Poiseuille flow over a wavy surface

Simon J. Haward, Amy Q. Shen, Jacob Page, and Tamer A. Zaki
Phys. Rev. Fluids 2, 124102 – Published 8 December 2017

Abstract

We present a detailed series of experiments using spatially resolved flow velocimetry to examine the flow of Newtonian fluids through rectangular channels with one wavy surface of wave number k. The glass channels are fabricated by the method of selective laser-induced etching, which allows them to be made with a high (quasi-2D) aspect ratio (width/depth, w/2d=5) and with an accurate wave profile of small relative amplitude (A/d=0.05,A<k). Following the prior theoretical work for plane Couette flow over a wavy surface [Charru and Hinch, J. Fluid Mech. 414, 195 (2000)], we examine the influence of two dimensionless parameters (the normalized channel half-depth α=kd and the viscous length scale θ) on the penetration depth P of the perturbations that the wavy surface induces to the Poiseuille base flow. The asymptotic analysis by Charru and Hinch predicted three regimes of behavior classified as “shallow viscous” (Pα), “deep viscous” (P1), and “inviscid” (Pθ). All three regimes are here verified experimentally. Minor differences in details of the “phase diagram” for the flow regimes in αθ parameter space observed between Poiseuille and plane Couette flow are attributed to the contrasting boundary conditions in the different flow configurations. Our experimental results also compare favorably to results from linear theory for a Poiseuille base flow and thus establish a detailed experimental complement to the theory.

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  • Received 26 July 2017
  • Corrected 16 January 2018

DOI:https://doi.org/10.1103/PhysRevFluids.2.124102

©2017 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Corrections

16 January 2018

Erratum

Publisher's Note: Poiseuille flow over a wavy surface [Phys. Rev. Fluids 2, 124102 (2017)]

Simon J. Haward, Amy Q. Shen, Jacob Page, and Tamer A. Zaki
Phys. Rev. Fluids 3, 019901 (2018)

Authors & Affiliations

Simon J. Haward* and Amy Q. Shen

  • Okinawa Institute of Science and Technology Graduate University 1919-1 Tancha, Onna-son, Okinawa 904-0495, Japan

Jacob Page

  • School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom

Tamer A. Zaki

  • Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA

  • *Corresponding author: simon.haward@oist.jp

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Vol. 2, Iss. 12 — December 2017

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