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Research Papers: Micro/Nanoscale Heat Transfer

Liquid Slippage in Confined Flows: Effect of Periodic Micropatterns of Arbitrary Pitch and Amplitude

[+] Author and Article Information
Avinash Kumar

Department of Mechanical Engineering,
Indian Institute of Technology Delhi,
New Delhi 110016, India
e-mail: avikr.iitk@gmail.com

Subhra Datta

Department of Mechanical Engineering,
Indian Institute of Technology Delhi,
New Delhi 110016, India
e-mail: subhra.datta@mech.iitd.ernet.in

Dinesh Kalyanasundaram

Centre for Biomedical Engineering,
Indian Institute of Technology Delhi,
New Delhi 110016, India
e-mails: dineshk@cbme.iitd.ac.in;
dineshk.iitdelhi@gmail.com

1Corresponding author.

Presented at the 5th ASME 2016 Micro/Nanoscale Heat & Mass Transfer International Conference. Paper No. MNHMT2016-6491.Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 6, 2016; final manuscript received March 17, 2017; published online August 23, 2017. Assoc. Editor: Chun Yang.

J. Heat Transfer 140(1), 012403 (Aug 23, 2017) (7 pages) Paper No: HT-16-1357; doi: 10.1115/1.4037363 History: Received June 06, 2016; Revised March 17, 2017

The recently confirmed violation of the no-slip boundary condition in the flow of small-molecule liquids through microchannels and nanochannels has technological implications such as friction reduction. However, for significant friction reduction at low cost, the microchannel wall needs to be chemically inhomogeneous. The direct fluid dynamic consequence of this requirement is a spatial variation in the local degree of liquid slippage. In this work, the pressure-driven flow in a channel with periodically patterned slippage on the channel walls is studied using a spectrally accurate semi-analytical approach based on Fourier decomposition. The method puts no restrictions on the pitch (or wavelength) and amplitude of the pattern. The predicted effective slip length in the limits of small pattern amplitude and thick channels is found to be consistent with previously published results. The effective degree of slippage decreases with the patterning amplitude. Finer microchannels and longer pattern wavelengths promote slippage.

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Figures

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Fig. 1

Illustration of channel geometry and co-ordinate system

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Fig. 2

Channel with longitudinal stripes. The corresponding flow is termed as “longitudinal slip flow”.

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Fig. 3

Comparison of semi-analytic method with numerical method and small amplitude theory for b0/h = 1 and λ = 2π

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Fig. 4

Variation of effective slip length with amplitude for different dimensionless wavelengths (λ = 0.1, 1, 10) with b0/h = 1: comparison between semi-analytical and small amplitude theory [27]

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Fig. 5

Variation of beff/b0 with dimensionless wave number of the pattern (2πh/L) for α = 0, 0.5, 0.9 and 1 with b0/h = 1

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Fig. 6

Variation of dimensionless effective slip length with dimensionless channel height for b0/L = 0.1, 1, and 10 with α = 0.6

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Fig. 7

Velocity distribution in a periodic cell of flow with λ = L/h = 2π and b0/h = 1 for (a) α = 0.4 and (b) α = 1

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Fig. 8

Variation of fluid velocity over the surface and two dimensionless channel heights h/L = 0.01 and h/L = 10, when for α = 1 and b0/L = 1. The local slip length given by Eq. (3) is also shown for reference.

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