Abstract
In this study, we consider the permeability of hexagonal arrays of micro-square pillars. A semi-analytic model for predicting the permeability of micro-square pillar arrays is developed. In addition, a numerical analysis is performed with taking into account the effect of meniscus curvature. The analytic and numerical results are in good agreement, within an error of 3%. Based on our analytic and numerical results, the effects of the contact angle (0 < θ < 90°), nondimensional pillar diagonal length (0.1 < d* < 0.5), and nondimensional pillar height (0.5 < H* < 2.5) are investigated. The meniscus curvature is shown to reduce the permeability significantly, particularly when the contact angle is small or the pillar height is low. The permeability of the square pillar array is shown to be larger than that of a circular pillar array.
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Squires, T. M. and Quake, S. R., “Microfluidics: Fluid Physics at the Nanoliter Scale,” Reviews of Modern Physics, Vol. 77, No. 3, pp. 977, 2005.
Lips, S., Lefèvre, F., and Bonjour, J., “Thermohydraulic Study of a Flat Plate Heat Pipe by Means of Confocal Microscopy: Application to a 2D Capillary Structure,” Journal of Heat Transfer, Vol. 132, No. 11, Paper No. 112901, 2010.
He, B., Tait, N., and Regnier, F., “Fabrication of Nanocolumns for Liquid Chromatography,” Analytical Chemistry, Vol. 70, No. 18, pp. 3790–3797, 1998.
Cui, H. H. and Lim, K. M., “Pillar Array Microtraps with Negative Dielectrophoresis,” Langmuir, Vol. 25, No. 6, pp. 3336–3339, 2009.
Patel, N., Rohatgi, N., and Lee, L. J., “Micro Scale Flow Behavior and Void Formation Mechanism during Impregnation through a Unidirectional Stitched Fiberglass Mat,” Polymer Engineering and Science, Vol. 35, No, 10, pp. 837–851, 1995.
Nagrath, S., Sequist, L. V., Maheswaran, S., Bell, D. W., Irimia, D., et al., “Isolation of Rare Circulating Tumour Cells in Cancer Patients by Microchip Technology,” Nature, Vol. 450, No. 7173, pp. 1235–1239, 2007.
Byon, C. and Kim, S. J., “The Effect of Meniscus on the Permeability of Micro-Post Arrays,” Journal of Micromechanics and Microengineering, Vol. 21, No. 11, Paper No. 115011, 2011.
Bruschke, M. and Advani, S., “Flow of Generalized Newtonian Fluids Across a Periodic Array of Cylinders,” Journal of Rheology (1978-present), Vol. 37, No. 3, pp. 479–498, 1993.
Srivastava, N., Din, C., Judson, A., MacDonald, N. C., and Meinhart, C. D., “A Unified Scaling Model for Flow through a Lattice of Microfabricated Posts,” Lab on a Chip, Vol. 10, No. 9, pp. 1148–1152, 2010.
Ishino, C., Reyssat, M., Reyssat, E., Okumura, K., and Quere, D., “Wicking Within Forests of Micropillars,” EPL (Europhysics Letters), Vol. 79, No. 5, Paper No. 56005, 2007.
Brakke, K. A., “The Surface Evolver,” Experimental Mathematics, Vol. 1, No. 2, pp. 141–165, 1992.
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Hong, DP., Lim, J. & Byon, C. Semi-analytic correlation for predicting permeability of micro-square-pillar array. Int. J. Precis. Eng. Manuf. 15, 1383–1387 (2014). https://doi.org/10.1007/s12541-014-0480-0
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DOI: https://doi.org/10.1007/s12541-014-0480-0