Research Papers: Fundamental Issues and Canonical Flows

Lubrication of Highly Viscous Core-Annular Flows in Microfluidic Chambers

[+] Author and Article Information
Samira Darvishi

Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY 11794

Thomas Cubaud1

Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY 11794thomas.cubaud@stonybrook.edu


Corresponding author.

J. Fluids Eng 133(3), 031203 (Mar 29, 2011) (7 pages) doi:10.1115/1.4003733 History: Received December 17, 2010; Revised February 23, 2011; Published March 29, 2011; Online March 29, 2011

We investigate the lubrication transition of high-viscosity fluid threads flowing in sheaths of less viscous fluids, i.e., viscous core-annular flows, in microchannels. Focus is given on the flow behavior of threads as they traverse a quasi-two-dimensional diverging-converging slit microfluidic chamber. The role of the viscosity contrast is examined for both miscible and immiscible fluids, and, for the later case, both partially wetting and nonwetting threads are considered. The conditions for lubrication are established in relation to flow rates of injection, interfacial properties, viscosities, and phenomena such as viscous buckling, wetting, breakup, and coalescence.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Microfluidic chamber: (a) schematic of microchannel layout, (b) single-phase flow streamlines, and (c) folding morphology at the chamber inlet

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Figure 2

Lubrication failure of a viscous thread for χ=592. (a) Hysteresis loop between threading and piling regimes: increasing φ (●) and decreasing φ (○). Solid line: A/w=[1+(χφ)−1]−1. Experimental pictures with flow rates (μl/min): (b) Q1=2 and Q2=110 and (c) Q1=5 and Q2=40.

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Figure 3

Evolution of the amplitude A for χ=52 (◇), 106 (▷), 592 (○), 2796 (◻), and 5933 (△). Solid line: A/w=[1+φ−1]−1.

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Figure 4

Influence of viscosity contrast χ. (a) Critical flow rate ratio φc for lubrication transition. Solid line: φc=1.8χ−0.62. (b) Evolution of the prefactor k. Solid line: k=0.06χ0.35.

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Figure 5

Morphological features of folding threads (χ=106). (a) Apparent penetration length of lubrication XP/w as a function of flow rate ratio φ. (b) Location of maximum amplitude XM/w for various φ. Bottom: corresponding experimental micrographs (h=100 μm, flow rates in μl/min): (1) Q1=10 and Q2=180, (2) Q1=7 and Q2=40, and (3) Q1=5 and Q2=14.

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Figure 6

Liquid/liquid contact angle measurements on borosilicate glass. (a) L1: silicone oil, L2: ethanol, and θ12≈180 deg. (b) L1: heavy mineral oil, L2: silicone oil, and θ12≈70. Droplets are reflected on the glass surface.

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Figure 7

Deformation of nonwetting threads made of silicone oil in a sheath of ethanol (χ=419). Micrographs of threading and breakup regimes, flow rates in μl/min, Q2=130: (a) Q1=7, (b) Q1=10, and (c) Q1=13. (d) Phase-diagram of flow regimes, Ca versus φ: threading (●) and breakup (○). Gray dash-dot line: critical flow rate ratio φc=0.043 for the lubrication transition of miscible threads having similar χ. Red dash-dot line: φc=0.7Ca−1.

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Figure 8

Influence of capillary number Ca and wetting transition for fixed flow rate ratio φ=5×10−2 between heavy mineral oil (thread) and silicone oil (sheath). Flow rates in μl/min: (a) Q1=5, Q2=100, and Ca=37, (b) Q1=2.5, Q2=50, and Ca=18, and (c) Q1=1, Q2=20, and Ca=7.

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Figure 9

Evolution of the normalized envelope amplitude A/w for partially wetting threads as a function of the flow rate ratio φ for various fixed side flow rates (in μl/min) Q2=10 (◇), 20 (○), 50 (◻), 100 (△), and 150 (▷). (a), (b), and (c) correspond to data in Fig. 8. Solid line: A/w=[1+φ−1]−1, dashed-line: A/w=[1+χφ−1]−1, and gray line: A/w=0.3.

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Figure 10

Dewetting flow patterns between heavy mineral oil (thread) and silicone oil (sheath). Flow rates in μl/min: (a) Q1=1.5, Q2=5.4, φ=0.28, and Ca=2.4, (b) Q1=1.5, Q2=4, φ=0.37, and Ca=1.9, (c) Q1=1.5, Q2=3, φ=0.5, and Ca=1.6, and (d) Q1=5, Q2=2, φ=2.5, and Ca=2.5.



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