An analytical interface shape approximation of microscopic Taylor flows

Ulrich Mießner; Thorben Helmers; Ralph Lindken; Jerry Westerweel

doi:10.1007/s00348-019-2719-0

An analytical interface shape approximation of microscopic Taylor flows

Ulrich Mießner^*, Thorben Helmers, Ralph Lindken, Jerry Westerweel

^*Corresponding author for this work

Fluid Mechanics

Research output: Contribution to journal › Article › Scientific › peer-review

6 Citations (Scopus)

Abstract

Abstract: This paper presents a geometric model to approximate the interface shape of Taylor bubbles and droplets moving in rectangular microchannels. To retrieve the entire 3D interface geometry, the following apriori knowledge is required: the cross-sectional channel geometry, the droplet/bubble length, and the flow-related front and back cap deformation ratios retrieved, e.g., from instantaneous images of translating interfaces. The accuracy of the interface shape model is benchmarked with experimentally generated average images of the statistical distribution of a particulate tracer. In the experiment, the fluidic material system, the aspect ratio of the channel cross section, and the droplet/bubble length are varied. The mean overall deviation between the model and the experimental data remains below 2 %. The interface shape model is applicable for horizontal pressure-driven liquid–liquid and gas–liquid fluid systems in a range of Ca < 0.01 , Re≲ 1 and Bo≪ 1 with the liquid continuous phase wetting the wall. The model can be applied, e.g., to guide the 3D flow field reconstruction of multi-plane μ -PIV measurements of Taylor flows. Graphical abstract: [Figure not available: see fulltext.]

Original language	English
Article number	75
Number of pages	19
Journal	Experiments in Fluids
Volume	60
Issue number	4
DOIs	https://doi.org/10.1007/s00348-019-2719-0
Publication status	Published - 2019

Bibliographical note

Correction to: An analytical interface shape approximation of microscopic Taylor flows
In the original version of the article, the supplementary material was unintentionally omitted. The electronic supplementary material can be accessed through the link below
.https://static-content.springer.com/esm/art%3A10.1007%2Fs00348-019-2750-1/MediaObjects/348_2019_2750_MOESM1_ESM.m (21 kb)
DropletSurface_EiF (M 20 kb)
https://static-content.springer.com/esm/art%3A10.1007%2Fs00348-019-2750-1/MediaObjects/348_2019_2750_MOESM2_ESM.m (9 kb)
DynamicGutterRadius_EiF (M 9 kb)
https://static-content.springer.com/esm/art%3A10.1007%2Fs00348-019-2750-1/MediaObjects/348_2019_2750_MOESM3_ESM.m (1 kb)
STARTScript_dynGutter_TaylorDropSurface_EiF (M 1 kb)

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10.1007/s00348-019-2719-0

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title = "An analytical interface shape approximation of microscopic Taylor flows",

abstract = "Abstract: This paper presents a geometric model to approximate the interface shape of Taylor bubbles and droplets moving in rectangular microchannels. To retrieve the entire 3D interface geometry, the following apriori knowledge is required: the cross-sectional channel geometry, the droplet/bubble length, and the flow-related front and back cap deformation ratios retrieved, e.g., from instantaneous images of translating interfaces. The accuracy of the interface shape model is benchmarked with experimentally generated average images of the statistical distribution of a particulate tracer. In the experiment, the fluidic material system, the aspect ratio of the channel cross section, and the droplet/bubble length are varied. The mean overall deviation between the model and the experimental data remains below 2 %. The interface shape model is applicable for horizontal pressure-driven liquid–liquid and gas–liquid fluid systems in a range of Ca < 0.01 , Re≲ 1 and Bo≪ 1 with the liquid continuous phase wetting the wall. The model can be applied, e.g., to guide the 3D flow field reconstruction of multi-plane μ -PIV measurements of Taylor flows. Graphical abstract: [Figure not available: see fulltext.]",

author = "Ulrich Mie{\ss}ner and Thorben Helmers and Ralph Lindken and Jerry Westerweel",

note = "Correction to: An analytical interface shape approximation of microscopic Taylor flows In the original version of the article, the supplementary material was unintentionally omitted. The electronic supplementary material can be accessed through the link below .https://static-content.springer.com/esm/art%3A10.1007%2Fs00348-019-2750-1/MediaObjects/348_2019_2750_MOESM1_ESM.m (21 kb) DropletSurface_EiF (M 20 kb) https://static-content.springer.com/esm/art%3A10.1007%2Fs00348-019-2750-1/MediaObjects/348_2019_2750_MOESM2_ESM.m (9 kb) DynamicGutterRadius_EiF (M 9 kb) https://static-content.springer.com/esm/art%3A10.1007%2Fs00348-019-2750-1/MediaObjects/348_2019_2750_MOESM3_ESM.m (1 kb) STARTScript_dynGutter_TaylorDropSurface_EiF (M 1 kb) ",

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doi = "10.1007/s00348-019-2719-0",

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TY - JOUR

T1 - An analytical interface shape approximation of microscopic Taylor flows

AU - Mießner, Ulrich

AU - Helmers, Thorben

AU - Lindken, Ralph

AU - Westerweel, Jerry

N1 - Correction to: An analytical interface shape approximation of microscopic Taylor flows In the original version of the article, the supplementary material was unintentionally omitted. The electronic supplementary material can be accessed through the link below .https://static-content.springer.com/esm/art%3A10.1007%2Fs00348-019-2750-1/MediaObjects/348_2019_2750_MOESM1_ESM.m (21 kb) DropletSurface_EiF (M 20 kb) https://static-content.springer.com/esm/art%3A10.1007%2Fs00348-019-2750-1/MediaObjects/348_2019_2750_MOESM2_ESM.m (9 kb) DynamicGutterRadius_EiF (M 9 kb) https://static-content.springer.com/esm/art%3A10.1007%2Fs00348-019-2750-1/MediaObjects/348_2019_2750_MOESM3_ESM.m (1 kb) STARTScript_dynGutter_TaylorDropSurface_EiF (M 1 kb)

PY - 2019

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N2 - Abstract: This paper presents a geometric model to approximate the interface shape of Taylor bubbles and droplets moving in rectangular microchannels. To retrieve the entire 3D interface geometry, the following apriori knowledge is required: the cross-sectional channel geometry, the droplet/bubble length, and the flow-related front and back cap deformation ratios retrieved, e.g., from instantaneous images of translating interfaces. The accuracy of the interface shape model is benchmarked with experimentally generated average images of the statistical distribution of a particulate tracer. In the experiment, the fluidic material system, the aspect ratio of the channel cross section, and the droplet/bubble length are varied. The mean overall deviation between the model and the experimental data remains below 2 %. The interface shape model is applicable for horizontal pressure-driven liquid–liquid and gas–liquid fluid systems in a range of Ca < 0.01 , Re≲ 1 and Bo≪ 1 with the liquid continuous phase wetting the wall. The model can be applied, e.g., to guide the 3D flow field reconstruction of multi-plane μ -PIV measurements of Taylor flows. Graphical abstract: [Figure not available: see fulltext.]

AB - Abstract: This paper presents a geometric model to approximate the interface shape of Taylor bubbles and droplets moving in rectangular microchannels. To retrieve the entire 3D interface geometry, the following apriori knowledge is required: the cross-sectional channel geometry, the droplet/bubble length, and the flow-related front and back cap deformation ratios retrieved, e.g., from instantaneous images of translating interfaces. The accuracy of the interface shape model is benchmarked with experimentally generated average images of the statistical distribution of a particulate tracer. In the experiment, the fluidic material system, the aspect ratio of the channel cross section, and the droplet/bubble length are varied. The mean overall deviation between the model and the experimental data remains below 2 %. The interface shape model is applicable for horizontal pressure-driven liquid–liquid and gas–liquid fluid systems in a range of Ca < 0.01 , Re≲ 1 and Bo≪ 1 with the liquid continuous phase wetting the wall. The model can be applied, e.g., to guide the 3D flow field reconstruction of multi-plane μ -PIV measurements of Taylor flows. Graphical abstract: [Figure not available: see fulltext.]

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DO - 10.1007/s00348-019-2719-0

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JO - Experiments in Fluids: experimental methods and their applications to fluid flow

JF - Experiments in Fluids: experimental methods and their applications to fluid flow

SN - 0723-4864

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ER -

An analytical interface shape approximation of microscopic Taylor flows

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Correction to an analytical interface shape approximation of microscopic Taylor flows (Experiments in Fluids, (2019), 60, 4, (75), 10.1007/s00348-019-2719-0)

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