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Research Papers: Fundamental Issues and Canonical Flows

Effect of Microstructure Geometric Form on Surface Shear Stress

[+] Author and Article Information
Kaushik K. Rangharajan

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: rangharajan.1@osu.edu

Matthew J. Gerber

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: gerber211@g.ucla.edu

Shaurya Prakash

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: prakash.31@osu.edu

1K. K. Rangharajan and M. J. Gerber contributed equally to this work.

2Present address: Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, Los Angeles, CA 90095.

3Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 8, 2015; final manuscript received July 21, 2016; published online September 20, 2016. Assoc. Editor: Daniel Maynes.

J. Fluids Eng 139(1), 011201 (Sep 20, 2016) (8 pages) Paper No: FE-15-1728; doi: 10.1115/1.4034363 History: Received October 08, 2015; Revised July 21, 2016

Low Reynolds number flow of liquids over micron-sized structures and the control of subsequently induced shear stress are critical for the performance and functionality of many different microfluidic platforms that are extensively used in present day lab-on-a-chip (LOC) domains. However, the role of geometric form in systematically altering surface shear on these microstructures remains poorly understood. In this study, 36 microstructures of diverse geometry were chosen, and the resultant overall and facet shear stresses were systematically characterized as a function of Reynolds number to provide a theoretical basis to design microstructures for a wide array of applications. Through a set of detailed numerical calculations over a broad parametric space, it was found that the top facet (with respect to incident flow) of the noncylindrical microstructures experiences the largest surface shear stress. By systematically studying the variation of the physical dimensions of the microstructures and the angle of incident flow, a comprehensive regime map was developed for low to high surface shear structures and compared against the widely studied right circular cylinder in cross flow.

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Figures

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Fig. 1

In total, 36 structures were considered for systematic determination of surface shear stress and are sorted according to the geometry of the top facet: rectilinear prisms (eight shapes with nonradial, uniform top facet), radial prisms (11 shapes with radial, uniform top facet), nonvertical prisms (ten shapes with top facet of varying height), and apex structures (seven shapes with no explicit top facet)

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Fig. 2

A regime map for the 36 structures separated into four categories studied for the overall surface shear stress on each structure for (a) Re = 0.1 and (b) Re = 100. Overall shear stress is nondimensionalized with respect to (τs)all of a cylinder (100 μm in diameter and height). For Re = 0.1, 100 (τs)all of a cylinder was estimated to be 7.5 mN/m2 and 16.1 N/m2, respectively. The direction of fluid flow is indicated by the gray arrow with the coordinate system shown near the bottom left of the regime map.

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Fig. 3

Plot showing (τ¯s)i, average facet shear stress of (a) front, (b) rear, (c) side, and (d) top facets of all the 36 structures shown in the regime map at Re = 0.1. Each microstructure was categorized into high and low shear based on critical shear stress determined for each facet. The classification threshold for defining “high” and “low” shear stress for identifying structures was based on the relative comparison to a cylinder in cross-flow as discussed in the main text. Side facets exhibit minimal changes to shear stress as a function of microstructure morphology. The average side facet shear stress of all the 36 microstructures was estimated to be 0.79 ± 0.13 (minimal standard deviation). In general, the magnitude of shear stress is maximum at the top facet, followed by the side facet.

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Fig. 4

Plot showing (τ¯s)i average facet shear stress of (a) front, (b) rear, (c) side, and (d) top facets of all the 36 structures shown in the regime map at Re = 100. The classification threshold for defining “high” and “low” shear stress for identifying structures was based on the relative comparison to a cylinder in cross-flow.

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Fig. 5

Variation of velocity gradients at the top facet, nondimensionalized with the overall shear rate of a cylinder (7.89 s−1) at Re = 0.1 with equivalent critical dimensions. The gradient of velocity components in a direction normal to the top facet along ẑ contributes significantly toward (τ¯s)top.

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Fig. 6

The gradient of velocity in the normal direction to the front, side, and rear facets of a cube at Re = 0.1. Since the flow is along x̂,  |u| > |v,w  |, and therefore, the side facet experiences a greater shear stress compared to the front and rear facets.

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Fig. 7

The results of incrementing four physical dimensions of a cube through a range of values are presented. Distinct points represent discrete model solutions; and lines have been added for clarity. Dimensionless values of (τ¯s)i represent average surface shear stress nondimensionalized with respect to (τ¯s)front of an unaltered cube (12.5 N/m2 and Re = 100) with side length of 100 μm. In (a), the flat facets of the cube were altered to approach triangular cross sections (0 ≤  θp  ≤ 26.6 deg) eventually reaching a right pyramid. In (b), the curvature of the front and side facets was increased (0 ≤  Rv  ≤ 50 μm) to eventually be a cylinder. In (c), the angle of the front facet to the incident flow was increased (0 ≤  θw  ≤ 45.0 deg) until the final structure was a wedge. In (d), the curvature of the top facet was increased (0 ≤  Rt  ≤ 50 μm) until the form shown was reached. The direction of flow is indicated by the gray arrow.

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Fig. 8

The effects on (τ¯s)i for different angles of orientation for (a) a right pyramid and (b) a cube at Re = 100. At ϕp  = 0 deg and ϕC  = 0 deg, the FOI is in the front facet position. Dimensionless values of (τ¯s)i represent average surface shear stress nondimensionalized with respect to the pyramid and cube at ϕp  = 0 deg and ϕC  = 0 deg, respectively. The direction of fluid flow is always fixed and indicated by the gray arrow; FOI is indicated by a darkened face.

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