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Effective slip in nanoscale flows through thin channels with sinusoidal patterns of wall wettability

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Abstract

Liquids are known to slip past non-wetting channel walls. The degree of slippage can be patterned locally through engineered variations in topography and/or chemistry. Electro-osmotic flow through a thin slit-like nanochannel with walls of sinusoidally varying slippage is studied through an asymptotic theory that uses the ratio of pattern amplitude to the average slip as a small parameter. The direction of patterning is perpendicular to the applied electric field. No restrictions are placed on the relative magnitudes of the channel height, wavelength of the pattern, the average slip length and the phase shift between the patterns on the walls. A closed-form analytical expression is provided for the effective slip length and tested against limits known from the literature. The results are also generalized for applicability to any unidirectional flow field that might originate from other driving forces such as pressure differential. The asymptotic results are compared with numerical simulations and are found to be in good mutual agreement even for moderate magnitudes of the small parameter in the asymptotic theory.

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Notes

  1. This expression evaluates to \(b_{eff} \kappa = - c_{0} + o(\alpha^{2} ) n\) with c 0 given by Eq. (19a), by virtue of the global arguments presented in the discussion following Eq. (7).

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Acknowledgments

Financial assistance from the SERB division, Department of Science and Technology, India (sanction letter no. SB/FTP/ETA-142/2012), is acknowledged. Abhinav Dhar and Shubham Agarwal of IIT Delhi are thanked for their preliminary findings on the numerical aspects of the problem.

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Authors and Affiliations

  1. Department of Mechanical Engineering, IIT Delhi, New Delhi, 110016, India

    J. N. Choudhary, Subhra Datta & Sanjeev Jain

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  1. J. N. Choudhary
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  2. Subhra Datta
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  3. Sanjeev Jain
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Correspondence to Subhra Datta.

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Choudhary, J.N., Datta, S. & Jain, S. Effective slip in nanoscale flows through thin channels with sinusoidal patterns of wall wettability. Microfluid Nanofluid 18, 931–942 (2015). https://doi.org/10.1007/s10404-014-1483-y

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