Viscous Fingering in Multiport Hele Shaw Cell for Controlled Shaping of Fluids

The pursuit of mimicking complex multiscale systems has been a tireless effort with many successes but a daunting task ahead. A new perspective to engineer complex cross-linked meshes and branched/tree-like structures at different scales is presented here. Control over Saffman-Taylor instability which otherwise randomly rearranges viscous fluid in a ‘lifted Hele-Shaw cell’ is proposed for the same. The proposed control employs multiple-ports or source-holes in this cell, to spontaneously shape a stretched fluid film into a network of well defined webs/meshes and ordered multiscale tree-like patterns. Use of multiple ports enables exercising strong control to fabricate such structures, in a robust and repeated fashion, which otherwise are completely non-characteristic to viscous fingering process. The proposed technique is capable of fabricating spontaneously families of wide variety of structures over micro and very large scale in a period of few seconds. Thus the proposed method forms a solid foundation to new pathways for engineering multiscale structures for several scientific applications including efficient gas exchange, heat transport, tissue engineering, organ-on-chip, and so on. Proposal of multi-port Hele-Shaw cell also opens new avenues for investigation of complex multiple finger interactions resulting in interesting fluid patterns.

[1]  O. Pla,et al.  Linear stability analysis of the Hele-Shaw cell with lifting plates , 1996, cond-mat/9610103.

[2]  Hsueh-Chia Chang,et al.  Fractal dewetting of a viscous adhesive film between separating parallel plates , 2001 .

[3]  V. Narayanan,et al.  Optimization of fractal-like branching microchannel heat sinks for single-phase flows , 2010 .

[4]  Shuichi Takayama,et al.  Fabrication of microfluidic mixers and artificial vasculatures using a high-brightness diode-pumped Nd:YAG laser direct write method. , 2003, Lab on a chip.

[5]  Sang-Hoon Lee,et al.  3D liver models on a microplatform: well-defined culture, engineering of liver tissue and liver-on-a-chip. , 2015, Lab on a chip.

[6]  J. Lewis,et al.  Direct-write assembly of biomimetic microvascular networks for efficient fluid transport , 2010 .

[7]  M. Shelley,et al.  Hele - Shaw flow and pattern formation in a time-dependent gap , 1997 .

[8]  Ali Khademhosseini,et al.  Microfluidic techniques for development of 3D vascularized tissue. , 2014, Biomaterials.

[9]  L. Gervais,et al.  Toward one-step point-of-care immunodiagnostics using capillary-driven microfluidics and PDMS substrates. , 2009, Lab on a chip.

[10]  M. Toner,et al.  Cellular Micropatterns on Biocompatible Materials , 1998, Biotechnology progress.

[11]  D. Di Carlo,et al.  Research highlights: Microtechnologies for engineering the cellular environment. , 2014, Lab on a chip.

[12]  M. Ostilli Cayley Trees and Bethe Lattices: A concise analysis for mathematicians and physicists , 2011, 1109.6725.

[13]  Woo-Tae Park,et al.  Rapid, low-cost fabrication of circular microchannels by air expansion into partially cured polymer , 2016 .

[14]  T. Wheeler,et al.  The transpiration of water at negative pressures in a synthetic tree , 2008, Nature.

[15]  Tanveer ul Islam,et al.  Spontaneous Fabrication of Three-Dimensional Multiscale Fractal Structures Using Hele-Shaw Cell , 2017 .

[16]  M. Mulvany,et al.  Structure and function of small arteries. , 1990, Physiological reviews.

[17]  Anke Lindner,et al.  Cohesive failure of thin layers of soft model adhesives under tension , 2003 .

[18]  Prasanna S. Gandhi,et al.  Fabrication of Multscale Fractal-Like Structures by Controlling Fluid Interface Instability , 2016, Scientific Reports.

[19]  A. Khademhosseini,et al.  Microscale technologies for tissue engineering and biology. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[20]  Adrian Bejan,et al.  Constructal tree-shaped flow structures , 2007 .

[21]  H. S. Hele-Shaw,et al.  The Flow of Water , 1898, Nature.

[22]  Shanglong Xu,et al.  Characteristics of heat transfer and fluid flow in a fractal multilayer silicon microchannel , 2016 .

[23]  Alexandre K. da Silva,et al.  Constructal multi-scale tree-shaped heat exchangers , 2004 .

[24]  Bing Han,et al.  Bio-inspired networks for optoelectronic applications , 2014, Nature Communications.

[25]  P. Gandhi,et al.  A scalable, lithography-less fabrication process for generating a bio-inspired, multi-scale channel network in polymers , 2017 .

[26]  S. Tarafdar,et al.  Radially interrupted viscous fingers in a lifting Hele-Shaw cell , 2003, cond-mat/0306093.

[27]  Deborah V. Pence,et al.  The simplicity of fractal-like flow networks for effective heat and mass transport , 2010 .

[28]  Johannes A. G. Rhodin,et al.  Architecture of the Vessel Wall , 1980 .

[29]  Yaxiong Liu,et al.  Fabrication of circular microfluidic network in enzymatically-crosslinked gelatin hydrogel. , 2016, Materials science & engineering. C, Materials for biological applications.

[30]  J. Vacanti,et al.  Microfabrication Technology for Vascularized Tissue Engineering , 2002 .

[31]  Martine Ben Amar,et al.  Fingering instabilities in adhesive failure , 2005 .

[32]  G. Taylor,et al.  The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid , 1958, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[33]  Arezki Boudaoud,et al.  In silico leaf venation networks: growth and reorganization driven by mechanical forces. , 2009, Journal of theoretical biology.

[34]  J. Vacanti,et al.  Silicon micromachining to tissue engineer branched vascular channels for liver fabrication. , 2000, Tissue engineering.

[35]  Mitra Damghanian,et al.  A Static Micromixer Inspired from Fractal-Like Natural Flow Systems , 2011 .