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Research Papers

Analysis of the Wicking and Thin-Film Evaporation Characteristics of Microstructures

[+] Author and Article Information
Ram Ranjan, Jayathi Y. Murthy

School of Mechanical Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907-2088

Suresh V. Garimella1

School of Mechanical Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907-2088sureshg@purdue.edu

1

Corresponding author.

J. Heat Transfer 131(10), 101001 (Jul 28, 2009) (11 pages) doi:10.1115/1.3160538 History: Received September 05, 2008; Revised February 19, 2009; Published July 28, 2009

The topology and geometry of microstructures play a crucial role in determining their heat transfer performance in passive cooling devices such as heat pipes. It is therefore important to characterize microstructures based on their wicking performance, the thermal conduction resistance of the liquid filling the microstructure, and the thin-film characteristics of the liquid meniscus. In the present study, the free-surface shapes of the static liquid meniscus in common microstructures are modeled using SURFACE EVOLVER for zero Bond number. Four well-defined topologies, viz., surfaces with parallel rectangular ribs, horizontal parallel cylinders, vertically aligned cylinders, and spheres (the latter two in both square and hexagonal packing arrangements), are considered. Nondimensional capillary pressure, average distance of the liquid free-surface from solid walls (a measure of the conduction resistance of the liquid), total exposed area, and thin-film area are computed. These performance parameters are presented as functions of the nondimensional geometrical parameters characterizing the microstructures, the volume of the liquid filling the structure, and the contact angle between the liquid and solid. Based on these performance parameters, hexagonally-packed spheres on a surface are identified to be the most efficient microstructure geometry for wicking and thin-film evaporation. The solid-liquid contact angle and the nondimensional liquid volume that yield the best performance are also identified. The optimum liquid level in the wick pore that yields the highest capillary pressure and heat transfer is obtained by analyzing the variation in capillary pressure and heat transfer with liquid level and using an effective thermal resistance model for the wick.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Side views of surface with (a) spheres (hexagonally packed), (c) spheres (square packed) and horizontal cylinders, (e) vertical cylinders, and parallel rectangular ribs. Plan views of surface with (b) spheres and cylinders (both hexagonally packed), (d) spheres and cylinders (both square packed), and (f) horizontal cylinders and rectangular ribs. The corresponding unit cell is also shown in each case.

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Figure 2

Schematic illustration and definition of the thin-film region of a liquid meniscus formed over a sphere

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Figure 3

Final liquid meniscus shape (dark gray) in (a) Topology 3, r=1, V=3.54(H=0.6), P=2.8, and θ=30 deg, and (b) Topology 1 (SP), r=1, V=3.6(H=0.5), P=2.8, and θ=45 deg

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Figure 4

(a) |ΔP|max and (b) maximum percentage thin-film area achieved in different topologies at any liquid volume for porosity=0.64 and θ=15 deg

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Figure 5

Capillary pressure versus nondimensional liquid volume for square and hexagonally-packed spheres for various contact angles (15–90 deg)

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Figure 6

Percentage thin-film area versus nondimensional liquid volume for (a) hexagonally packed and (b) square-packed spheres for various contact angles (15–90 deg)

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Figure 7

Non-dimensional area-averaged minimum meniscus distance versus nondimensional liquid volume for square- and hexagonally-packed spheres for various contact angles (15–90 deg)

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Figure 8

Total exposed liquid free-surface area versus nondimensional liquid volume for square- and hexagonally-packed spheres for various contact angles (15–90 deg)

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Figure 9

(a) Maximum |ΔP| and (b) maximum percentage thin-film area versus porosity in hexagonally-packed spheres on a surface, θ=15 deg

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Figure 10

Final liquid meniscus shape (dark gray) for (a) Topology 3, r=1, V=1.58(H=0.2), P=2.8; θ=15 deg between cylinder surface and liquid and θ=15 deg between bottom surface and liquid, and (b) Topology 1 (SP), r=1, V=0.75(H=0.1), P=2.8; θ=15 deg between sphere’s surface and liquid, and θ=0 deg between the bottom surface and liquid

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Figure 11

Final liquid meniscus shape (dark gray) for Topology 1 (HP), r=1, H=1, P=2.8; θ=15 deg between sphere surface and liquid

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Figure 12

(a) Area-averaged meniscus distance from solid walls versus nondimensional liquid height, and (b) percentage thin-film area of the meniscus for top and bottom layers of spheres in two-layer configuration versus nondimensional liquid height; θ=15 deg, porosity=0.56

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Figure 13

(a) Thermal resistance model for heat transfer in a wick (shown for hexagonally-packed spheres on a surface with simple-cubic packing in the z-direction), and (b) equivalent resistance network

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Figure 14

(a) Thermal resistance variation with nondimensional liquid level (H) in the wick pore, and (b) thermal resistances in thin-film and non-thin-film (extrinsic meniscus) paths for heat transfer versus nondimensional liquid level; θ=45 deg, porosity=0.56

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Figure 15

Total thermal resistance for evaporation and conduction in the wick versus nondimensional liquid height in the wick pore for θ=15, 30, and 45 deg, porosity=0.56

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