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Viscous Taylor droplets in axisymmetric and planar tubes: from Bretherton’s theory to empirical models
KTH, School of Engineering Sciences (SCI), Mechanics.
2018 (English)In: Microfluidics and Nanofluidics, ISSN 1613-4982, E-ISSN 1613-4990, Vol. 22, no 6, article id 67Article in journal (Refereed) Published
Abstract [en]

The aim of this study is to derive accurate models for quantities characterizing the dynamics of droplets of non-vanishing viscosity in capillaries. In particular, we propose models for the uniform-film thickness separating the droplet from the tube walls, for the droplet front and rear curvatures and pressure jumps, and for the droplet velocity in a range of capillary numbers, Ca, from 10 - 4 to 1 and inner-to-outer viscosity ratios, λ, from 0, i.e. a bubble, to high-viscosity droplets. Theoretical asymptotic results obtained in the limit of small capillary number are combined with accurate numerical simulations at larger Ca. With these models at hand, we can compute the pressure drop induced by the droplet. The film thickness at low capillary numbers (Ca< 10 - 3) agrees well with Bretherton’s scaling for bubbles as long as λ< 1. For larger viscosity ratios, the film thickness increases monotonically, before saturating for λ> 10 3 to a value 2 2 / 3 times larger than the film thickness of a bubble. At larger capillary numbers, the film thickness follows the rational function proposed by Aussillous and Quéré (Phys Fluids 12(10):2367–2371, 2000) for bubbles, with a fitting coefficient which is viscosity-ratio dependent. This coefficient modifies the value to which the film thickness saturates at large capillary numbers. The velocity of the droplet is found to be strongly dependent on the capillary number and viscosity ratio. We also show that the normal viscous stresses at the front and rear caps of the droplets cannot be neglected when calculating the pressure drop for Ca> 10 - 3.

Place, publisher, year, edition, pages
Springer Verlag , 2018. Vol. 22, no 6, article id 67
Keywords [en]
Droplet velocity, Film thickness, Lubrication theory, Numerical simulations, Pressure drop, Capillarity, Computer simulation, Numerical models, Polymer blends, Rational functions, Viscosity, Asymptotic results, Capillary numbers, Fitting coefficient, High viscosities, Low capillary numbers, Vanishing viscosity, Drops
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-231726DOI: 10.1007/s10404-018-2084-yISI: 000435345700001Scopus ID: 2-s2.0-85048571428OAI: oai:DiVA.org:kth-231726DiVA, id: diva2:1229760
Note

QC 20180702

Available from: 2018-07-02 Created: 2018-07-02 Last updated: 2018-07-02Bibliographically approved

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Zhu, Lailai

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