- Access by Xinjiang University
Effect of shear thinning on superhydrophobic slip: Perturbative corrections to the effective slip length
Phys. Rev. Fluids 2, 124201 – Published 6 December, 2017
DOI: https://doi.org/10.1103/PhysRevFluids.2.124201
Abstract
Analytical expressions are derived for the first-order correction to the effective slip length of a weakly shear-thinning Carreau-Yasuda fluid in both longitudinal and transverse semi-infinite shear flow over a unidirectional superhydrophobic surface of flat no-shear slots. The formulas, which are derived using suitably generalized forms of the standard reciprocal theorem for Stokes flow, are given by explicit integrals which require only numerical quadrature for their evaluation. For both longitudinal and transverse flow we find that for a given no-shear fraction of the superhydrophobic surface and a given power-law index characterizing the Carreau-Yasuda fluid, there is a critical imposed strain rate of the shear at which the enhancement of effective slip is maximal. The theoretical results are qualitatively consistent with recent numerical work by other authors for the transverse case.
Physics Subject Headings (PhySH)
Article Text
References (26)
- J. P. Rothstein, Slip on superhydrophobic surfaces, Annu. Rev. Fluid Mech. 42, 89 (2010).
- E. Lauga, M. P. Brenner, and H. A. Stone, in Springer Handbook of Experimental Fluid Dynamics, edited by C. Tropea, A. Yarin, and J. F. Foss (Springer, New York, 2007), Chap. 19.
- E. Lauga and H. A. Stone, Effective slip in pressure-driven Stokes flow, J. Fluid Mech. 489, 55 (2003).
- P. Yager, T. Edwards, E. Fu, K. Helton, K. Nelson, M. R. Tam, and B. H. Weigl, Microfluidic diagnostic technologies for global public health, Nature (London) 442, 412 (2006).
- F. J. H. Gijsen, E. Allanic, F. N. van de Vosse, and J. D. Janssen, The influence of the non-Newtonian properties of blood on the flow in large arteries: Unsteady flow in a 903 curved tube, J. Biomech. 32, 705 (1999).
- S. A. Vagner and S. A. Patlazhan, Hydrodynamics of Newtonian and power-law fluids in microchannel with superhydrophobic wall, J. Phys.: Conf. Ser. 774, 012027 (2016).
- R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, Vol 1: Fluid Mechanics (Wiley, New York, 1987).
- G. G. Pereira, Effect of variable slip boundary conditions on flows of pressure driven non-Newtonian fluids, J. Non-Newtonian Fluid Mech. 157, 197 (2009).
- S. Dhondi, G. G. Pereira, and S. C. Hendy, Molecular dynamics simulations of polymeric fluids in narrow channels: Methods to enhance mixing, Phys. Rev. E 80, 036309 (2009).
- A. S. Haase, J. A. Wood, L. M. J. Sprakel, and R. G. H. Lammertink, Inelastic non-Newtonian flow over heterogeneously slippery surfaces, Phys. Rev. E 95, 023105 (2017).
- A. Steinberger, C. Cottin-Bizonne, P. Kleimann, and E. Charlaix, High friction on a bubble mattress, Nat. Mater. 6, 665 (2007).
- A. M. J. Davis and E. Lauga, Geometric transition in friction for flow over a bubble mattress, Phys. Fluids 21, 011701 (2009).
- L. G. Leal, Particle motions in a viscous fluid, Annu. Rev. Fluid Mech. 12, 435 (1980).
- J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Springer Netherlands, The Hague, 1983).
- E. Lauga, Locomotion in complex fluids: Integral theorems, Phys. Fluids 26, 081902 (2014).
- C. Datt, L. Zhu, G. Elfring, and O.-S. Pak, Squirming through shear-thinning fluids, J. Fluid Mech. 784, R1 (2015).
- S. Yazdi, A. M. Ardekani, and A. Borhan, Swimming dynamics near a wall in a weakly elastic fluid, J. Nonlinear Sci. 25, 1153 (2015).
- D. G. Crowdy, Perturbation analysis of subphase gas and meniscus curvature effects for longitudinal flows over superhydrophobic surfaces, J. Fluid Mech. 822, 307 (2017).
- M. Sbragaglia and A. Prosperetti, A note on the effective slip properties for microchannel flows with ultrahydrophobic surfaces, Phys. Fluids 19, 043603 (2007).
- T. M. Squires, Electrokinetic flows of inhomogeneously slipping surfaces, Phys. Fluids 20, 092105 (2008).
- T. Baier, C. Steffes, and S. Hardt, Thermocapillary flow on superhydrophobic surfaces, Phys. Rev. E 82, 037301 (2010).
- J. R. Philip, Flows satisfying mixed no-slip and no-shear conditions, J. Appl. Math. Phys. 23, 353 (1972).
- D. G. Crowdy, Frictional slip lengths for unidirectional superhydrophobic grooved surfaces, Phys. Fluids 23, 072001 (2011).
- E. Karatay, A. S. Haase, C. W. Visser, C. Sun, D. Lohse, P. A. Tsai, and R. G. H. Lammertink, Control of slippage with tunable bubble mattresses, Proc. Natl. Acad. Sci. U.S.A. 110, 8422 (2013).
- D. G. Crowdy, Slip length for longitudinal shear flow over a dilute periodic mattress of protruding bubbles, Phys. Fluids 22, 121703 (2011).
- D. G. Crowdy, Analytical formulas for longitudinal slip lengths over unidirectional superhydrophobic surfaces with curved menisci, J. Fluid Mech. 791, R7 (2016).