Co‐current stratified laminar flow of two immiscible liquids in a rectangular conduit

Charles, M. E.; Lilleleht, L. U.

doi:10.1002/cjce.5450430303

Cited by 39 publications

(11 citation statements)

References 8 publications

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“…Similar to our results, in other studies of gravity driven currents, the observed characteristic velocity in three dimensional experiments is always smaller than that predicted by a two dimensional analysis because of the outer geometry and boundary conditions. 56,67,68 Despite the discrepancy in the magnitudes of the time scales, the scaling of the characteristic time scales for the gravity current with fluid properties and drop geometry agrees well with the observed behavior, suggesting that the lubrication model captures most of the essential physics in the problem.Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 128.2.20.…”

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confidence: 52%

Gravity driven current during the coalescence of two sessile drops

et al. 2015

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Coalescence of liquid drops is critical in many phenomena such as emulsion stability, inkjet printing, and coating applications. For sessile drops on a solid surface, the coalescence process is more complicated than the coalescence of drops suspended in a fluid medium as a result of the coupling of the contact line motions to the fluid flow. In this paper, we use video microscopy to track the evolution of the interfaces and contact lines as well as the internal fluid motion within a merged sessile droplet. In this study, the fluids in the coalescing drops are miscible and have similar surface tensions and drop volumes but different viscosities and densities. Coalescence occurs in three stages. During the first stage, rapid healing of the bridge between the drops occurs just after they touch. In the second stage, slower rearrangement of the liquids occurs. We show that these intermediate rearrangements are driven by gravity even for density differences of the two fluids as small as 1%. For the systems examined, little to no mixing occurs during these first two stages. Finally, in the third stage, diffusion leads to mixing of the fluids. Dimensional analysis reveals the scaling of the intermediate flow behavior as a function of density difference and geometric dimensions of the merged drop; however, the scaling with viscosity is more complicated, motivating development of a lubrication analysis of the coalescence problem. Numerical calculations based on the lubrication analysis capture aspects of the experimental observations and reveal the governing forces and time scales of the coalescence process. The results reveal that internal fluid motions persist over much longer time scales than imaging of the external interface alone would reveal. Furthermore, nearly imperceptible motions of the external composite drop interface can lead to important deviations from the predominant gravity current scaling, where viscous resistance of the lighter fluid layer plays a significant role in the internal fluid motion. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4907725] INTRODUCTIONCoalescence of drops is critically important to numerous technological and natural processes. For example, coalescence of drops on surfaces leads to the formation of a uniform film in spray coating and influences heat transfer in spray cooling. [1][2][3] While the coalescence of drops suspended in a fluid medium has been examined extensively, 4,5 coalescence of two sessile drops on a solid surface adds the feature that the contact lines of the drops must move during the merging process. Coalescence of sessile drops of identical fluids shows a rapid bridge healing process and a slow contact line relaxation. In the rapid process, which is controlled by the interplay of inertia, viscosity, and capillarity, 7,8 the drops touch and a bridge rapidly forms and heals while the contact line does not move appreciably. 6,[9][10][11] In the slow process, contact lines move and the drop relaxes to a circular shape over longer time scales, slowed by th...

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confidence: 52%

Gravity driven current during the coalescence of two sessile drops

et al. 2015

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“…In the development of the model, we were inspired by a number of papers using two-layer fluid flows in rectangular ducts in different contexts. 6,14,25 In terms of the mathematics, we extend these models to three-layer fluid flows. As well, and perhaps more importantly, we employ such methods to extract specific variables of the flow that can be effectively used for biofilm growth applications.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…In order to solve the differential equation (2), we rely on the series decomposition (in terms of hyperbolic functions) of the velocity field, which has been used for similar two-layer fluid mechanics problems. 6,14,25 The common method is to split the velocity into two terms, V i ðx;ẑÞ ¼V I i ðẑÞ þV II i ðx;ẑÞ. The first term is the unperturbed velocity far away from the interface while the second term is expected to vanish far away from the interface and it satisfies Laplace equation r 2V II i ðx;ẑÞ ¼ 0.…”

Section: Mathematical Modelmentioning

confidence: 99%

A microfluidic method and custom model for continuous, non-intrusive biofilm viscosity measurements under different nutrient conditions

et al. 2016

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Straight, low-aspect ratio micro flow cells are used to support biofilm attachment and preferential accumulation at the short side-wall, which progressively reduces the effective channel width. The biofilm shifts downstream at measurable velocities under the imposed force from the constant laminar co-flowing nutrient stream. The dynamic behaviour of the biofilm viscosity is modeled semi-analytically, based on experimental measurements of biofilm dimensions and velocity as inputs. The technique advances the study of biofilm mechanical properties by strongly limiting biases related to non-Newtonian biofilm properties (e.g., shear dependent viscosity) with excellent time resolution. To demonstrate the proof of principle, young Pseudomonas sp. biofilms were analyzed under different nutrient concentrations and constant micro-flow conditions. The striking results show that large initial differences in biofilm viscosities grown under different nutrient concentrations become nearly identical in less than one day, followed by a continuous thickening process. The technique verifies that in 50 h from inoculation to early maturation stages, biofilm viscosity could grow by over 2 orders of magnitude. The approach opens the way for detailed studies of mechanical properties under a wide variety of physiochemical conditions, such as ionic strength, temperature, and shear stress. Published by AIP Publishing. [http://dx

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“…The energy required to transport heavy viscous crude oil in long pipes can be considerably reduced by the addition of small amounts of water to the crude resulting in reduced pumping costs, Russel and Charles [164] and Charles and Lilleleht [165]. In the fiber industry, stratified flow is used to make bicomponent fibers by coextruding two components in a side-by-side semi-circular configuration to produce unique fiber properties resembling those of natural wools called crimped or wool fibers, Blais et al [166].…”

Section: An Industrial Application: Viscous Encapsulationmentioning

confidence: 99%

Developments in the Flow of Complex Fluids in Tubes

Siginer

2015

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Co‐current stratified laminar flow of two immiscible liquids in a rectangular conduit

Cited by 39 publications

References 8 publications

Gravity driven current during the coalescence of two sessile drops

Gravity driven current during the coalescence of two sessile drops

A microfluidic method and custom model for continuous, non-intrusive biofilm viscosity measurements under different nutrient conditions

Developments in the Flow of Complex Fluids in Tubes

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