×

A rheo-lodgical half century. (English) Zbl 1163.76005

Summary: The following topics are included: ideas received from Max Born and Karl Weissenberg; Born’s definitions of internal energy and heat flow; features common to science and religion; fallacious improbability arguments in the evolution literature; comparison of elementary particle theory and rheology; contrast between early constitutive proposals of Weissenberg and Reiner; elementary definitions of body tensors; recoil; molecular network and tube theories; liquidating a solid: the rubberlike liquid; the stressmeter: measurement of the first normal stress difference in steady shear flow at shear rates up to \(10^{6} \)s\(^{ - 1}\) and shear stresses up to 200 kPa; cP-liquid viscosity measurement at shear rates above \(10^{6} \)s\(^{ - 1}\), with a scatter of 0.2% (new results); on-line detection of very small changes in the high molecular weight tail of a polymer molecular weight distribution; measurement of 0.004 psi pressure differences under ambient pressures of 2000 psi (new results).

MSC:

76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76-05 Experimental work for problems pertaining to fluid mechanics
76-03 History of fluid mechanics
01A60 History of mathematics in the 20th century
82D15 Statistical mechanics of liquids
Full Text: DOI

References:

[1] Sober, E.: From a biological point of view: essays in evolutionary philosophy, (1994)
[2] Lean, G.: A.lunng.leanchapter 12: faith by experiment, christian counterattack, Chapter 12: faith by experiment, christian counterattack (1969)
[3] The King James Bible, I Kings 18, pp. 20 – 40.
[4] Davison, J. A.: Semi-meiosis as an evolutionary mechanism, J. theor. Biol. 111, 725 (1984)
[5] Greenspan, N. T.: The end of the certain world: the life and science of MAX Born, (2005) · Zbl 1165.81003
[6] Dembski, W.: The design inference, (1998) · Zbl 0947.62002
[7] Huxley, J.: J.huxleya.c.hardye.b.fordevolution as a process, Evolution as a process, 5 (1954)
[8] Fisher, R. A.: J.huxleya.c.hardye.b.fordevolution as a process, Evolution as a process, 91-92 (1954)
[9] Callen, H. B.: Thermodynamics: an introduction to the physical theories of equilibrium thermodynamics and irreversible thermodynamics, (1960) · Zbl 0095.23301
[10] Öttinger, H. C.: Beyond equilibrium thermodynamics, (2005)
[11] Truesdell, C. A.: Rational thermodynamics, (1969) · Zbl 0598.73002
[12] Born, M.: Natural philosophy of cause and chance, (1964) · Zbl 0032.24403
[13] Lodge, A. S.: Low-shear-rate rheometry and polymer quality control, Chem. eng. Commun. 32, 1 (1985)
[14] Oldroyd, J. G.: On the formulation of rheological equations of state, Proc. roy. Soc. A 200, 523 (1950) · Zbl 1157.76305 · doi:10.1098/rspa.1950.0035
[15] Lodge, A. S.: Body tensor fields in continuum mechanics, (1974)
[16] Lodge, A. S.: Some finite-strain generalizations of Boltzmann’s equation, , 229 (1954) · Zbl 0058.39901
[17] Kaye, A.; Saunders, D. W.: A concentric cylinder viscometer for the measurement of flow birefringence and viscosity in concentrated polymer solutions, J. sci. Instrum. 41, 139 (1964)
[18] Kaye, A.; Lodge, A. S.; Vale, D. G.: Determination of normal stress differences in steady shear flow, II flow birefringence, viscosity, and normal stress data for a polyisobutylene liquid, Rheol. acta 7, 368 (1968)
[19] Miller, M. J.; Christiansen, E. B.: The stress state of elastic fluids in viscometric flow, Aiche J. 18, 600 (1972)
[20] Lodge, A. S.: Low-compliance diaphragm-capacitance pressure gauge for measurement of liquid pressures of the order of 1in. Water, J. sci. Instrum. 37, 401 (1960)
[21] Lodge, A. S.: Rheological properties of concentrated polymer solutions. I. growth of pressure fluctuations during prolonged shear flow, Polymer 2, 195 (1961)
[22] Imaeda, T.; Furukawa, A.; Onuki, A.: Viscoelastic phase separation in shear flow, Phys. rev. E 70, 051503 (2004)
[23] Weissenberg, K.: A continuum theory of rheological phenomena, Nature (London) 159, 310 (1947)
[24] Reiner, M.: A mathematical theory of dilatancy, Am. J. Maths 67, 350 (1945) · Zbl 0063.06464 · doi:10.2307/2371950
[25] Lodge, A. S.: Elastic liquids, (1964)
[26] Lodge, A. S.: An introduction to elastomer molecular network theory, (1999)
[27] Meissner, J.: Dehnungsverhalten von polyäthylen-schmelzen, Rheol. acta 10, 230 (1971)
[28] H. Chang, Elongational flow and spinnability of viscoelastic fluids, Ph.D. Thesis, University of Wisconsin-Madison, 1973.
[29] Gramespacher, H.; Meissner, J.: Melt elongation and recovery of polymer blends, morphology and influence of interfacial tension, J. rheol. 41, 27-44 (1997)
[30] Lodge, A. S.: Elastic recovery and polymer-polymer interactions, Rheol. acta 28, 351 (1989)
[31] Doi, M.; Edwards, S. F.: Dynamics of concentrated polymer systems. Part I. Brownian motion in the equilibrium state. Part 2. Molecular motion under flow, J. chem. Soc. Faraday trans. II 74, No. 1978, 1789 (1802)
[32] Mcleish, T. C. B.: Tube theory of entangled polymer dynamics, Adv. phys. 51, No. 4, 1379 (2002)
[33] Greensmith, H. W.; Rivlin, R. S.: The hydrodynamics of non-Newtonian fluids, III. The normal stress effect in high-polymer solutions, Phil. trans. Roy. soc. A 245, 399 (1953)
[34] Broadbent, J. M.; Kaye, A.; Lodge, A. S.; Vale, D. G.: Possible systematic error in the measurement of normal stress differences in polymer solutions in steady shear flow, Nature (London) 217, 55 (1968)
[35] Tanner, R. I.; Pipkin, A. C.: Intrinsic errors in pressure-hole measurements, Trans. soc. Rheol. 13, 471 (1969)
[36] R. Schefenacker, Numerische Integration der Navier-Stokes-Gleichungen zur Berechnung der Transversalströmung in Mischteilen und der Strömung in Breitschlitzwerkzeugen mit ”pressure holes”, Inst. f. Kunststoff Technologie Studienarbeit, Stuttgart, 1973.
[37] Cochrane, T.; Walters, K.; Webster, M. F.: On Newtonian and non-Newtonian flow in complex geometries, Phil. trans. Roy. soc. 301, 163-181 (1981)
[38] Higashitani, K.; Pritchard, W. G.: A kinematic calculation of intrinsic errors in pressure measurements made with holes, Trans. soc. Rheol. 16, 687 (1972)
[39] D.G. Baird, In-line stress measurements in polymer solutions flowing through a slit die, Ph.D. Thesis, University of Wisconsin-Madison, 1974.
[40] A.S. Lodge, A new method of measuring multigrade oil shear elasticity and viscosity at high shear rates, SAE Technical Paper Series #872043, 1987.
[41] Lodge, A. S.; Al-Hadithi, T. S. R.; Walters, K.: Measurement of the first normal stress difference at high shear rates for a polyisobutylene/decalin solution ”D2”, Rheol. acta 26, 516 (1987)
[42] Lodge, A. S.: An attempt to measure the first normal stress difference N1 in shear flow for a polyisobutylene/decalin solution ”d2b” at shear rates up to 106s - 1, J. rheol. 33, No. 4, 821 (1989)
[43] Lodge, A. S.: On-line measurement of elasticity and viscosity in flowing polymeric liquids, Rheol. acta 35, 110 (1996)
[44] Yao, M.; Malkus, D. S.: Cancellation of errors in the higahitani – pritchard treatment of hole pressures generated by viscoelastic liquids in creeping flow past a transverse slot, Rheol. acta 29, 310 (1990) · Zbl 0712.76019 · doi:10.1007/BF01339886
[45] Young-soo Ko, Study of the effect of viscous heating in high shear rate slit die viscometry, Ph.D. Thesis, The University of Wisconsin-Madison, 1990.
[46] Lodge, A. S.: A.a.collyerd.w.cleggrheological measurement, Rheological measurement, 320 (1998)
[47] Wilson, E. O.: Systematics and the future of biology, Proc. natl. Acad. sci. 102, No. Suppl. 1, 2905 (2005)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.