Linear instability of pressure-driven channel flow of a Newtonian and a Herschel-Bulkley fluid

Sahu, Kirti Chandra; Valluri, Prashant; Spelt, Peter D. M.; Matar, Omar

doi:10.1063/1.2814385

Cited by 93 publications

(66 citation statements)

References 23 publications

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“…The stability analysis conducted here is similar to the one given in Sahu et al 7,8,63 We recover Eqs. (28)- (36) from the stability equations and boundary conditions given in Sahu et al 8 for Newtonian fluids.…”

Section: Linear Stability Analysismentioning

confidence: 63%

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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: Linear Stability Analysismentioning

confidence: 63%

“…5. 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.…”

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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“…(10) and (11), only half of the channel is considered, y ∈ [1/2, 1]. This domain is decomposed into three regions, 1/2 ≤ y ≤ 1/2 + h, 1/2 + h ≤ y ≤ 1/2 + h + q and 1/2 + h + q ≤ y ≤ 1, and the eigenfunctions in each region are then expanded using Chebyshev polynomials through a spectral method [53,59,60]. The decomposition of the domain endows the edges of the mixed layer with more points than its interior, thereby enhancing the resolution of the numerical solutions where the base state concentration and its derivatives must be continuous [53].…”

Section: Linear Stability Analysismentioning

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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“… hot water: in personal products processing it is common to clean by circulation of hot water; removal is thus by fluid flow alone (Sahu et al, 2007)  hot cleaning fluid: many deposits are impossible to remove by water alone. Cleaning chemicals are thus used to speed the cleaning process and complex interactions between cleaning time, chemistry and flowrate are found (for example, Gillham et al, 1999Gillham et al, , 2000Christian et al, 2006).…”

Section: Introductionmentioning

confidence: 99%

Matching the nano- to the meso-scale: Measuring deposit–surface interactions with atomic force microscopy and micromanipulation

Akhtar

Bowen

Asteriadou

et al. 2010

Food and Bioproducts Processing

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Many researchers have studied the effects of changing the surface on fouling and cleaning. In biofouling the 'Baier curve' is a well-known result which relates adhesion to surface energy, and papers on the effect of changing surface energy to food fouling can be found more than 40 years ago. Recently the use of modified surfaces, at least at a research level, has been widespread. Here two different ways of studying surface-deposit interactions have been compared. Atomic force microscopy (AFM) is a method for probing interactions at a molecular level, and can measure (for example) the interaction between substrate and surfaces at a nm-scale. At a μm-mm level, we have developed a micromanipulation tool that can measure the force required to remove the deposit; the measure incorporates both surface and bulk deformation effects. The two methods have been compared by studying a range of model soils: toothpaste, as an example of a soil that can be removed by fluid flow alone, and confectionery soils. Removal has been studied from glass, stainless steel and fluorinated surfaces as examples of the sort of surfaces that can be found in practice. AFM measurements were made by using functionalized tips in force mode. The two types of probe give similar results, although the rheology of the soil affects the measurement from the micromanipulation probe under some circumstances. The data suggests that either method could be used to test candidate surfaces. 2 INTRODUCTIONThe cleaning of process plant is a difficult multiscale problem; metre-scale plant becomes clean as a result of fluid and chemical action on surfaces of individual plant items, acting at the meso-and nano scale. A sketch of the different length scales involved in cleaning process plant is given as Figure 1. To remove deposit from surfaces is difficult both to understand scientifically and to do industrially (Wilson, 2005; Fryer et al., 2006)

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Linear instability of pressure-driven channel flow of a Newtonian and a Herschel-Bulkley fluid

Cited by 93 publications

References 23 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

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

Matching the nano- to the meso-scale: Measuring deposit–surface interactions with atomic force microscopy and micromanipulation

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