Research Papers

Spontaneous Fabrication of Three-Dimensional Multiscale Fractal Structures Using Hele-Shaw Cell

[+] Author and Article Information
Tanveer ul Islam

Suman Mashruwala Advanced
Micro Engineering Laboratory,
Department of Mechanical Engineering,
Indian Institute of Technology Bombay,
Mumbai 400076, India
e-mail: tanveerkamgar@gmail.com

Prasanna S. Gandhi

Suman Mashruwala Advanced
Micro Engineering Laboratory,
Department of Mechanical Engineering,
Indian Institute of Technology Bombay,
Mumbai 400076, India
e-mail: gandhi@iitb.ac.in

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received August 2, 2016; final manuscript received September 1, 2016; published online October 3, 2016. Editor: Y. Lawrence Yao.

J. Manuf. Sci. Eng 139(3), 031007 (Oct 03, 2016) (6 pages) Paper No: MANU-16-1414; doi: 10.1115/1.4034624 History: Received August 02, 2016; Revised September 01, 2016

Several biosystems such as leaf veins, respiratory system, blood circulation, and some plant xylem involving multiscale fractal topologies are being mimic for their inherent natural optimization. Three-dimensional fractal structures spanning multiple scales are difficult to fabricate. In this paper, we demonstrate a new method to fabricate structures spanning meso- and microscale in a relatively easy and inexpensive manner. A well-known Saffman–Taylor instability is exploited for the same in a lifted Hele-Shaw cell. In this cell, a thin layer of liquid is squeezed between two plates being lifted angularly leaving behind the fractal rearrangement of fluid which is proposed to be solidified later. We demonstrate and characterize fractal structures fabricated using two different fluids and corresponding methods of solidification. The first one is ceramic suspension in a photopolymer and another is polystyrene solution with photopolymerization and solvent vaporization as methods of solidification, respectively. The fabrication process is completed in period of a few seconds.

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Fig. 4

(a) SEM image of a section of branch after fabrication (top) and (b) 3D view of a fractal structure branch, fabricated from the ceramic suspension

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Fig. 5

Cross-sectional profile of structure branches plotted from the data obtained from WLI by mapping the branch topography, and the smooth curve is a Gaussian fit

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Fig. 3

Three-dimensional fractal structure fabricated (a) without tip-splitting from a film thickness of 35 μm and film radius of 15 mm and (b) with tip-splitting from a film thickness of 35 μm and 30 mm

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Fig. 2

Viscosity profile of the fluid as measured by modular compact Rheometer (Anton Paar Physica MCR301) with parallel plate method, and a gap of 0.5 mm

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Fig. 1

Schematic representation of Hele-Shaw cell with lifted plates in which the bottom plate is first pressed against the top plate (position 1) and then pulled from the edge to separate it at an angle (position 2)

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Fig. 6

Branch thickness variation for generations 1–4 with initial film thickness of 35, 50, and 65 μm

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Fig. 7

Graph shows the variation of branch width at the base with overall branch thickness. The best fit to the plot is a linear fit (r2 = 0.975) indicated by a straight line.

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Fig. 8

Graph shows that the number of extra branches increases with the increase in force of plate separation for b0 = 35 μm. Force of separation increases the velocity of finger penetration.

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Fig. 9

Microscopic view of fractal pattern fabricated with polystyrene as the high viscous fluid and different features indicated

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Fig. 10

Three-dimensional branch section fabricated from the polystyrene, mapped using WLI shows a square profile with a small depression in the middle

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Fig. 11

Cross-sectional profile of a structure branch plotted from the data points obtained by mapping the branch topography using WLI. The approximate fitted square cross section is also shown.

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Fig. 12

Variation of branch width and thickness for different branch generations

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Fig. 13

A branch fabricated from polystyrene solution: (a) SEM image of the molded channel section and (b) 3D view of the channel section obtained through WLI



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