Steady and unsteady non-Newtonian inelastic flows in a planar T-junction☆

Steady and unsteady laminar flows in a planar 2D T-junction, having a dividing or bifurcating flow arrangement (one main channel with a side branch at 90°), are studied numerically for non-Newtonian inelastic fluids whose rheological characteristics are similar to those of blood. These computational fluid dynamics simulations explore a wide range of variation of inertia (through the Reynolds number, Re), flow rate ratio (proportion of extracted to inlet flow rates, β) and shear thinning (the power-law index of the model, n), and investigate their influence on the sizes and intensities of the recirculating eddies formed near the bifurcation, and on the resulting distribution of the shear stress fields. Such flow characteristics are relevant to hemodynamics, being related to the genesis and development of vascular diseases, like the formation of atherosclerotic plaques and thrombi near arterial bifurcations. To represent the decay of viscosity with shear rate we apply the Carreau-Yasuda equation, one of the most utilized Generalized Newtonian Fluid model in blood simulations. In many comparisons of the present parametric study it was require that the level of inertia was kept approximately the same when n was varied. This implied a consistent definition of Re with the viscosity calculated at a representative shear rate.

[1]  A Study of Local Hydrodynamics in a 90° Branched Vessel with Extreme Pulsatile Flows , 1998 .

[2]  Fernando T. Pinho,et al.  Fully developed laminar flow of non-Newtonian liquids through annuli: comparison of numerical calculations with experiments , 2002 .

[3]  F. Pinho,et al.  Numerical simulation of non-linear elastic flows with a general collocated finite-volume method , 1998 .

[4]  Petr Louda,et al.  Numerical solution of incompressible flow through branched channels , 2011 .

[5]  I. Owen,et al.  Dynamic scaling of unsteady shear-thinning non-Newtonian fluid flows in a large-scale model of a distal anastomosis , 2007 .

[6]  F. Pinho,et al.  A convergent and universally bounded interpolation scheme for the treatment of advection , 2003 .

[7]  Chih-Ming Ho,et al.  Monocyte recruitment to endothelial cells in response to oscillatory shear stress , 2003, FASEB journal : official publication of the Federation of American Societies for Experimental Biology.

[8]  S. Chien.  Effects of Disturbed Flow on Endothelial Cells , 2008, Annals of Biomedical Engineering.

[9]  D. Ku,et al.  Pulsatile Flow and Atherosclerosis in the Human Carotid Bifurcation: Positive Correlation between Plaque Location and Low and Oscillating Shear Stress , 1985, Arteriosclerosis.

[10]  Shah Ebrahim,et al.  European Guidelines on Cardiovascular Disease Prevention in Clinical Practice (Version 2012) , 2012, International Journal of Behavioral Medicine.

[11]  M. Debakey,et al.  Patterns of Atherosclerosis and their Surgical Significance , 1985, Annals of surgery.

[12]  R. Issa,et al.  NUMERICAL PREDICTION OF PHASE SEPARATION IN TWO-PHASE FLOW THROUGH T-JUNCTIONS , 1994 .

[13]  N. Moshkin,et al.  Steady viscous incompressible flow driven by a pressure difference in a planar T-junction channel , 2009 .

[14]  M. Crowther,et al.  Pathogenesis of atherosclerosis. , 2005, Hematology. American Society of Hematology. Education Program.

[15]  K. Cunningham,et al.  The role of shear stress in the pathogenesis of atherosclerosis , 2005, Laboratory Investigation.

[16]  F. Pinho,et al.  NUMERICAL PROCEDURE FOR THE COMPUTATION OF FLUID FLOW WITH ARBITRARY STRESS-STRAIN RELATIONSHIPS , 1999 .

[17]  Steven Deutsch,et al.  Viscoelasticity of Pediatric Blood and its Implications for the Testing of a Pulsatile Pediatric Blood Pump , 2005, ASAIO journal.

[18]  K. Yasuda,et al.  Shear flow properties of concentrated solutions of linear and star branched polystyrenes , 1981 .

[19]  S. Berger,et al.  Flows in Stenotic Vessels , 2000 .

[20]  D. L. Fry.  Certain Histological and Chemical Responses of the Vascular Interface to Acutely Induced Mechanical Stress in the Aorta of the Dog , 1969, Circulation research.

[21]  Shah Ebrahim,et al.  European guidelines on cardiovascular disease prevention in clinical practice. Third Joint Task Force of European and Other Societies on Cardiovascular Disease Prevention in Clinical Practice. , 2003 .

[22]  J. P. V. Doormaal,et al.  ENHANCEMENTS OF THE SIMPLE METHOD FOR PREDICTING INCOMPRESSIBLE FLUID FLOWS , 1984 .

[23]  Y. Tsui,et al.  A study of the recirculating flow in planar, symmetrical branching channels , 2006 .

[24]  R. Ross,et al.  Atherosclerosis is an inflammatory disease. , 1998, American heart journal.

[25]  Paulo J. Oliveira,et al.  Method for time-dependent simulations of viscoelastic flows: vortex shedding behind cylinder , 2001 .

[26]  Joel H. Ferziger,et al.  Computational methods for fluid dynamics , 1996 .

[27]  R. Schroter,et al.  Atheroma and arterial wall shear - Observation, correlation and proposal of a shear dependent mass transfer mechanism for atherogenesis , 1971, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[28]  Fotis Sotiropoulos,et al.  Numerical investigation of laminar flows through 90-degree diversions of rectangular cross-section , 1996 .

[29]  P. Nithiarasu,et al.  An investigation of pulsatile flow in a model cavo-pulmonary vascular system , 2009 .

[30]  Fernando T. Pinho,et al.  Steady and unsteady laminar flows of Newtonian and generalized Newtonian fluids in a planar T‐junction , 2008 .

[31]  Fernando T. Pinho,et al.  Edge Effects on the Flow Characteristics in a 90deg Tee Junction , 2006 .

[32]  C. Balan,et al.  Mixing process of immiscible fluids in microchannels , 2010 .

[33]  K. Cunningham,et al.  The role of shear stress in the pathogenesis of atherosclerosis , 2005, Laboratory Investigation.

[34]  Manuel A. Alves,et al.  New Formulation for Stress Calculation: Application to Viscoelastic Flow in a T-Junction , 2010 .

[35]  G. Majno,et al.  Hydrodynamic injury of the endothelium in acute aortic stenosis. , 1982, The American journal of pathology.

[36]  Robert G. Owens,et al.  A new microstructure-based constitutive model for human blood , 2006 .

[37]  C. Zarins,et al.  Carotid Bifurcation Atherosclerosis: Quantitative Correlation of Plaque Localization with Flow Velocity Profiles and Wall Shear Stress , 1983, Circulation research.

[38]  Y. Cho,et al.  Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part 1: Steady flows. , 1991, Biorheology.

[39]  C. Rhie,et al.  Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation , 1983 .

[40]  Peter Spedding,et al.  Fluid Flow in an Impacting Symmetrical Tee Junction: II Two-Phase Air/Water Flow , 2009 .

[41]  D. Liepsch,et al.  Measurement and calculations of laminar flow in a ninety degree bifurcation. , 1982, Journal of biomechanics.

[42]  D. Liepsch,et al.  LDA measurements and numerical prediction of pulsatile laminar flow in a plane 90-degree bifurcation. , 1988, Journal of biomechanical engineering.

[43]  F. Sotiropoulos,et al.  THREE-DIMENSIONAL NUMERICAL MODEL OF LATERAL-INTAKE INFLOWS , 1999 .

[44]  R. Shah.  Laminar Flow Forced convection in ducts , 1978 .