Separation of particles in non-Newtonian fluids flowing in T-shaped microchannels

BackgroundThe flow of suspensions through bifurcations is encountered in several applications. It is known that the partitioning of particles at a bifurcation is different from the partitioning of the suspending fluid, which allows particle separation and fractionation. Previous works have mainly investigated the dynamics of particles suspended in Newtonian liquids.Methods In this work, we study through 2D direct numerical simulations the partitioning of particles suspended in non-Newtonian fluids flowing in a T-junction. We adopt a flow configuration such that the two outlets are orthogonal, and their flow rates can be tuned. A fictitious domain method combined with a grid deformation procedure is used. The effect of fluid rheology on the partitioning of particles between the two outlets is investigated by selecting different constitutive equations to model the suspending liquid. Specifically, an inelastic shear-thinning (Bird-Carreau) and a viscoelastic shear-thinning (Giesekus) models have been chosen; the results are also compared with the case of a Newtonian suspending liquid.ResultsSimulations are carried out by varying the confinement, the inlet flow rate and the relative weight of the two outlet flow rates. For each condition, the fluxes of particles through the two outflow channels are computed. The results show that shear-thinning does not have a relevant effect as compared to the equivalent Newtonian case, i.e., with the same choice of the relative outlet flow rates. On the other hand, fluid elasticity strongly alters the fraction of particles exiting the two outlets as compared to the inlet. Such effect is more pronounced for larger particles and inlet flow rates.ConclusionsThe results illustrated here show the feasibility to efficiently separate/fractionate particles by size, through the use of viscoelastic suspending liquids.

[1]  F. Plum Handbook of Physiology. , 1960 .

[2]  Patrick Jenny,et al.  Red blood cell distribution in simplified capillary networks , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[3]  Anugrah Singh,et al.  Numerical simulation of particle migration in asymmetric bifurcation channel , 2011 .

[4]  Anugrah Singh,et al.  Flow of concentrated suspension through oblique bifurcating channels , 2014 .

[5]  P. Gaehtgens,et al.  Effect of bifurcations on hematocrit reduction in the microcirculation. I. Fluid dynamic concepts of phase separation. , 1979, Bibliotheca anatomica.

[6]  W. Olbricht,et al.  Effects of particle concentration on the partitioning of suspensions at small divergent bifurcations. , 1996, Journal of biomechanical engineering.

[7]  R M Heethaar,et al.  Blood platelets are concentrated near the wall and red blood cells, in the center in flowing blood. , 1988, Arteriosclerosis.

[8]  A. Pries,et al.  Radial distribution of white cells during blood flow in small tubes. , 1985, Microvascular research.

[9]  S. Lee,et al.  Microfluidic particle separator utilizing sheathless elasto-inertial focusing , 2015 .

[10]  Pier Luca Maffettone,et al.  Single line particle focusing induced by viscoelasticity of the suspending liquid: theory, experiments and simulations to design a micropipe flow-focuser. , 2012, Lab on a chip.

[11]  Robert C. Armstrong,et al.  Dynamics of polymeric liquids: Fluid mechanics , 1987 .

[12]  B. W. Roberts,et al.  The distribution of freely suspended particles at microfluidic bifurcations , 2006 .

[13]  Chongyoup Kim,et al.  Separation of Particles of Different Sizes from Non-Newtonian Suspension by Using Branched Capillaries , 2007 .

[14]  M. Fortin,et al.  A new mixed finite element method for computing viscoelastic flows , 1995 .

[15]  P. Maffettone,et al.  Particle dynamics in viscoelastic liquids , 2015 .

[16]  Wenjuan Xiong,et al.  Two-dimensional lattice Boltzmann study of red blood cell motion through microvascular bifurcation: cell deformability and suspending viscosity effects , 2011, Biomechanics and Modeling in Mechanobiology.

[17]  S. Quake,et al.  Microfluidics: Fluid physics at the nanoliter scale , 2005 .

[18]  M. Villone,et al.  Numerical simulations of particle migration in a viscoelastic fluid subjected to Poiseuille flow , 2010 .

[19]  Axel R. Pries,et al.  Blood Flow in Microvascular Networks , 2011 .

[20]  M. Yamada,et al.  Microfluidic particle sorter employing flow splitting and recombining. , 2006, Analytical chemistry.

[21]  U Dinnar,et al.  Tunable nonlinear viscoelastic "focusing" in a microfluidic device. , 2007, Physical review letters.

[22]  M. Yamada,et al.  Continuous particle separation in a microchannel having asymmetrically arranged multiple branches. , 2005, Lab on a chip.

[23]  D. Fotiadis,et al.  Newtonian and Power-Law fluid flow in a T-junction of rectangular ducts , 2014 .

[24]  N. Shapley,et al.  Flows of concentrated suspensions through an asymmetric bifurcation , 2008 .

[25]  G. G. Peters,et al.  Numerical simulation of planar elongational flow of concentrated rigid particle suspensions in a viscoelastic fluid , 2008 .

[26]  R. Glowinski,et al.  A distributed Lagrange multiplier/fictitious domain method for particulate flows , 1999 .

[27]  László Baranyi,et al.  Laminar flow of non-Newtonian shear-thinning fluids in a T-channel , 2015 .

[28]  Paulo J. Oliveira,et al.  Steady and unsteady non-Newtonian inelastic flows in a planar T-junction☆ , 2013 .

[29]  W. Olbricht,et al.  The motion of model cells at capillary bifurcations. , 1987, Microvascular research.

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

[31]  Wook Ryol Hwang,et al.  Direct simulation of particle suspensions in sliding bi-periodic frames , 2004 .

[32]  Pier Luca Maffettone,et al.  Viscoelastic flow-focusing in microchannels: scaling properties of the particle radial distributions. , 2013, Lab on a chip.

[33]  Gaetano D'Avino,et al.  Particle alignment in a viscoelastic liquid flowing in a square-shaped microchannel. , 2013, Lab on a chip.

[34]  R. Larson Constitutive equations for polymer melts and solutions , 1988 .

[35]  Siyang Zheng,et al.  Streamline-Based Microfluidic Devices for Erythrocytes and Leukocytes Separation , 2008, Journal of microelectromechanical systems.

[36]  Juan M. Restrepo,et al.  Simulated Two-dimensional Red Blood Cell Motion, Deformation, and Partitioning in Microvessel Bifurcations , 2008, Annals of Biomedical Engineering.

[37]  P. Gaehtgens,et al.  Flow of blood through narrow capillaries: rheological mechanisms determining capillary hematocrit and apparent viscosity. , 1980, Biorheology.

[38]  M. Villone,et al.  Simulations of viscoelasticity-induced focusing of particles in pressure-driven micro-slit flow , 2011 .

[39]  Timothy W. Secomb,et al.  A model for red blood cell motion in bifurcating microvessels , 2000 .

[40]  B. W. Roberts,et al.  Flow‐induced particulate separations , 2003 .

[41]  Anne M Grillet,et al.  Stability analysis of polymer shear flows using the extended Pom-Pom constitutive equations , 2002 .

[42]  Sehyun Shin,et al.  Continuous separation of microparticles in a microfluidic channel via the elasto-inertial effect of non-Newtonian fluid. , 2011, Lab on a chip.

[43]  Wook Ryol Hwang,et al.  Direct simulations of particle suspensions in a viscoelastic fluid in sliding bi-periodic frames , 2004 .

[44]  Pape Hd,et al.  Effect of bifurcations on hematocrit reduction in the microcirculation. I. Fluid dynamic concepts of phase separation. , 1979 .

[45]  Y. Fung Stochastic flow in capillary blood vessels. , 1973, Microvascular research.

[46]  P. Maffettone,et al.  Numerical simulations of particle migration in a viscoelastic fluid subjected to shear flow , 2010 .

[47]  M. Manga Dynamics of drops in branched tubes , 1996, Journal of Fluid Mechanics.

[48]  Jeffrey M. Davis,et al.  Chapter 6 – Blood Flow Through Capillary Networks , 2013 .

[49]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[50]  L. G. Leal,et al.  Migration of rigid spheres in a two-dimensional unidirectional shear flow of a second-order fluid , 1976, Journal of Fluid Mechanics.

[51]  S. G. Mason,et al.  Particle motions in non-newtonian media , 1975 .

[52]  S. Lee,et al.  Sheathless elasto-inertial particle focusing and continuous separation in a straight rectangular microchannel. , 2011, Lab on a chip.

[53]  Hugh C. Woolfenden,et al.  Motion of a two-dimensional elastic capsule in a branching channel flow , 2011, Journal of Fluid Mechanics.

[54]  Raanan Fattal,et al.  Flow of viscoelastic fluids past a cylinder at high Weissenberg number : stabilized simulations using matrix logarithms , 2005 .

[55]  Raanan Fattal,et al.  Constitutive laws for the matrix-logarithm of the conformation tensor , 2004 .

[56]  Stefan Turek,et al.  Mathematical and Numerical Analysis of a Robust and Efficient Grid Deformation Method in the Finite Element Context , 2008, SIAM J. Sci. Comput..

[57]  F. Gauthier,et al.  Particle Motions in Non‐Newtonian Media. II. Poiseuille Flow , 1971 .

[58]  G. D’Avino,et al.  A comparison between a collocation and weak implementation of the rigid‐body motion constraint on a particle surface , 2009 .

[59]  Howard H. Hu,et al.  Direct numerical simulations of fluid-solid systems using the arbitrary Langrangian-Eulerian technique , 2001 .

[60]  Pier Luca Maffettone,et al.  A numerical method for simulating concentrated rigid particle suspensions in an elongational flow using a fixed grid , 2007, J. Comput. Phys..

[61]  P. Oliveira,et al.  Steady flows of constant-viscosity viscoelastic fluids in a planar T-junction , 2014 .

[62]  M. Yamada,et al.  Pinched flow fractionation: continuous size separation of particles utilizing a laminar flow profile in a pinched microchannel. , 2004, Analytical chemistry.