Barber, Robert W.

Emerson, David

Oliveira, Monica

Zografos, Konstantinos

Name not available

Flow of power law fluids in microfluidic bifurcating networks designed using biomimetic principles

University of Strathclyde Institutional Repository

Strathprints Institutional RepositoryZografos, Konstantinos and Barber, Robert W. and Emerson, David and Oliveira, Monica (2014) Flow of power law fluids in microfluidic bifurcating networks designed using biomimetic principles. In: 9th Annual European Rheology Conference, AERC 2014, 2014-04-08 - 2014-04-11. , This version is available at http://strathprints.strath.ac.uk/55070/Strathprints is  designed  to  allow  users  to  access  the  research  output  of  the  University  of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may  not  engage  in  further  distribution  of  the  material  for  any  profitmaking  activities  or  any commercial gain. You may freely distribute both the url (http://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge. Any  correspondence  concerning  this  service  should  be  sent  to  Strathprints  administrator: strathprints@strath.ac.ukFlow of power-law fluids in microfluidic bifurcating networks designed using biomimetic principles  Zografos, K.,1 Barber, R. W.,2 Emerson, D. R.,2 Oliveira, M.S.N.1  1 James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering, University of Strathclyde, G1 1XQ, Glasgow, UK 2 Centre for Microfluidics and Microsystems Modelling, STFC Daresbury Laboratory, Daresbury, Warrington, UK   The flow of a non-Newtonian power-law fluid, described by the Ostwald-de Waele relationship is investigated numerically in rectangular-shaped bifurcating networks designed using biomimetic principles. Murrays law is based on the principle of minimum work and in its original form establishes the optimum ratio between the diameters of the parent (d0) and daughter vessels (d1 and d2) for circular cross-sectional networks. The  relationship derived by Murray can be written as d03 = d13+ d23 [1]. The theory has recently been extended to consider rectangular cross-sectional networks containing Newtonian fluids [2]. In the present work, we demonstrate numerically the ability to customise these networks for use with power-law fluids and to generate particular resistance gradients in microfluidic distribution systems. The problem is investigated using a fully-implicit numerical code based on the finite volume method for collocated meshes [3]. We consider isothermal, laminar flow of a power-law fluid for power law indices ranging from 0.2 to 3 to study the behaviour of both shear-thinning and shear-thickening fluids. A range of geometries has been designed to generate precise resistance gradients and initially tested using creeping flow conditions (Reynolds ŶƵŵďĞƌ ?ZĞA? ? ? ?ǁŚŝĐŚŝƐĂƌĞĂƐŽŶĂďůĞĂƉƉƌŽǆŝŵĂƚŝŽŶŝŶŵŝĐƌŽĨůƵŝĚŝĐƐ ?ŶƵŵďĞƌŽĨsimulations using different initial channel aspect ratios and different Re were also performed to assess the flow characteristics and examine the limits of the validity of the biomimetic rule for power-law fluids under various flow conditions. Analysis of the tangential wall shear stress and flow resistance distribution shows the ability of the network design to impart the desired flow characteristics.  [1] C.D. Murray, Proc Natl Acad Sci USA 12 (1926) 207-214. [2] R. W. Barber, D. R. Emerson, Microfluid Nanofluid 4 (2008) 179-191. [3] P.J. Oliveira, F.T. Pinho, G.A. Pinto, J Non-Newtonian Fluid Mech 79 (1998) 1-43.  

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Flow of power law fluids in microfluidic bifurcating networks designed using biomimetic principles

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