height (symmetric channel flow) and R is the pipe radius depending on the configuration studied. In the cases CTT1, CHSYM1, CHONE1 and PIPE1 the solutions have been previously derived (Joseph et al 1984;Than et al 1987;Joseph & Renardy 1992). In the Couette flow cases the presence of the gas layer leads to a reduction of the shear rate in the liquid layer.…”

Section: Velocity Profilesmentioning

confidence: 99%

“…The resulting values are listed in table 5 and the optimum gas layer thickness is indicated in figure 5 by TABLE 6. Values for the optimum change in drag D opt , optimum relative gas layer thickness d opt and the relative gas layer thicknesses needed to achieve 90 and 50 % of the optimum for a viscosity contrast of c µ = 50. the optimum gas layer thickness given in table 5 for the cases CHSYM1 and PIPE1 have been previously derived in the context of PCAF (Joseph et al 1984;Than et al 1987). In the PIPE2 case no analytic solution could be found.…”

Section: Optimum Gas Layer Thicknessmentioning

confidence: 99%

“…The assumption that the gas on a superhydrophobic surface is trapped, i.e. zero net mass flow downstream, leads to different results for change in drag, the optimum air layer thickness and apparent slip length compared to h h R Gas Gas Gas Gas Gas previous approaches (Joseph, Nguyen & Beavers 1984;Than, Rosso & Joseph 1987;Vinogradova 1999) where a finite mass flow rate is allowed in the air layer.…”

Section: Introductionmentioning

confidence: 99%

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Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface

et al. 2013

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Analytic results are derived for the apparent slip length, the change in drag and the optimum air layer thickness of laminar channel and pipe flow over an idealised superhydrophobic surface, i.e. a gas layer of constant thickness retained on a wall. For a simple Couette flow the gas layer always has a drag reducing effect, and the apparent slip length is positive, assuming that there is a favourable viscosity contrast between liquid and gas. In pressure-driven pipe and channel flow blockage limits the drag reduction caused by the lubricating effects of the gas layer; thus an optimum gas layer thickness can be derived. The values for the change in drag and the apparent slip length are strongly affected by the assumptions made for the flow in the gas phase. The standard assumptions of a constant shear rate in the gas layer or an equal pressure gradient in the gas layer and liquid layer give considerably higher values for the drag reduction and the apparent slip length than an alternative assumption of a vanishing mass flow rate in the gas layer. Similarly, a minimum viscosity contrast of four must be exceeded to achieve drag reduction under the zero mass flow rate assumption whereas the drag can be reduced for a viscosity contrast greater than unity under the conventional assumptions. Thus, traditional formulae from lubrication theory lead to an overestimation of the optimum slip length and drag reduction when applied to superhydrophobic surfaces, where the gas is trapped.

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Section: Velocity Profilesmentioning

confidence: 99%

Section: Optimum Gas Layer Thicknessmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface

et al. 2013

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“…This is because we have limited ourselves to two-layer flow. The papers by Li (1969), Akhtaruzzaman et al (1978), Wang et al (1978), Than et al (1987), Anturkar et al (1990) and Weinstein and Kurz (1991) nevertheless consider, among others, physical situations in which only viscosity stratification is a possible cause of instability. Figure 3.…”

Section: Viscosity-induced Instabilitymentioning

confidence: 99%

Classification of instabilities in parallel two-phase flow

Boomkamp

1996

International Journal of Multiphase Flow

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Abstract--There is extensive literature on the stability of parallel two-phase flow, both in the context of liquid-liquid as well as gas-liquid flow. Aimed at making this literature more transparent, this paper presents a classification scheme for the various instabilities arising in parallel two-phase flow..To achieve such a classification, the equation governing the rate of change of the kinetic energy of the disturbances is evaluated for relevant values of the physical parameters. This shows the existence of five different ways of energy transfer from the primary to the disturbed flow, which have their origin in density stratification, velocity profile curvature, viscosity stratification or shear effects. Each class is discussed on the basis of references covering the developments over the last 35 years. © 1997 Elsevier Science Ltd.

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“…The stability of 2-D bicomponent flows has also been the subject of several investigations [4,8,15,16].…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional studies on bicomponent extrusion

1990

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The present work is concerned with the mathematical modelling and numerical simulation of three-dimensional (3-D) bicomponent extrusion. The objective is to provide an understanding of the flow phenomena involved and to investigate their impact on the free surface shape and interface configuration of the extruded article. A finite element algorithm for the 3-D numerical simulation of bicomponent stratified free surface flows is described. The presence of multiple free surfaces (layer interface and external free surfaces) requires special free surface update schemes. The pressure and viscous stress discontinuity due to viscosity mismatch at the interface between the two stratified components is handled with both a double node ( u -v -w -P 1 -P 2 -h l -h 2) formulation and a penalty function ( u -v -w -P -h 1-h2) formulation.The experimentally observed tendency of the less viscous layer to encapsulate the more viscous layer in stratified bicomponent flows of side-by-side configuration is established with the aid of a fully 3-D analysis in agreement with experimental evidence. The direction and degree of encapsulation depend directly on the viscosity ratio of the two melts. For shear thinning melts exhibiting a viscosity crossover point, it is demonstrated that interface curvature reversal may occur if the shearing level is such that the crossover point is exceeded. Extrudate bending and distortion of the bicomponent system because of the viscosity mismatch is shown. For flows in a sheath-core configuration it is shown that the viscosity ratio may have a severe effect on the swelling ratio of the bicomponent system.Modelling of the die section showed that the boundary condition imposed at the fluid/fluid/wall contact point is critical to the accuracy of the overall solution.

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Instability of Poiseuille flow of two immiscible liquids with different viscosities in a channel

Cited by 24 publications

References 11 publications

Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface

Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface

Classification of instabilities in parallel two-phase flow

Three-dimensional studies on bicomponent extrusion

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