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Research Papers: Fundamental Issues and Canonical Flows

Analysis of Multi-Layer Immiscible Fluid Flow in a Microchannel

[+] Author and Article Information
Jie Li, Paul S. Sheeran

 Department of Mechanical and Aerospace Engineering, NC State University, Raleigh, NC 27695-7910 Joint Departments of Biomedical Engineering, UNC Chapel Hill and NC State University, Chapel Hill, NC 27599

Clement Kleinstreuer1

 Department of Mechanical and Aerospace Engineering, NC State University, Raleigh, NC 27695-7910; Joint Departments of Biomedical Engineering, UNC Chapel Hill and NC State University, Chapel Hill, NC 27599ck@eos.ncsu.edu

1

Corresponding Author.

J. Fluids Eng 133(11), 111202 (Oct 19, 2011) (10 pages) doi:10.1115/1.4005134 History: Received June 30, 2011; Accepted September 16, 2011; Published October 19, 2011; Online October 19, 2011

The development of microfluidics platforms in recent years has led to an increase in the number of applications involving the flow of multiple immiscible layers of viscous electrolyte fluids. In this study, numerical results as well as analytic equations for velocity and shear stress profiles were derived for N layers with known viscosities, assuming steady laminar flow in a microchannel driven by pressure and/or electro-static (Coulomb) forces. Numerical simulation results, using a commercial software package, match analytical results for fully-developed flow. Entrance flow effects with centered fluid-layer shrinking were studied as well. Specifically, cases with larger viscosities in the inner layers show a very good agreement with experimental correlations for the dimensionless entrance length as a function of inlet Reynolds number. However, significant deviations may occur for multilayer flows with smaller viscosities in the inner layers. A correlation was deduced for the two-layer electroosmotic flow and the pressure driven flow, both being more complex when compared with single-layer flows. The impact of using power-law fluids on resulting velocity profiles has also been explored and compared to Newtonian fluid flows. The present model readily allows for an exploration of the impact of design choices on velocity profiles, shear stress, and channel distribution in multilayer microchannel flows as a function of layered viscosity distribution and type of driving force.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Profile of the electric potential φ(y) in an electric double layer (EDL)

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Figure 2

N-layer immiscible fluid Poiseuille-type flow

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Figure 3

Idealized n-layer electro-osmotic flow in a microchannel with zero pressure gradient and electric double layer (EDL)

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Figure 4

Three-layer pressure-driven flow

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Figure 5

Three-layer electroosmotic flow with ζNmax=ζ1=-24.4mV

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Figure 6

Three-layer electroosmotic flow with ζNmax=2ζ1=-48.8mV

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Figure 7

Three-layer combined electroosmotic and pressure-driven flow

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Figure 8

Four-layer pressure-driven flow

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Figure 9

Four-layer electroosmotic flow

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Figure 10

Entrance effect for three-layer pressure-driven flow

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Figure 11

Three-layer pressure-driven flow with power-law fluid in the middle layer

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Figure 12

Three-layer electroosmotic flow with power-law fluid in the middle layer

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