화학공학소재연구정보센터
홈 로그인 로그아웃 연락처 사이트맵
Korea-Australia Rheology Journal, Vol.13, No.2, 67-81, June, 2001
Export Citation
Advances in measuring linear viscoelastic properties using novel deformation geometries and Fourier transform techniques
Howard See†
  • School of Aerospace, Mechanical & Mechatronic Engineering, The University of Sydney, NSW 2006, Australia
E-mail:
The development of new techniques for the dynamic measurement of linear viscoelastic properties is an active area of rheometry, and this paper surveys some novel deformation geometries which have been recently reported e.g. oscillating probe-type devices which are imbedded in or placed on the surface of the sample. Small amplitude band-limited pseudorandom noise is used for the displacement signal, with Fourier analysis of the complex waveform of the resistance force yielding the frequency dependent viscoelastic material functions (e.g. storage and loss moduli G', G''). Theoretical calculations of the fundamental equations relating force to displacement and instrument geometry, were carried out with the aid of the correspondence principle of linear viscoelasticity. The rapidity of the tests and flexibility in terms of sample preparation and stiffness mean that this basic technique should find many applications in rheometry. Three examples of oscillatory tests are presented in detail : squeeze flow, imbedded needle and concentric sliding cylinder geometries.
Keywords:linear viscoelasticity;correspondence principle;pseudorandom noise strain;squeeze flow;needle
  1. Affrossman S, Hayward D, McKee A, Mackinnon A, Lairez D, Pethrick RA, Vatalis A, Baker FS, Carter RE, in Carter R.E. (ed.), Rheology of food, Pharmaceutical and biological materials with general rheology, Elsevier, London, 304-314 (1990)
  2. Banfill PFG, Carter RE, Weaver PJ, Cement Concrete Res., 21, 1148 (1991) 
  3. Bikerman JJ, J. Colloid Sci., 3, 75 (1948) 
  4. Bird RB, Armstrong RC, Hassager O, Dynamics of polymeric liquids vol. 1, 2ed, John Wiley & Sons, New York, p. 44 (1987)
  5. Bland DR, The theory of linear viscoelasticity, Pergamon, Oxford (1960)
  6. Bracewell RN, The Fourier transform and its applications 3ed, McGraw-Hill, New York (2000)
  7. Christensen RM, Mechanics of composite materials, John Wiley & Sons, New York (1979)
  8. Collyer AA, Techniques in rheological measurement, Chapman & Hall, London (1993)
  9. Collyer AA, Clegg DW, Rheological measurement, 2ed, Chapman & Hall, London (1998)
  10. Coolyer JW, Tukey JW, Math. Comp., 19, 297 (1965) 
  11. Dealy JM, Giacomin AJ, Sliding plate and sliding cylinder rheometers, in Collyer A.A. and D.W. Clegg (eds.), rheological measurement, 2ed, Chapman & Hall, London, 237-259 (1998)
  12. Ferry JD, Viscoelastic properties of polymers, 3ed, John Wiley & Sons, New York (1980)
  13. Field JS, Determination of materials properties from the deformation of small volumes, Ph.D. Thesis, University of Sydney (1995)
  14. Field JS, Swain MV, PhanThien N, J. Non-Newton. Fluid Mech., 65(2), 177 (1996) 
  15. Gibson AG, Kotsikos G, Bland JH, Toll S, Squeeze flow, in Collyer A.A. and D.W. Clegg (eds.), Rheological measurement, 2ed, Chapman Hall, London, 550-592 (1998)
  16. Gonsalkorale S, Thomas G, See H, Swain M, The viscoelastic properties of alginate hydrocolloid impression material, in Proc. 39th Annual Scientific Meeting of International Association for Dental Research (ANZ Division), Adelaide Australia, 27-29 Sep. 1999, 41 (1999)
  17. Haddad YM, Viscoelasticity of engineering materials, Chapman & Hall, London (1995)
  18. Hashin Z, Int. J. Solids Structures, 6, 359 (1970)
  19. Hibberd GE, Parker NS, Rheol. Acta, 14, 151 (1975) 
  20. Hills DA, Nowell D, Sackfield A, Mechanics of elastic contacts, Butterworth-Heinemann, Oxford (1993)
  21. Holly E, Ventakaram SK, Chambon F, Winter H, J. Non-Newton. Fluid Mech., 27, 17 (1988) 
  22. Honerkamp J, Weese J, Rheol. Acta, 32, 65 (1993) 
  23. Horowitz P, Hill W, The art of electronics, 2ed., Cambridge University Press, Cambridge (1989)
  24. Hutton JF, Pearson JRA, Walters K, Theoretical rheology, Applied Science, London (1975)
  25. Jiang P, See H, Swain M, Rheological characterisation of dental composite resin cements during curing, to be presented at 3rd Pacific Rim Conference on Rheology, Vancouver Canada, 8-13 July 2001 (2001)
  26. Johnson KL, Contact mechanics, Cambridge Univ Press, Cambridge (1987)
  27. Lee EH, Radok JRM, The contact problem for viscoelastic bodies, Trans. ASME J. Applied Mech. Sept 1960, 438-444 (1960)
  28. Goodfriend M, Machine Design, 63, 147 (1991)
  29. Mackay ME, Rheological measurements on small samples, in Collyer A.A.(ed.), Techniques in Rheological Measurement, Chapman & Hall, London, 225-258 (1993)
  30. Mackay ME, Rheological measurements on small samples, in Collyer A.A. and D.W. Clegg (eds.) Rheological Measurement, 2ed, Chapman & Hall, London, 635-665 (1998)
  31. McCarthy RV, J. Rheol., 22, 623 (1978) 
  32. Macosko CW, Rheology principles, measurements, and applicatioins, VCH Publishers, New York (1994)
  33. Nelson BI, Dealy JM, Dynamic mechanical analysis using complex waveforms, in Collyer A.A. (ed.), Techniques in Rheological Measurement, Chapman & Hall, London, 197-224 (1993)
  34. Nelson BI, Broadhead TO, Paterson WI, Dealy JM, Int. Polym. Proc., 9, 219 (1994)
  35. Nelson BI, Dealy JM, Dynamic mechanical analysis using complex waveforms, in Collyer A.A. and D.W. Clegg (eds.), Rheological Measurement, 2ed, Chapman & Hall, London, 138-164 (1998)
  36. Oka S, The principles of rheometry, in Eirich F.R. (ed.), Rheology theory and applications vol. 3, Academic Press, New York, 17-82 (1960)
  37. Pethrick RA, Rheological studies using a vibrating probemethod, in Collyer A.A. (ed.), Techniques in rheological measurement, Chapman & Hall, London, 161-195 (1993)
  38. Pethrick RA, Rheological studies using a vibrating probe, in Collyer A.A. and D.W. Clegg (eds.), Rheological measurement, 2ed, Chapman & Hall, London, 99-137 (1998)
  39. Phan-Thien N, Goh CJ, ZAMM, 61, 89 (1981)
  40. Phan-Thien N, Pantelis G, Bush MB, ZAMP, 33, 251 (1982) 
  41. Phan-Thien N, Kim S, Microstructures in elasticmedia: principles and computational methods, Oxford University Press, New York (1994)
  42. PhanThien N, Field JS, Swain MV, Rheol. Acta, 35(5), 410 (1996) 
  43. Phan-Thien N, Nasseri S, Bilston LE, Rheol. Acta, 39(4), 409 (2000) 
  44. Pipkin AC, Lectures on viscoelasticity theory, Springer Verlag, New York (1986)
  45. Radhakrishnan S, Pethrick RA, J. Appl. Polym. Sci., 51(5), 863 (1994) 
  46. Ramirez RW, The FFT fundamentals and concepts, Prentice-Hall, Englewood Cliffs, New Jersey (1985)
  47. Russel WB, ZAMP, 24, 581 (1973) 
  48. Schapery RA, Viscoelastic behavior and analysis of composite materials, in Sendeckyj G.P.(ed.), Composite materials, vol. 2, Academic Press, New York (1974)
  49. See H, Field J, Pfister B, Swain M, Phan-Thien N, Electrorheological fluid under squeezing flow, IUTAM 97-9 Rheology and computation, Sydney Australia, 21-25 Jul. 1997 (1997)
  50. See H, Ho CY, Phan-Thien N, In situ determination of matrix viscoelasticity of concentrated filler composites, in Nguyen Q.D. and R.R. Huilgol (eds.) 1988, Proc. 8th National Conf. on Rheol., Adelaide Australia, 19-22 Jul. 195-196 (1998)
  51. See H, Field JS, Pfister B, J. Non-Newton. Fluid Mech., 84(2), 149 (1999) 
  52. See H, Maher AM, Field J, Pfister B, Swain M, Phan-Thien N, Rheol. Acta, 38(5), 443 (1999) 
  53. See H, Meas. Sci. Technol., 11, 1414 (2000) 
  54. See H, Maher AM, Field J, Pfister B, Swain M, Phan-Thien N, The oscillating needle technique for measuring viscoelastic properties, in Binding D.M., N.E. Hudson, J. Mewis, J.M. Piau, C.J.S. Petrie, P. Townsend, M.H. Wagner and K. Walters (eds.), Proc. XIIIth International Congress on Rheology, Cambridge UK, 20-25 Aug. 2000, vol. 3, 37-39 (2000)
  55. See H, Jiang P, Phan-Thien N, Rheol. Acta, 39(2), 131 (2000) 
  56. Shikata T, Niwa H, Morishima Y, J. Soc. Rheol. Jpn., 25, 19 (1997)
  57. Smith TL, Ferry JD, Schremp FW, J. Appl. Phys., 20, 144 (1949) 
  58. Swain MV, Meydan A, Field JS, Pfister B, Bell TJ, Anderssen RS, Development of a microrheometer for binder in pavements, in Proc. 10th Australian Asphalt and Pavement Assoc. International Flexible Pavements Conference, 16-20 Nov 1997, Perth, Australia, 28, 1-13 (1997)
  59. Tanner RI, Engineering Rheology, 2ed, Oxford University Press, Oxford (2000)
  60. Tsai AT, Soong DS, J. Rheol., 29, 1 (1985) 
  61. Van Loan C, Computational frameworks for the fast Fourier transform, Society of Industrial and Applied Mathematics, Philadelphia (1992)
  62. Walker JS, Fast Fourier transforms, 2ed, CRC Press, Boca Raton, Florida (1996)
  63. Walters K, Rheometry, Chapman and Hall, London (1974)
  64. Whorlow RW, Rheological techniques, 2ed, Ellis Horwood, Chichester (1992)