Skip to main content
Log in

Instabilities in viscoelastic flows

  • Review
  • Published:
Rheologica Acta Aims and scope Submit manuscript

Abstract

Viscoelastic instabilities are of practical importance, and are the subject of growing interest. Reviewed here are the fresh developments as well as earlier work in this area, organized into the following categories: instabilities in Taylor-Couette flows, instabilities in cone-and-plate and plate-and-plate flows, instabilities in parallel shear flows, extrudate distortions and fracture, instabilities in shear flows with interfaces, instabilities in extensional flows, instabilities in multidimensional flows, and thermohydrodynamic instabilities. Emphasized in the review are comparisons between theory and experiment and suggested directions for future work.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Adrian DW, Giacomin AJ (1992) J Rheol (in press)

  • Alvarez GA, Lodge AS, Cantow H-J (1985) Rheol Acta 24:368

    Google Scholar 

  • Anturkar NR, Papanastasiou TC, Wilkes JO (1990) AIChE J 36:710

    Google Scholar 

  • Astarita G, Apuzzo G (1965) AIChE J 11:815

    Google Scholar 

  • Atwood B (1982) PhD Thesis. Dept Chem Eng, Princeton University, Princeton

    Google Scholar 

  • Avgousti M, Beris AN (1991) J Fluid Mech (submitted)

  • Avgousti M, Liu B, Beris AN (1991) J Fluid Mech (submitted)

  • Babcock K, Ahlers G, Cannell DS (1991) Presentation at Amer Phys Soc Annual Meeting

  • Batchelor GK (1951) Q J Mech Appl Math 4:29

    Google Scholar 

  • Bazilevsky AV, Entov VM, Rozhkov AN, Yarin AL (1990) Proceedings of the Third European Rheology Conference and Golden Jubilee Meeting of the British Society of Rheology. Elsevier, London

    Google Scholar 

  • Beard DW, Davies MH, Walters K (1966) J Fluid Mech 24:321

    Google Scholar 

  • Beavers GS, Joseph DD (1974) Phys Fluids 17:650

    Google Scholar 

  • Benbow JJ, Lamb P (1963) SPE Trans 3:7

    Google Scholar 

  • Benny DJ (1966) J Math Phys 45:150

    Google Scholar 

  • Benjamin TB (1957) J Fluid Mech 2:554

    Google Scholar 

  • Bensimon D, Kolodner P, Surko CM, Williams H, Croquette V (1990) J Fluid Mech 217:441

    Google Scholar 

  • Beris AN, Armstrong RC, Brown RA (1983) J Non-Newt Fluid Mech 13:109

    Google Scholar 

  • Bernstein B, Kearsley EA, Zapas LJ (1963) Trans Soc Rheol 7:391

    Google Scholar 

  • Bhatnagar RK, Giesekus H (1970a) Rheol Acta 9:53

    Google Scholar 

  • Bhatnagar RK, Giesekus H (1970b) Rheol Acta 9:412

    Google Scholar 

  • Bird RB, Curtiss CF, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids, 2nd ed, vol 2. Wiley, New York

    Google Scholar 

  • Bisgaard C (1983) J Non-Newt Fluid Mech 12:283

    Google Scholar 

  • Boger DV (1977/78) J Non-Newt Fluid Mech 3:87

    Google Scholar 

  • Boger DV, Hur DU, Binnington RJ (1986) J Non-Newt Fluid Mech 20:31

    Google Scholar 

  • Boudreaux ED, Cuculo JA (1978) J Macromol Sci — Rev Macromol Chem 16:39

    Google Scholar 

  • Bousfield DW, Keunings R, Marrucci G, Denn MM (1986) J Non-Newt Fluid Mech 21:79

    Google Scholar 

  • Brand HR, Zielinska BJA (1986) Phy Rev Lett 57:3167

    Google Scholar 

  • Busse WF (1964) Phys Today 9 (September)

  • Cable PJ, Boger DV (1978a) AIChE J 24:869

    Google Scholar 

  • Cable PJ, Boger DV (1978b) AIChE J 24:882

    Google Scholar 

  • Cable PJ, Boger DV (1979) AIChE J 25:152

    Google Scholar 

  • Cain JJ, Denn MM (1988) Polym Engng Sci 28:1527

    Google Scholar 

  • Chandrasekhar S (1961) Hydrodynamic stability. Clarendon Press, Oxford

    Google Scholar 

  • Chang JC, Denn MM (1980) In: Astarita G, Marrucci G, Nicolais L (eds) Rheolgy, vol 3. Plenum Press, New York

    Google Scholar 

  • Chen K (1991a) J Non-Newt Fluid Mech 40:155

    Google Scholar 

  • Chen K (1991b) J Non-Newt Fluid Mech 40:261

    Google Scholar 

  • Chen K (1991c) private communication

  • Chen K, Joseph DD (1991) J Non-Newt Fluid Mech (submitted)

  • Chen K, Bak P, Obukhov SP (1991) Phys Rev A 43:625

    Google Scholar 

  • Cheng DC-H (1968) Chem Eng Sci 23:895

    Google Scholar 

  • Chiao S-MF, Chang H-C (1990) J Non-Newt Fluid Mech 36:361

    Google Scholar 

  • Chiba K, Sakatani T, Nakamura K (1990) J Non-Newt Fluid Mech 36:193

    Google Scholar 

  • Chilcott MD, Rallison JM (1988) J Non-Newt Fluid Mech 29:381

    Google Scholar 

  • Christensen RE (1962) SPE J 18:751

    Google Scholar 

  • Coates PJ, Armstrong RC, Brown RA (1991) J Non-Newt Fluid Mech (in press)

  • Coleman BD, Noll W (1960) Arch Rat Mech Anal 6:355

    Google Scholar 

  • Coleman BD, Noll W (1961) Rev Mod Phys 33:239

    Google Scholar 

  • Crawley RL, Graessley WW (1977) Trans Soc Rheol 21:19

    Google Scholar 

  • Criminale WO Jr, Ericksen JL, Filbey GL Jr (1958) Arch Ratl Mech Anal 1:410

    Google Scholar 

  • Currie PK (1980) Proceedings of the Eighth International Congress on Rheology, Naples, Italy

  • Dandapat BS, Gupta AS (1978) Rheol Acta 17:492

    Google Scholar 

  • Davey A, Di Prima RC, Stuart JT (1968) J Fluid Mech 31:17

    Google Scholar 

  • de Gennes PG (1971) J Chem Phys 55:572

    Google Scholar 

  • Dean WR (1928) Proc Roy Soc London A121:402

    Google Scholar 

  • Deiber JA, Schowalter WR (1991) J Non-Newt Fluid Mech 40:141

    Google Scholar 

  • Denn MM, Roisman JJ (1969) AIChE J 15:454

    Google Scholar 

  • Denn MM (1990) Annu Rev Fluid Mech 22:13

    Google Scholar 

  • Di Prima RC, Pridor A (1979) Proc Roy Soc A366:555

    Google Scholar 

  • Di Prima RC, Swinney HL (1985) In: Swinney HL, Gollub JP (eds) Hydrodynamic instabilities and the transition to turbulence. Springer, New York

    Google Scholar 

  • Dijkstra DD, van Heijst PJ (1983) J Fluid Mech 128:123

    Google Scholar 

  • Doi M, Edwards SF (1978) J Chem Soc, Faraday Trans II 74:1789, 74:1802, 74:1818

    Google Scholar 

  • Doi M, Edwards SF (1979) J Chem Soc, Faraday Trans II 75:32

    Google Scholar 

  • Drazin PG, Reid WH (1981) Hydrodynamic stability. Cambridge University Press, Cambridge, United Kingdom

    Google Scholar 

  • Eckhaus W (1965) Studies in nonlinear stability theory. Springer, New York

    Google Scholar 

  • El Kissi N, Piau JM (1990) J Non-Newt Fluid Mech 37:55

    Google Scholar 

  • Eltayeb IA (1977) Proc Roy Soc London A356:161

    Google Scholar 

  • Entov VM, Yarin AL (1984a) J Fluid Mech 140:91

    Google Scholar 

  • Entov VM, Yarin AL (1984b) Fluid Dynamics 19(1):27

    Google Scholar 

  • Ericksen JL (1956) Quart Appl Math 14:318

    Google Scholar 

  • Escudier MP (1984) Exp Fluids 2:189

    Google Scholar 

  • Evans RE, Walters K (1986) J Non-Newt Fluid Mech 20:11

    Google Scholar 

  • Evans RE, Walters K (1989) J Non-Newt Fluid Mech 32:95

    Google Scholar 

  • Ferry JD (1980) Viscoelastic properties of polymers, 3rd ed. Wiley, New York

    Google Scholar 

  • Fisher RJ, Denn MM (1975) Chem Eng Sci 20:1129

    Google Scholar 

  • Fisher RJ, Denn MM (1976) AIChE J 22:236

    Google Scholar 

  • Flory PJ (1969) Statistical mechanics of chain molecules. Wiley, New York

    Google Scholar 

  • Friebe HW (1976) Rheol Acta 15:329

    Google Scholar 

  • Fukuda M, Osaki K, Kurata M (1975) J Polym Sci: Polym Phys Ed 13:1563

    Google Scholar 

  • Giesekus H (1965) Rheol Acta 2:85

    Google Scholar 

  • Giesekus H (1966a) Rheol Acta 5:29

    Google Scholar 

  • Giesekus H (1966b) Rheol Acta 5:239

    Google Scholar 

  • Giesekus H (1968) Rheol Acta 7:127

    Google Scholar 

  • Giesekus H (1970) Rheol Acta 9:30

    Google Scholar 

  • Giesekus H, Bhatnagar RK (1971) Rheol Acta 10:266

    Google Scholar 

  • Giesekus H (1972) In: Schowalter WR, Luikov AV, Mikowycz WJ, Afgan NH (eds) Prog in Heat and Mass Transfer 5:195

  • Giesekus H (1982) J Non-Newt Fluid Mech 11:69

    Google Scholar 

  • Ginn RF, Denn MM (1969) AIChE J 15:450

    Google Scholar 

  • Goldin M, Yerushalmi H, Pfeffer R, Shinnar R (1969) J Fluid Mech 38:689

    Google Scholar 

  • Golubitsky M, Schaeffer DG, Stewart IN (1988) Singularities and groups in bifurcation theory, vol II. Springer, New York

    Google Scholar 

  • Gorodtsov VA, Leonov AI (1967) J Appl Math Mech 31:310

    Google Scholar 

  • Green T III (1968) Phys Fluids 11:1410

    Google Scholar 

  • Greenberg MD (1978) Foundations of applied mathematics. Prentice-Hall Inc, Englewood Cliffs, NJ

    Google Scholar 

  • Griffiths JD, Thomas RH (1966) J de Mec 5:101

    Google Scholar 

  • Gupta AS (1967) J Fluid Mech 28:17

    Google Scholar 

  • Gupta AS, Rai L (1967) Proc Camb Phil Soc 63:527

    Google Scholar 

  • Haas R, Bühler K (1989) Rheol Acta 28:402

    Google Scholar 

  • Han CD, Park JY (1975) J Appl Polym Sci 19:3291

    Google Scholar 

  • Harlen OG, Hinch EJ, Rallison JM (1991) Presentation at the International Conference on Dynamics of Polymeric Liquids, Capri

  • Hassager O (1979) Nature 279:5712

    Google Scholar 

  • Hatzikiriakos SG, Dealy JM (1991) J Rheol 35:497

    Google Scholar 

  • Hayes JW, Hutton FJ (1972) In: Schowalter WR, Luikov AV, Minkowycz WJ, Afgan NH (eds) Prog in Heat and Mass Transfer 5:195

  • Heisenberg W (1924) Ann Phys Lpz (4) 74:577; translated in Tech Memor Nat Adv Comm Aero, Wash No 1291

    Google Scholar 

  • Hill CT (1972) Trans Soc Rheol 16:213

    Google Scholar 

  • Hill DA, Hasegawa T, Denn MM (1990) J Rheol 34:891

    Google Scholar 

  • Hinch EJ (1992) J Non-Newt Fluid Mech (submitted)

  • Ho TC, Denn MM (1977/78) J Non-Newt Fluid Mech 3:179

    Google Scholar 

  • Hohenberg PC, Cross MC (1987) In: Garrido L (ed) Fluctuations and stochastic phenomena in condensed matter. Springer, Berlin

    Google Scholar 

  • Hohenberg PC, Swift JB (1987) Phys Rev A35:3855

    Google Scholar 

  • Holodniok M, Kubicek M, Hlavacek V (1981) J Fluid Mech 108:227

    Google Scholar 

  • Hooper AP (1985) Phys Fluids 28:1613

    Google Scholar 

  • Hoyt JW, Taylor JJ (1977) Phys Fluids 20:S253

    Google Scholar 

  • Hsieh DY (1990) Phys Fluids A2:1145

    Google Scholar 

  • Huseby TW (1966) J Rheol 10:181

    Google Scholar 

  • Hutton JF (1969) Rheol Acta 8:54

    Google Scholar 

  • Ishihara H, Kase S (1975) J Appl Polym Sci 14:1597

    Google Scholar 

  • Jackson KP, Walters K, Williams RW (1985) J Non-Newt Fluid Mech 14:173

    Google Scholar 

  • Johnson MW Jr, Segalman D (1977) J Non-Newt Fluid Mech 2:225

    Google Scholar 

  • Joo YL, Shaqfeh ESG (1991) Phys Fluids A3:1691

    Google Scholar 

  • Joo YL, Shaqfeh ESG (1992) Phys Fluids A (to be submitted)

  • Joseph DD, Renardy M, Saut JC (1985) Arch Rat Mech Anal 87:213

    Google Scholar 

  • Kalika DS, Denn MM (1987) J Rheol 31:815

    Google Scholar 

  • Kanai T, White JL (1984) Polym Engng Sci 24:1185

    Google Scholar 

  • Kapitza PL (1965) Collected papers of P. L. Kapitza, vol 2. Pergamon Press, New York, p 662

    Google Scholar 

  • Karlsson SKIT, Solokov M, Tanner RI (1971) Drag Reduction. Am Inst Chem Engrs Symp Series 67:11

    Google Scholar 

  • Kase S, Matsuo T, Yoshimoto Y (1966) Seni Kikai Gakkaishi 19:T63

    Google Scholar 

  • Kase S (1974) J Appl Polym Sci 18:3279

    Google Scholar 

  • Kaye A (1962) College of Aeronautics. Cranford, UK, Note No 134

  • Keentok M, Georgescu AG, Sherwood AA, Tanner RI (1980) J Non-Newt Fluid Mech 26:303

    Google Scholar 

  • Keller A, Odell AJ (1985) Coll Polym Sci 263:181

    Google Scholar 

  • Keunings R (1986) J Non-Newt Fluid Mech 20:209

    Google Scholar 

  • Keunings R (1987) In: Tucker CL III (ed) Fundamentals of computer modeling for polymer processing. Carl Hanser Verlag, New York

    Google Scholar 

  • Kheshgi HS, Scriven LE (1984) In: Gallagher RH, Oden FT, Zienkiewicz OC, Kanai T, Kawahara M (eds) Finite elements in fluids, vol 5. Wiley, New York

    Google Scholar 

  • Khomami B (1990) J Non-Newt Fluid Mech 36:289

    Google Scholar 

  • Koelling KW, Prud'homme RK (1991) Rheol Acta 30:511

    Google Scholar 

  • Kolkka RW, Ierley GR (1987) J Non-Newt Fluid Mech 25:209

    Google Scholar 

  • Kolkka RW, Malkus DS, Hansen MG, Ierley GR, Worthing RA (1988) J Non-Newt Fluid Mech 29:303

    Google Scholar 

  • Kolkka RW, Ierley GR (1989) J Non-Newt Fluid Mech 33:305

    Google Scholar 

  • Kolkka RW, Malkus DS, Rose TR (1991) Rheol Acta 30:430

    Google Scholar 

  • Kulicke W-M, Jeberien H-E, Kiss H, Porter RS (1979) Rheol Acta 18:711

    Google Scholar 

  • Kulicke W-M, Porter RS (1979) J App Polym Sci 23:953

    Google Scholar 

  • Kulicke W-M, Wallbaum U (1985) Chem Eng Sci 40:961

    Google Scholar 

  • Kurtz SJ (1984) In: Mena B, Garcia-Rejon A, Rangel-Nafaile C (eds) Advances in rheology. Universidad Nacional Autonoma de Mexico p 399

  • Kundu PK (1990) Fluid mechanics. Academic Press, New York

    Google Scholar 

  • Lai W (1967) Phys Fluids 10:844

    Google Scholar 

  • Larson RG (1983) J Non-Newt Fluid Mech 13:279

    Google Scholar 

  • Larson RG (1984) J Rheol 28:545

    Google Scholar 

  • Larson RG (1988) Constitutive equations for polymer melts and solutions. Butterworths, Boston

    Google Scholar 

  • Larson RG, Khan SA, Raju VR (1988) J Rheol 32:145

    Google Scholar 

  • Larson RG (1989) Rheol Acta 28:504

    Google Scholar 

  • Larson RG, Shagfeh ESGS, Muller SJ (1990) J Fluid Mech 218:573

    Google Scholar 

  • Larson RG, Muller SJ, Shagfeh ESGS (1992) J Non-Newt Fluid Mech (to be submitted)

  • Larson RG (1992) Rheol Acta (to be submitted)

  • Laun HM (1978) Rheol Acta 17:1

    Google Scholar 

  • Laun HM, Hingmann R (1990) J Non-Newt Fluid Mech 35:137

    Google Scholar 

  • Lawler JV, Muller SJ, Brown RA, Armstrong RC (1986) J Non-Newt Fluid Mech 20:51

    Google Scholar 

  • Lee B, White JL (1974) Trans Soc Rheol 18:467

    Google Scholar 

  • Lee CS, Magda JJ, Tripp B (1992a) Rheol Acta (submitted)

  • Lee CS, Magda JJ, Muller SJ, Larson RG (1991b) (work in progress)

  • Lee CS, Magda JJ, Tripp B (1992) Rheol Acta (submitted)

  • Lee K-C, Finlayson BA (1986) J Non-Newt Fluid Mech 21:65

    Google Scholar 

  • Li C-H (1969) Phys Fluids 12:531

    Google Scholar 

  • Lim FJ, Schowalter WR (1987) J Non-Newt Fluid Mech 26:135

    Google Scholar 

  • Lin CC (1945) Quart Appl Math 3:117, 3:218; 3:277

    Google Scholar 

  • Lockett FJ (1969) Int J Engng Sci 7:337

    Google Scholar 

  • Lockett FJ, Rivlin RS (1968) J Mec 7:475

    Google Scholar 

  • Lunsmann WJ, Armstrong RC, Brown RA (1991) J Non-Newt Fluid Mech (submitted)

  • Luo X-L, Tanner RI (1985) Polym Eng Sci 25:620

    Google Scholar 

  • Mackay ME, Boger DV (1987) J Non-Newt Fluid Mech 22:235

    Google Scholar 

  • Mackley MR, Keller A (1973) Polymer 14:16

    Google Scholar 

  • Magda JJ, Larson RG (1988) J Non-Newt Fluid Mech 30:1

    Google Scholar 

  • Magda JJ, Lou J, Baek SG, De Vries KL (1991) Polymer 32:2000

    Google Scholar 

  • Malkus DS, Nohel JA, Plohr BJ (1990) J Comput Phys 87:464

    Google Scholar 

  • Marchal JM, Crochet MJ (1987) J Non-Newt Fluid Mech 26:77

    Google Scholar 

  • Marrucci G (1984) In: Mujamdar AS, Mashelkar RA (eds) Advances in transport process, vol V. Wiley, New York

    Google Scholar 

  • Matovich MA, Pearson JRA (1969) Ind Eng Chem Fund 8:512

    Google Scholar 

  • Matthys EF (1988) J Rheol 32:773

    Google Scholar 

  • McComb WD (1990) The physics of fluid turbulence, Chapter 14. Clarendon Press, New York

    Google Scholar 

  • McIntire LV, Schowalter WR (1972) AIChE J 18:102

    Google Scholar 

  • McKinley GH, Byars JA, Brown RA, Armstrong RC (1991a) J Non-Newt Fluid Mech 40:201

    Google Scholar 

  • McKinley GH, Raiford WP, Brown RA, Armstrong RC (1991b) J Fluid Mech 223:411

    Google Scholar 

  • McKinley GH, Lunsman WJ, Brown RA, Armstrong RC (1991c) Proc Roy Soc Lond (submitted)

  • McLeish TCB, Ball RC (1986) J Polym Sci: Polym Phys Ed 24:1735

    Google Scholar 

  • McLeish TCB (1987) J Polym Sci: Polym Phys Ed 25:2253

    Google Scholar 

  • Miller C, Goddard JD (1979) An appendix appearing in Goddard JD. Advances Appl Mech 19:143

    Google Scholar 

  • Minoshima W, White JL (1986) J Non-Newt Fluid Mech 19:275

    Google Scholar 

  • Moffat HK (1964) J Fluid Mech 18:1

    Google Scholar 

  • Morrison FA, Larson RG (1992) J Poly Sci: Polym Phys Ed (in press)

  • Moynihan RH, Baird DG, Ramanathan R (1990) J Non-Newt Fluid Mech 36:255

    Google Scholar 

  • Muller SJ (1986) PhD Thesis Dept Chem Eng. MIT, Boston

    Google Scholar 

  • Muller SJ, Larson RG, Shagfeh ESG (1989) Rheol Acta 28:499

    Google Scholar 

  • Muller SJ (1991) private communication

  • Nguyêñ H, Boger DV (1979) J Non-Newt Fluid Mech 5:353

    Google Scholar 

  • Nirschl JP, Stewart WE (1984) J Non-Newt Fluid Mech 16:233

    Google Scholar 

  • Nishioka M, Iida S, Ichikawa Y (1975) J Fluid Mech 72:731

    Google Scholar 

  • Noll W (1958) Arch Rat Mech Anal 2:197

    Google Scholar 

  • Northey P, Armstrong RC, Brown RA (1991) J Non-Newt Fluid Mech (in press)

  • Odell JA, Müller AJ, Keller A (1988) Polymer 29:1179

    Google Scholar 

  • Ohlsen DR, Yamamoto SY, Surko CM (1990) Phys Rev Lett 65:1431

    Google Scholar 

  • Oldroyd JG (1950) Proc Roy Soc A200:523

    Google Scholar 

  • Oldroyd JG (1958) Proc Roy Soc A245:278

    Google Scholar 

  • Osaki K, Doi M (1991) J Rheol 35:89

    Google Scholar 

  • Osaki K, Fukuda M, Kurata M (1975) J Polym Sci 13:775

    Google Scholar 

  • Palierne JF, Lequeux F (1991) J Non-Newt Fluid Mech 40:289

    Google Scholar 

  • Palm E (1960) J Fluid Mech 8:183

    Google Scholar 

  • Paul DR, Southern JH (1975) J Appl Polym Sci 19:3375

    Google Scholar 

  • Pearson JRA, Matovich MA (1969) Ind Eng Chem Fund 8:605

    Google Scholar 

  • Pearson JRA, Petrie CJS (1968) In: Wetton RE, Whorlow RW (eds) Polymer systems, deformation and flow. Macmillan, London

    Google Scholar 

  • Pearson JRA, Petrie CJS (1970a) J Fluid Mech 40:1

    Google Scholar 

  • Pearson JRA, Petrie CJS (1970b) J Fluid Mech 40:609

    Google Scholar 

  • Pearson JRA, Shah YT (1972) Trans Soc Rheol 16:519

    Google Scholar 

  • Pearson JRA, Shah YT (1974) Ind Eng Chem Fund 13:134

    Google Scholar 

  • Pearson JRA, Shah YT, Mhaskar RD (1976) Ind Eng Chem Fund 15:31

    Google Scholar 

  • Pearson DS, Rochefort WE (1982) J Polym Sci: Polym Phys Ed 20:83

    Google Scholar 

  • Petrie CJS, Denn MM (1976) AIChE J 22:209

    Google Scholar 

  • Phan-Thien N, Tanner RI (1977) J Non-Newt Fluid Mech 2:353

    Google Scholar 

  • Phan-Thien N (1978) J Rheol 22:259

    Google Scholar 

  • Phan-Thien N (1983) J Non-Newt Fluid Mech 13:325

    Google Scholar 

  • Phan-Thien N (1985) J Non-Newt Fluid Mech 17:37

    Google Scholar 

  • Phan-Thien N, Huilgol RR (1985) Rheol Acta 24:551

    Google Scholar 

  • Phan-Thien N, Zheng R, Tanner RI (1991) J Non-Newt Fluid Mech 41:151

    Google Scholar 

  • Piau JM, El Kissi N, Tremblay B (1990) J Non-Newt Fluid Mech 34:145

    Google Scholar 

  • Pilitsis S, Beris AN (1989) J Non-Newt Fluid Mech 31:231

    Google Scholar 

  • Porteous KC, Denn MM (1972a) Trans Soc Rheol 16:295

    Google Scholar 

  • Porteous KC, Denn MM (1972b) Trans Soc Rheol 16:309

    Google Scholar 

  • Preziosi L, Chen K, Joseph DD (1989) J Fluid Mech 201:323

    Google Scholar 

  • Rangel-Nafaile C, Metzner AB, Wissbrun KF (1984) Macromolecules 17:1187

    Google Scholar 

  • Raiford WP, Quinzani LM, Coates PJ, Armstrong RC, Brown RA (1989) J Non-Newt Fluid Mech 32:39

    Google Scholar 

  • Ramachandran S, Gao HW, Christiansen EB (1985) Macromolecules 18:695

    Google Scholar 

  • Ramamurthy AV (1986) J Rheol 30:337

    Google Scholar 

  • Rayleigh Lord (1879) Proc Lond Math Soc 10:4

    Google Scholar 

  • Rayleigh Lord (1916) Phil Mag 32:529

    Google Scholar 

  • Renardy M (1990) J Non-Newt Fluid Mech 35:73

    Google Scholar 

  • Renardy M, Renardy Y (1986) J Non-Newt Fluid Mech 22:23

    Google Scholar 

  • Renardy M, Ranardy Y (1989) J Non-Newt Fluid Mech 32:145

    Google Scholar 

  • Renardy Y (1987) Phys Fluids 30:1627

    Google Scholar 

  • Renardy Y (1988) J Non-Newt Fluid Mech 28:99

    Google Scholar 

  • Riddle MJ, Narvaez C, Bird RB (1977) J Non-Newt Fluid Mech 2:23

    Google Scholar 

  • Rivlin RS, Ericksen JL (1955) J Ratl Mech Anal 4:323

    Google Scholar 

  • Romanov VA (1973) Funkcional Anal i Prolozen 7 (no 2): 62; translated in Functional Anal Appl 7:137

    Google Scholar 

  • Rutkevich IM (1969) J Appl Math Mech 33:42

    Google Scholar 

  • Schowalter WR (1988) J Non-Newt Fluid Mech 29:25

    Google Scholar 

  • Shaqfeh ESG, Larson RG, Frederickson GH (1989) J Non-Newt Fluid Mech 31:87

    Google Scholar 

  • Shaqfeh ESG, Muller SJ, Larson RG (1992) J Fluid Mech 235:285

    Google Scholar 

  • Sivashinsky GI, Michelson DM (1980) Prog Theor Phys 63:2112

    Google Scholar 

  • Sokolov M, Tanner RI (1972) Phys Fluids 15:534

    Google Scholar 

  • Spruiell JR, White JL (1975) Polym Engng Sci 15:660

    Google Scholar 

  • Squire HB (1933) Proc Roy Soc A142:621

    Google Scholar 

  • Stern ME (1960) Tellus 12:172

    Google Scholar 

  • Stewartson K (1953) Proc Camb Phil Soc 29:333

    Google Scholar 

  • Stommel H, Arons AB, Blanchard D (1956) Deep-sea research 3:152

    Google Scholar 

  • Strauss K, Kinast R (1974) Colloid Polym Sci 252:753

    Google Scholar 

  • Stuart JT (1960) J Fluid Mech 9:353

    Google Scholar 

  • Sun Z-S, Denn MM (1972) AIChE J 18:1010

    Google Scholar 

  • Sukanek PC, Goldstein CA, Laurence RL (1973) J Fluid Mech 57:651

    Google Scholar 

  • Sukanek PC, Laurence RL (1974) AIChE J 20:474

    Google Scholar 

  • Takaki T, Bogue DC (1975) J Appl Polym Sci 19:419

    Google Scholar 

  • Tanner RI (1985) Engineering Rheology. Oxford Press, New York

    Google Scholar 

  • Tanner RI, Keentok M (1983) J Rheol 27:47

    Google Scholar 

  • Taylor GI (1923) Phil Trans Roy Soc London Ser A223:289

    Google Scholar 

  • Taylor GI (1932) Proc Roy Soc London Ser A138:41

    Google Scholar 

  • Taylor GI (1934) Proc Roy Soc London A146:501

    Google Scholar 

  • Tekeuchi DI, Jankowski DF (1981) J Fluid Mech 102:102

    Google Scholar 

  • Thomas LH (1953) Phys Rev (2)91:780

    Google Scholar 

  • Tlapa G, Bernstein B (1970) Phys Fluids 13:565

    Google Scholar 

  • Tordella JP (1969) In: Eirich FR (ed) Rheology, vol 5. Academic Press, New York

    Google Scholar 

  • Tremblay B (1991) J Rheol 35:985

    Google Scholar 

  • Ver Strate G, Philippoff W (1974) J Polym Sci: Polym Lett Ed 12:267

    Google Scholar 

  • Vest CM, Arpaci VS (1969) J Fluid Mech 36:613

    Google Scholar 

  • Vinogradov GV (1975) Rheol Acta 14:942

    Google Scholar 

  • Vinogradov GV, Malkin AYa, Yankovskii YuG, Borisenkova EK, Yarlykov BV, Berezhnaya GV (1972) J Polym Sci A-2 10:1061

    Google Scholar 

  • von Karman T (1921) Z Angew Math Mech 1:233

    Google Scholar 

  • Vrentas CM, Graessley WW (1982) 26:359

  • Walsh WP (1987) J App Math Phys (ZAMP) 38:495

    Google Scholar 

  • Waters ND, Keeley AM (1987) J Non-Newt Fluid Mech 24:161

    Google Scholar 

  • Watson J (1960) J Fluid Mech 14:211

    Google Scholar 

  • Weinstein SJ (1990) AIChE J 36:1873

    Google Scholar 

  • Weissenberg K (1947) Nature 159:310

    Google Scholar 

  • Whitaker S (1964) Ind Eng Chem Fund 3:132

    Google Scholar 

  • Wilson GM, Khomami B (1992) J Non-Newt Fluid Mech (submitted)

  • Wong WT, Jeng CC (1987) J Non-Newt Fluid Mech 22:359

    Google Scholar 

  • Yeow YL (1972) PhD Thesis Dept Chem Eng. Univ of Cambridge

  • Yiantsos SG, Higgins BG (1988) Phys Fluids 31:3225

    Google Scholar 

  • Yih CS (1963) Phys Fluids 6:321

    Google Scholar 

  • Yih CS (1967) J Fluid Mech 27:337;

    Google Scholar 

  • Yu HS, Sparrow EM (1969) J Heat Trans 91:51

    Google Scholar 

  • Zeichner G (1973) Masters Chem Eng Thesis. Univ of Delaware

  • Zheng R, Phan-Thien N, Tanner RI (1990) J Non-Newt Fluid Mech 36:27

    Google Scholar 

  • Zielinska BJA, Demay Y (1988) Phys Rev A38:897

    Google Scholar 

  • Zielinska BJA, Mukamel D, Steinberg V (1986) Phys Rev A33:1454

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Larson, R.G. Instabilities in viscoelastic flows. Rheola Acta 31, 213–263 (1992). https://doi.org/10.1007/BF00366504

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00366504

Keywords

Navigation