Top

Rheologica Acta

Published in:

01-10-2015 | Original Contribution

Mechanisms of onset for moderate Mach number instabilities of viscoelastic flows around confined cylinders

Authors: Xueda Shi, Stephen Kenney, Ganesh Chapagain, Gordon F. Christopher

Published in: Rheologica Acta | Issue 9-10/2015

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

An examination of the upstream and downstream instabilities that occur for highly confined and bounded viscoelastic flows around a cylinder is presented. An elasticity number-Mach number (El-Ma) phase space is used to demonstrate that the onset of downstream instabilities at Ma = 1; these instabilities are instigated by the disturbance of the base flow by traveling elastic waves. After the onset of the downstream instability, an upstream instability eventually occurs for Ma _crit ~ 10; however, this number is affected by both channel geometry and fluid properties. The upstream instability is instigated by perturbations of the flow field caused by the downstream instability and does not occur until a critical perturbation size at a given velocity is exceeded. The effects of these flow regimes on flow resistance are characterized by examining excess pressure drop; a significant increase in flow resistance is observed at the onset of the upstream instability.

previous article Rheological characterization of H-shaped poly(methyl methacrylate)s

next article Structural breakdown and recovery of waxy crude oil emulsion gels

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Afonso A, Oliveira PJ, Pinho FT, Alves MA (2009) The log-conformation tensor approach in the finite-volume method framework. J Non-Newtonian Fluid Mech 157(1–2):55–65. doi:10.1016/j.jnnfm.2008.09.007 CrossRef

Amarouchene Y, Bonn D, Meunier J, Kellay H (2001) Inhibition of the finite-time singularity during droplet fission of a polymeric fluid. Phys Rev Lett 86(16):3558–3561CrossRef

Arora K, Sureshkumar R, Khomami B (2002) Experimental investigation of purely elastic instabilities in periodic flows. J Non-Newtonian Fluid Mech 108(1):209–226CrossRef

Chakraborty J, Verma N, Chhabra RP (2004) Wall effects in flow past a circular cylinder in a plane channel: a numerical study. Chem Eng Process Process Intensif 43(12):1529–1537. doi:10.1016/j.cep.2004.02.004 CrossRef

Chmielewski C, Jayaraman K (1993) Elastic instability in crossflow of polymer solutions through periodic arrays of cylinders. J Non-Newtonian Fluid Mech 48(3):285–301CrossRef

Christanti Y, Walker LM (2002) Effect of fluid relaxation time of dilute polymer solutions on jet breakup due to a forced disturbance. J Rheol 46(3):733–748. doi:10.1122/1.1463418 CrossRef

Christopher GF, Anna SL (2009) Passive breakup of viscoelastic droplets and filament self-thinning at a microfluidic T-junction. J Rheol 53(3):663–683. doi:10.1122/1.3086871 CrossRef

Coelho PM, Pinho FT (2003) Vortex shedding in cylinder flow of shear-thinning fluids I. Identification and demarcation of flow regimes. J Non-Newtonian Fluid Mech 110(2–3):143–176. doi:10.1016/s0377-0257(03)00007-7 CrossRef

Dou HS, Phan-Thien N (2008) An instability criterion for viscoelastic flow past a confined cylinder. Korea-Aust Rheol J 20(1):15–26

Duffy DC, McDonald JC, Schueller OJA, Whitesides GM (1998) Rapid prototyping of microfluidic systems in poly(dimethylsiloxane). Anal Chem 70(23):4974–4984CrossRef

Eggers J, Villermaux E (2008) Physics of liquid jets. Rep Prog Phys 71(3)

Ellero M, Adams N (2011) SPH simulations of flow around a periodic array of cylinders confined in a channel. Int J Numer Methods Eng 86(8):1027–1040CrossRef

Fouxon A, Lebedev V (2003) Spectra of turbulence in dilute polymer solutions. Phys Fluids (1994-present) 15(7):2060–2072CrossRef

Galindo-Rosales FJ, Campo-Deaño L, Sousa PC, Ribeiro VM, Oliveira MS, Alves MA, Pinho FT (2014) Viscoelastic instabilities in micro-scale flows. Exp Therm Fluid Sci 59:128–139

Gervais T, El-Ali J, Günther A, Jensen KF (2006) Flow-induced deformation of shallow microfluidic channels. Lab Chip 6(4):500–507CrossRef

Grilli M, Vázquez-Quesada A, Ellero M (2013) Transition to turbulence and mixing in a viscoelastic fluid flowing inside a channel with a periodic array of cylindrical obstacles. Phys Rev Lett 110(17):174501CrossRef

Gulati S, Liepmann D, Muller SJ (2008) Elastic secondary flows of semidilute DNA solutions in abrupt 90 degrees microbends. Phys Rev E 78 (3) doi:10.1103/PhysRevE.78.036314

Gulati S, Dutcher CS, Liepmann D, Muller SJ (2010) Elastic secondary flows in sharp 90 degree micro-bends: a comparison of PEO and DNA solutions. J Rheol 54(2):375–392. doi:10.1122/1.3308643 CrossRef

Hardy BS, Uechi K, Zhen J, Kavehpour HP (2009) The deformation of flexible PDMS microchannels under a pressure driven flow. Lab Chip 9(7):935–938CrossRef

Hohne DN, Younger JG, Solomon MJ (2009) Flexible microfluidic device for mechanical property characterization of soft viscoelastic solids such as bacterial biofilms. Langmuir 25(13):7743–7751. doi:10.1021/la803413x CrossRef

Hulsen MA, Fattal R, Kupferman R (2005) Flow of viscoelastic fluids past a cylinder at high Weissenberg number: stabilized simulations using matrix logarithms. J Non-Newtonian Fluid Mech 127(1):27–39. doi:10.1016/j.jnnfm.2005.01.002 CrossRef

Kenney S, Poper K, Chapagain G, Christopher G (2013) Large Deborah number flows around confined microfluidic cylinders. Rheol Acta 52(5):485–497. doi:10.1007/s00397-013-0712-8 CrossRef

Khomami B, Moreno LD (1997) Stability of viscoelastic flow around periodic arrays of cylinders. Rheol Acta 36(4):367–383CrossRef

Kim JM, Kim C, Chung C, Ahn KH, Lee SJ (2004) Vortex behavior in the inertial flow of viscoelastic fluids past a confined cylinder. Korea-Aust Rheol J 16(3):117–128

Kohl MJ, Abdel-Khalik SI, Jeter SM, Sadowski DL (2005) An experimental investigation of microchannel flow with internal pressure measurements. Int J Heat Mass Transf 48(8):1518–1533. doi:10.1016/j.ijheatmasstransfer.2004.10.030 CrossRef

Lee T, Budwig R (1991) A study of the effect of aspect ratio on vortex shedding behind circular cylinders. Phys Fluids A: Fluid Dyn 3(2):309–315CrossRef

McKinley GH, Armstrong RC, Brown RA (1993) The wake instability in viscoelastic flow past confined circular-cylinders. Philos Trans R Soc Lond Ser a-Math Phys Eng Sci 344(1671):265–304CrossRef

McKinley GH, Pakdel P, Öztekin A (1996) Rheological and geometric scaling of purely elastic flow instabilities. J Non-Newtonian Fluid Mech 67:19–47CrossRef

Oliveira PJ, Miranda AIP (2005) A numerical study of steady and unsteady viscoelastic flow past bounded cylinders. J Non-Newtonian Fluid Mech 127(1):51–66. doi:10.1016/j.jnnfm.2005.02.003 CrossRef

Öttinger HC (1996) Stochastic processes in polymeric liquids. Springer, BerlinCrossRef

Pakdel P, McKinley GH (1996) Elastic instability and curved streamlines. Phys Rev Lett 77(12):2459–2462. doi:10.1103/PhysRevLett.77.2459 CrossRef

Pan L, Morozov A, Wagner C, Arratia P (2013) Nonlinear elastic instability in channel flows at low Reynolds numbers. Phys Rev Lett 110(17):174502CrossRef

Pathak JA, Ross D, Migler KB (2004) Elastic flow instability, curved streamlines, and mixing in microfluidic flows. Phys Fluids 16(11):4028–4034. doi:10.1063/1.1792011 CrossRef

Pipe CJ, Monkewtiz PA (2006) Vortex shedding in flows of dilute polymer solutions. J Non-Newtonian Fluid Mech 139(1–2):54–67. doi:10.1016/j.jnnfm.2006.07.003 CrossRef

Ribeiro V, Coelho P, Pinho F, Alves M (2012) Three-dimensional effects in laminar flow past a confined cylinder. Chem Eng Sci 84:155–169

Ribeiro VM, Coelho PM, Pinho FT, Alves MA (2014) Viscoelastic fluid flow past a confined cylinder: three-dimensional effects and stability. Chem Eng Sci 111:364–380. doi:10.1016/j.ces.2014.02.033 CrossRef

Richter D, Iaccarino G, Shaqfeh ESG (2010) Simulations of three-dimensional viscoelastic flows past a circular cylinder at moderate Reynolds numbers. J Fluid Mech 651:415–442. doi:10.1017/s0022112009994083 CrossRef

Rodd LE, Scott TP, Boger DV, Cooper-White JJ, McKinley GH (2005) The inertio-elastic planar entry flow of low-viscosity elastic fluids in micro-fabricated geometries. J Non-Newtonian Fluid Mech 129(1):1–22. doi:10.1016/j.jnnfm.2005.04.006 CrossRef

Rodd LE, Cooper-White JJ, Boger DV, McKinley GH (2007) Role of the elasticity number in the entry flow of dilute polymer solutions in micro-fabricated contraction geometries. J Non-Newtonian Fluid Mech 143(2–3):170–191. doi:10.1016/j.jnnfm.2007.02.006 CrossRef

Sahin M, Owens RG (2004a) A numerical investigation of wall effects up to high blockage ratios on two-dimensional flow past a confined circular cylinder. Phys Fluids 16(5):1305–1320. doi:10.1063/1.1668285 CrossRef

Sahin M, Owens RG (2004b) On the effects of viscoelasticity on two-dimensional vortex dynamics in the cylinder wake. J Non-Newtonian Fluid Mech 123(2–3):121–139CrossRef

Sen S, Mittal S, Biswas G (2009) Steady separated flow past a circular cylinder at low Reynolds numbers. J Fluid Mech 620:89–119. doi:10.1017/S0022112008004904 CrossRef

Shiang AH, Lin JC, Öztekin A, Rockwell D (1997) Viscoelastic flow around a confined circular cylinder: measurements using high-image-density particle image velocimetry. J Non-Newtonian Fluid Mech 73(1–2):29–49CrossRef

Shiang AH, Öztekin A, Lin JC, Rockwell D (2000) Hydroelastic instabilities in viscoelastic flow past a cylinder confined in a channel. Exp Fluids 28(2):128–142CrossRef

Sousa PC, Pinho FT, Oliveira MSN, Alves MA (2010) Efficient microfluidic rectifiers for viscoelastic fluid flow. J Non-Newtonian Fluid Mech 165(11–12):652–671. doi:10.1016/j.jnnfm.2010.03.005 CrossRef

Steinhaus B, Shen AQ, Sureshkumar R (2007) Dynamics of viscoelastic fluid filaments in microfluidic devices. Phys Fluids 19(7)

Tirtaatmadja V, McKinley GH, Cooper-White JJ (2006) Drop formation and breakup of low viscosity elastic fluids: effects of molecular weight and concentration. Phys Fluids 18(4)

Usui H, Shibata T, Sano Y (1980) Kármán vortex behind a circular cylinder in dilute polymer solutions. J Chem Eng Jpn 13(1):77–79CrossRef

Verhelst JM, Nieuwstadt EM (2004) Visco-elastic flow past circular cylinders mounted in a channel: experimental measurements of velocity and drag. J Non-Newtonian Fluid Mech 116(2–3):301–328. doi:10.1016/j.jnnfm.2003.08.006 CrossRef

Wagner C, Amarouchene Y, Bonn D, Eggers J (2005) Droplet detachment and satellite bead formation in viscoelastic fluids. Phys Rev Lett 95(16)

Williamson CHK (1996) Vortex dynamics in the cylinder wake. Annu Rev Fluid Mech 28:477–539CrossRef

Title: Mechanisms of onset for moderate Mach number instabilities of viscoelastic flows around confined cylinders
Authors: Xueda Shi
Stephen Kenney
Ganesh Chapagain
Gordon F. Christopher
Publication date: 01-10-2015
Publisher: Springer Berlin Heidelberg
Published in: Rheologica Acta / Issue 9-10/2015
Print ISSN: 0035-4511
Electronic ISSN: 1435-1528
DOI: https://doi.org/10.1007/s00397-015-0875-6

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Other articles of this Issue 9-10/2015

Rheological characterization of H-shaped poly(methyl methacrylate)s

Modeling confinement in polymer nanocomposites from linear viscoelasticity data

Startup shear of a highly entangled polystyrene solution deep into the nonlinear viscoelastic regime

A hierarchical multi-mode MSF model for long-chain branched polymer melts part I: elongational flow

Stick-slip behavior of magnetorheological fluids in simple linear shearing mode

Quiescent and shear-induced crystallization of linear and branched polylactides

Premium Partners