A computational study of two-phase viscoelastic systems in a capillary tube with a sudden contraction/expansion

Physics of Fluids - Tập 28 Số 1 - 2016
Daulet Izbassarov1, Metin Muradoğlu1
1Koç University Department of Mechanical Engineering, , Rumelifeneri Yolu, 34450 Sariyer, Istanbul, Turkey

Tóm tắt

Two-phase viscoelastic systems are computationally studied in a pressure-driven flow with a sudden contraction and expansion using a finite-difference/front-tracking method. The effects of viscoelasticity in drop and bulk fluids are investigated including high Weissenberg and Reynolds number cases up to Wi = 100 and Re = 100. The Finitely Extensible Non-linear Elastic–Chilcott and Rallison (FENE-CR) model is used to account for the fluid viscoelasticity. Extensive computations are performed to examine drop dynamics for a wide range of parameters. It is found that viscoelasticity interacts with drop interface in a non-monotonic and complicated way, and the two-phase viscoelastic systems exhibit very rich dynamics especially in the expansion region. At high Re, the drop undergoes large deformation in the contraction region followed by strong shape oscillations in the downstream of the expansion. For a highly viscous drop, a re-entrant cavity develops in the contraction region at the trailing edge which, in certain cases, grows and eventually causes encapsulation of ambient fluid. The re-entrant cavity formation is initiated at the entrance of the contraction and is highly influenced by the viscoelasticity. Compared to the corresponding straight channel case, the effects of viscoelasticity are reversed in the constricted channel: Viscoelasticity in drop/continuous phase hinders/enhances formation of the re-entrant cavity and entrainment of ambient fluid into main drop. Encapsulation of ambient fluid into main droplet may be another route to produce a compound droplet in microfluidic applications.

Từ khóa


Tài liệu tham khảo

2005, Microfluidics: Fluid physics at the nanoliter scale, Rev. Mod. Phys., 77, 977, 10.1103/RevModPhys.77.977

2004, Engineering flows in small devices: Microfluidics toward a lab-on-a-chip, Annu. Rev. Fluid Mech., 36, 381, 10.1146/annurev.fluid.36.050802.122124

1996, Pore-scale prototypes of multiphase flow in porous media, Annu. Rev. Fluid Mech., 28, 128, 10.1146/annurev.fl.28.010196.001155

2010, The dynamic behavior of chemically stiffened red blood cells in microchannel flows, Microvasc. Res., 80, 37, 10.1016/j.mvr.2010.03.008

2009, A particle-based model for the transport of erythrocytes in capillaries, Chem. Eng. Sci., 64, 4488, 10.1016/j.ces.2008.11.028

2013, Simulation of malaria-infected red blood cells in microfluidic channels: Passage and blockage, Biomicrofluidics, 7, 044115, 10.1063/1.4817959

2014, The effects of 3D channel geometry on CTC passing pressure-towards deformability-based cancer cell separation, Lab Chip, 14, 2576, 10.1039/c4lc00301b

1981, Multiphase Flow in Polymer Processing

2003, Microfluidic memory and control devices, Science, 300, 955, 10.1126/science.1083694

2004, A microfluidic rectifier: Anisotropic flow resistance at low Reynolds numbers, Phys. Rev. Lett., 92, 094501, 10.1103/PhysRevLett.92.094501

2005, Controlled synthesis of nonspherical microparticles using microfluidics, Langmuir, 21, 2113, 10.1021/la047368k

2001, Efficient mixing at low Reynolds numbers using polymer additives, Nature, 410, 905, 10.1038/35073524

2011, An experimental and numerical investigation of the dynamics of microconfined droplets in systems with one viscoelastic phase, J. Non-Newtonian Fluid Mech., 166, 52, 10.1016/j.jnnfm.2010.10.005

2013, Flow focusing with viscoelastic liquids, Phys. Fluids, 25, 092001, 10.1063/1.4817995

2008, Deformation of a viscoelastic droplet passing through a microfluidic contraction, J. Non-Newtonian Fluid Mech., 155, 67, 10.1016/j.jnnfm.2008.05.002

2014, Deformation and breakup of viscoelastic droplets in confined shear flow, Phys. Rev. E, 90, 023305, 10.1103/PhysRevE.90.023305

1985, A study on polymer blending microrheology: Part I, Polym. Eng. Sci., 25, 1041, 10.1002/pen.760251608

1972, Drop breakup in simple shear fields of viscoelastic fluids, Ind. Eng. Chem. Fundam., 11, 312, 10.1021/i160043a005

1997, Influence of elastic properties on drop deformation in elongational flow, J. Rheol., 41, 1183, 10.1122/1.550853

1998, Influence of elastic properties on drop deformation and breakup in shear flow, J. Rheol., 42, 1477, 10.1122/1.550897

2005, Viscoelastic effects on drop deformation in steady shear, J. Fluid Mech., 540, 427, 10.1017/S0022112005006166

2008, Effects of matrix viscoelasticity on viscous and viscoelastic drop deformation in a shear flow, J. Fluid Mech., 601, 63, 10.1017/S0022112008000451

1999, The deformation of a Newtonian drop in the uniaxial extensional flow of a viscoelastic liquid, J. Non-Newtonian Fluid Mech., 88, 149, 10.1016/S0377-0257(99)00010-5

1999, The deformation of a viscoelastic drop subjected to steady uniaxial extensional flow of a Newtonian fluid, J. Non-Newtonian Fluid Mech., 85, 127, 10.1016/S0377-0257(98)00212-2

1979, Studies on droplet deformation and breakup. I. Droplet deformation in extensional flow, J. Rheol., 23, 557, 10.1122/1.549510

1998, Boundary element analysis of planar drop deformation in confined flow. Part II. Viscoelastic fluids, Eng. Anal. Boundary Elem., 22, 291, 10.1016/S0955-7997(98)00056-3

2008, Viscoelastic effects on drop deformation in a converging pipe flow, J. Rheol., 522, 469, 10.1122/1.2837525

2010, Droplet dynamics passing through obstructions in confined microchannel flow, Microfluid. Nanofluid., 9, 1151, 10.1007/s10404-010-0636-x

2010, Multilayer deposition on patterned posts using alternating polyelectrolyte droplets in a microfluidic device, Lab Chip, 10, 1160, 10.1039/b919753b

1975, The creeping motion of liquid drops through a circular tube of comparable diameter, J. Fluid Mech., 71, 361, 10.1017/S0022112075002625

S. S. Khobdeh, Ph.D. thesis, Pennsylvania State University, 2011.

1982, The creeping motion of liquid drops through a circular tube of comparable diameter: The effect of density differences between the fluids, J. Fluid Mech., 115, 187, 10.1017/S0022112082000718

H. Wu, Ph.D. thesis, University of Virginia, 2008.

2009, Confined drop motion in viscoelastic two-phase systems, Phys. Fluids, 21, 013102, 10.1063/1.3054156

2005, A parametric study of droplet deformation through a microfluidic contraction, ANZIAM J., 46, C150

2006, A parametric study of droplet deformation through a microfluidic contraction: Low viscosity Newtonian droplets, Chem. Eng. Sci., 61, 5149, 10.1016/j.ces.2006.03.011

2007, A parametric study of droplet deformation through a microfluidic contraction: Shear thinning liquids, Int. J. Multiphase Flow, 33, 545, 10.1016/j.ijmultiphaseflow.2006.12.002

2007, Simulation of neutrophil deformation and transport in capillaries using Newtonian and viscoelastic drop models, Ann. Biomed. Eng., 35, 766, 10.1007/s10439-007-9286-x

2008, Numerical study on the effect of viscoelasticity on drop deformation in simple shear and 5:1:5 plannar contraction/expansion microchannel, J. Non-Newtonian Fluid Mech., 155, 80, 10.1016/j.jnnfm.2008.06.002

2009, Effect of viscoelasticity on drop dynamics in 5:1:5 plannar contraction/expansion microchannel flow, Chem. Eng. Sci., 64, 4515, 10.1016/j.ces.2009.05.049

2014, Inertial microfluidic physics, Lab Chip, 14, 2739, 10.1039/c4lc00128a

2009, Inertial microfluidics, Lab Chip, 9, 3038, 10.1039/b912547g

R. Carroll, Ph.D. thesis, University of New Hampshire, 2014.

1995, Effects of inertia on the deformation of liquid drops in simple shear flow, Comput. Fluids, 24, 101, 10.1016/0045-7930(94)00025-T

2015, A front-tracking method for computational modeling of viscoelastic two-phase systems, J. Non-Newtonian Fluid Mech., 223, 122, 10.1016/j.jnnfm.2015.05.012

1992, A front-tracking method for viscous, incompressible, multi-fluid flows, J. Comput. Phys., 100, 25, 10.1016/0021-9991(92)90307-K

1988, Creeping flow of dilute polymer solutions past cylinders and spheres, J. Non-Newtonian Fluid Mech., 29, 381, 10.1016/0377-0257(88)85062-6

1968, Numerical solution of the Navier-Stokes equations, Math. Comput., 22, 745, 10.1090/S0025-5718-1968-0242392-2

2005, Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation, J. Non-Newtonian Fluid Mech., 126, 23, 10.1016/j.jnnfm.2004.12.003

2008, An improved weighted essentially non-oscillatory sheme for hyperbolic conservation laws, J. Comput. Phys., 227, 3191, 10.1016/j.jcp.2007.11.038

2001, A front-tracking method for the computations of multiphase flow, J. Comput. Phys., 169, 708, 10.1006/jcph.2001.6726

1990, Axisymmetric creeping motion of drops through circular tubes, J. Fluid Mech., 210, 565, 10.1017/S0022112090001409

2007, Low-Reynolds-number motion of a deformable drop between two parallel plane walls, Int. J. Multiphase Flow, 33, 182, 10.1016/j.ijmultiphaseflow.2006.06.012

1992, The deformation and breakup of liquid drops in low Reynolds number flow through a capillary, Phys. Fluids, 4, 1347, 10.1063/1.858412

1994, Dynamics of a drop in a constricted capillary tube, J. Fluid Mech., 274, 197, 10.1017/S0022112094002090

2001, Transient polymeric drop extension and retraction in uniaxial extensional flows, J. Non-Newtonian Fluid Mech., 98, 141, 10.1016/S0377-0257(01)00112-4

2004, Break-up of a Newtonian drop in a viscoelastic matrix under simple shear flow, Rheol. Acta, 43, 449, 10.1007/s00397-004-0374-7