All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.

Related Documents

Share

Description

The Origins of Rheology: A Short Historical Excursion
Deepak Doraiswamy
DuPont iTechnologies, Experimental Station
Wilmington, DE 19880-0334
I. Prelude to rheology
This article provides a brief historical perspective on the
evolution of rheology and the long gestation period before the
birth of the subject. It is not intended to be a comprehensive
state-of-the-art review but rather to capture key events in the
historical progression of the discipline, which was far from
mon

Transcript

The Origins of Rheology: A Short Historical Excursion
Deepak Doraiswamy
DuPont iTechnologies, Experimental Station Wilmington, DE 19880-0334
I. Prelude to rheology
This article provides a brief historical perspective on the evolution of rheology and the long gestation period before the birth of the subject. It is not intended to be a comprehensive state-of-the-art review but rather to capture key events in the historical progression of the discipline, which was far from monotonic, and the significant contributions from a variety of specialists. Considerable liberty has been taken in identifying key players and avoiding repetitive mention of different efforts by the same workers in order to emphasize the diversity of influences and individuals who have molded the discipline, and to satisfy severe space constraints. Some valuable resources for the historical aspects of rheology are Bingham (1922), Scott Blair (1949), Markowitz (1968), Bird et al. (1987a,b), White (1990), and Tanner and Walters (1998), and the reader is referred to these works for further details. As per the strict definition, rheology is concerned with the description of the flow behavior of all types of matter. By convention, however, rheologists’ main interests are restricted to industrially relevant materials with properties intermediate between those of ideal solids and liquids. A useful engineering definition of rheology is the description of materials using “constitutive equations” between the stress history and the strain history. Table 1 provides a convenient reference for the accompanying discussion regarding the period prior to the formal creation of the discipline of rheology in 1929.
1) Ideal materials
a)
Rigid solids
: The entire subject of general mechanics deals with ideal Euclidean bodies where only the mass (or density) of the bodies is relevant (Euclidean geometry is based on rigid bodies which do not undergo deformation). In fact, Newton's “Principia” was primarily concerned with rigid body mechanics and his comment on viscosity was only a corollary of his prescient mind. Solid mechanics is the oldest branch of the physical sciences and it is appropriate to recall the apocryphal, if time worn, story of Archimedes (~250 BCE) who claimed that he could move the world if he were provided the right leverage. b)
Elastic solids
: At the other end of the spectrum, where pure elastic solid-like behavior is concerned, Robert Hooke (Hooke (1678)) proposed that “the power of any spring is in the same proportion with the tension thereof” (i.e., the stress is proportional to the strain). It is worth noting that Robert Boyle had actually come up with a similar rule related to a “spring of air” as far back as1660. The constant of proportionality was later identified as an intrinsic property of the material – the elastic (or Young’s) modulus – by the great English polymath Thomas Young in 1807 (see Markowitz (1968)). Cauchy set up the first fundamental equations of classical (small deformation) elasticity in 1827 based largely on the work of investigators like C. L. M. H. Navier, C. A. Coulomb and S. D. Poisson. c)
Inviscid fluids
: A class of ideal materials is the so-called Pascalian (or inviscid) fluids which exhibit no resistance to flow. Blaise Pascal in 1663 first made the equivalent statement that the pressure in a liquid is the same in all directions
Table 1: Significant rheological works prior to the formal inception of rheology in 1929
# FLUIDS/MODELS CLASS KEY TIME REPRESENTATIVE WORKS
a) Perfect, rigid bodies Anti-quity Archimedes (~250 BCE), Newton (1687) b) Ideal elastic solids 1600s Boyle (1660), Hooke (1678), Young (1807), Cauchy (1827) c) Inviscid fluids 1700s Pascal (1663), Bernoulli
(1738), Euler (1755) 1 Ideal mater-ials d) Newton-ian liquids Early 1800s Newton (1687), Navier (1823), Stokes (1845), Hagen (1839), Poiseuille(1841), Weidemann (1856) 2 Linear viscoelasticity Mid 1800s Weber (1835), Kohlrausch (1863), Wiechert (1893), Maxwell (1867), Boltzmann (1878), Poynting & Thomson (1902) 3 Generalized Newtonian (viscous) liquids Late 1800s- Early 1900s Schwedoff (1890), Trouton & Andrews (1904), Hatchek (1913), Bingham(1922), Ostwald (1925) - de Waele (1923), Herschel & Bulkley (1926) 4 Non-linear viscoelasticity Early 1900s Poynting (1913), Zaremba (1903), Jaumann (1905), Hencky (1929) a) Suspen-sions Einstein (1906), Jeffrey (1922) b) Poly-mers Schonbein (1847), Baekeland (1909), Staudinger (1920), Carothers (1929) 5 Key material descrip-tions c) Exten-sional viscosity Early 1900s Barus (1893), Trouton (1906), Fano (1908), Tamman & Jenckel (1930) 6 The genesis of rheology 1929 Bingham, Reiner and others
2
(although the principle of the ideal fluid was conceived by Archimedes in classical times). The related field of hydrodynamics which formally deals with the motion of fluids where viscosity effects are absent was well developed at the turn of the 18
th
century thanks largely to the classic studies of workers like Bernoulli (1738) and Euler (1755). d)
Newtonian fluids
: Tracing the genealogy of any discipline to the “Principia” of Sir Isaac Newton serves to enhance the “gravity” of any subject, no pun intended. In his masterpiece, Newton stated his famous definition of the resistance of an ideal fluid (what we today call viscosity) which is the key property of relevance to rheology (Newton, 1687): “The resistance which arises from the lack of slipperiness srcinating in a fluid – other things being equal – is proportional to the velocity by which the parts of the fluid are being separated from each other.” The earliest quantitative application of “real fluid” or viscosity effects (albeit empirical) was by the ancient Egyptian scientist Amenemhet (~1600 BCE) (Scott Blair (1949)) who might perhaps be called the first “rheologist.” Amenemhet made a 7 degree correction to the drainage angle of a water clock to account for the viscosity change of water with temperature (which can be significant between day and night in the tropics). Hagen's work in 1839 was the first clear recorded study of the viscosity of a liquid; he determined that the pressure drop for capillary flow is the sum of two quantities: a viscosity term and a kinetic energy correction. The next key research related to capillary was the painstaking work of Poiseuille (1841). These were both entirely empirical studies in narrow tubes and showed that the flow rate was proportional to the pressure gradient and the fourth power of the radius. Pioneering work on the laws of motion for real fluids (with finite viscosities) was carried out by Navier (1823) which was followed up on by Stokes (1845). The celebrated Navier-Stokes equations enabled, for example, prediction of velocity distributions and flow between rotating cylinders and cylindrical tubes. Stokes was apparently not able to show experimental validity of his result for discharge through tubes (Markowitz (1968)); Wiedemann (1856) first showed agreement between the Hagen-Poiseuille data and the Navier-Stokes prediction. It was finally left to M. M. Couette to show that the viscosity value obtained using a special concentric cylinder set-up (to avoid end-effects) and in tube flow were identical – first establishing that the viscosity was an intrinsic property of the material (see, for e. g., Piau et al. (1994)).
2) Linear viscoelasticity
Initial work on viscoelasticity was primarily targeted towards creep and relaxation behavior of metals until the explosive growth of the polymers industry. The earliest systematic study of materials that were neither Hookean nor Newtonian was carried out by Weber (1835) using silk threads (because of their application in electromagnetic instruments). The removal of an extensional load led to an immediate contraction followed by further gradual contraction until the initial (pre-loaded) length was attained – he had identified the phenomenon of stress relaxation (which he called “the after effect”). Thus Weber had qualitatively captured the phenomenon of viscoelasticity even before Poiseuelle’s results on tube flow and Stoke’s work on viscous liquids. Kohlrausch (who extended his father’s work ) then experimentally established the linearity of the phenomenon in 1863 based on his work with glass. During this same period a major contribution to rheology came from Maxwell (1867) who postulated his famous first-order empirical differential equation relating the shear stress to the deformation and the accompanying simple exponential stress relaxation. The results of Weber and Kohlrausch enabled Ludwig Boltzmann (1878) to arrive at his “principle of superposition:” “The value of a characteristic function of a system is equal to the sum of all changes induced in the system by the driving functions which have been applied to it throughout its history.” He arrived at an integral representation of linear viscoelasticity in its full 3-D generality. The next major modification was by Wiechert (1893) and Thomson (1888), who independently introduced the concept of a distribution of relaxation times. The well-known “spring-and-dashpot” analogy for the Maxwell model was not introduced until 1902 by Poynting and Thomson.
3) Generalized Newtonian materials
Schwedoff’s (1890) experimental work on colloidal gelatin solutions using a Couette device was one of the first results on non-Newtonian systems. His data indicated a non-linearity of torque-angular velocity data in a Couette instrument; he also had to incorporate a yield value to describe his results. Hess (1910) and Hatchek (1913) were some of the other early pioneers who postulated that the viscosity was a function of the rate of shear based on results analogous to those of Schwedoff for gelatin sols. Trouton and Andrews (1904), in their studies on pitch, had to subtract a small “initial stress” in order to obtain a flow rate proportional to the stress. This type of fluid behavior is now associated with Bingham (1922), who proposed a “yield stress” to describe the flow of paints. Equations for shear rate-dependent viscosities were proposed by Ostwald (1925)-de Waele(1923), and Herschel and Bulkley (1926).
4) Non-linear viscoelasticity prior to 1929
Poynting (1913) performed some very elegant experiments in non-linear elasticity. He determined that loaded wires increased by a length that was proportional to the square of the twist against all expectations of linear elasticity theory. Zaremba (1903) extended linear viscoelasticity theory to the
3
non-linear regime by introducing a corotational derivative to incorporate a frame of reference that was translating and rotating with the material. Similar work was done by Jaumann (1905) and, despite Zaremba’s precedence, the derivatives are referred to as “Jaumann derivatives.” Hencky (1929) whose name is identified with the “logarithmic” (or instantaneous strain) also proposed analogous ideas.
5) Some key material descriptions prior to 1929
a)
Suspensions
:
Dispersions and suspensions have always been of great interest as typified by the importance of ink, blood, paints, and the silting of harbors. Thomas Graham (1805-1869) is regarded as the founder of the term colloidal dispersions (comprising particles with diameters less than 1
!
). Einstein (1906) was the first worker to develop an equation for the effective viscosity of dilute suspensions (< ~5%) and work has since expanded to cover a wide range of particle concentrations, sizes and shapes. Jeffrey’s (1922) seminal work on the orbits of elongated particles and fibers in dilute suspensions has been the basis for many later studies in suspension rheology. b)
Polymers
: The ability to define the structure of macromolecules was a relatively recent occurrence in human history in spite of our reliance on such materials (like cotton, silk, gums and resins) since ancient times. Some significant events in the development of industrial materials of relevance to rheology are (see, e. g., White (1990)): the development of a rubber industry based on coagulated rubber latex, procedures for vulcanizing (modifying) rubber with sulfur and heat, the development of cellulose nitrate and xanthate (Schonbein (1847)), and the development of gutta percha. One of the early founders of polymer chemistry was Staudinger (1920) who first proposed the now familiar “chain formula” for these large molecules. Carothers (1929) at the DuPont Company began synthesizing polyesters and polyamides in the 1930s which provided an impetus for the polymer industry in the U.S. Parallel efforts were initiated by Baekeland (1909) for phenol-formaldehyde resins and by Fritz Hofmann at Farbenfabriken Bayer (see, for example, Weil (1926)). During the Second World War the requirement to develop materials for flame throwers, which were known to be viscoelastic, triggered further interest in rheology. c)
Extensional viscosity effects
: The srcins of elongational flow measurements are largely due to Trouton (1906) who considered the uniaxial stretching of pitch and “shoemaker’s wax.” The next major study was by Tamman and Jenckel (1930) on elongational flow of molten glass filaments. Extrudate or die swell was first correctly identified with “stretching” by Merington (1943) although Barus (1893) had reported an analogous phenomenon much earlier which he attributed to shear recovery. Because of high extensional viscosities, polymer solutions can be drawn up through a nozzle even if it is raised above the free surface. This phenomenon is referred to as Fano flow because of his initial investigation on the subject (Fano (1908)). This effect appears to have been used as early as ca.55 C.E. to harvest bitumen from the Dead Sea (as concluded by Bird et al. (1987a) based on the Complete Works of Tacitus).
II. The genesis of rheology
Rheology is one of the very few disciplines whose coinage can be traced to an exact date: April 29, 1929 (Bingham (1944), Scott Blair (1949)); the first reference to a related term “microrheometer” actually appeared as far back as 1879 (Hannay, 1879). A Plasticity Symposium (to study viscosity) was held on October 17, 1924 as part of the 50
th
anniversary celebration of the career of a Prof. Edward Hart at Lafayette College, Penn. The high level of interest expressed in this subject eventually led to a Third Plasticity Symposium in 1929 at which a decision was made to form a permanent organization for the development of the new discipline of rheology. The preliminary scope of The Society of Rheology was set up by a committee which then met on April 29, 1929 at Columbus, Ohio
1
and some of the luminaries who participated in this pioneering event included Eugene C. Bingham, Winslow H. Herschel, Marcel Brillouin, Herbert Freundlich, Wolfgang Ostwald, Ludwig Prandtl and Markus Reiner. The name “rheology” was proposed to describe “the study of the flow and deformation of all forms of matter” by E .C. Bingham and M. Reiner; Heraclitus’ quote “
#$%# '(
i” or “everything flows” was taken to be the motto of the subject (Reiner (1964)).
III. Rheology since its inception
Table 2 provides a convenient reference for key developments in rheology related to the post-inception period.
1) Constitutive equations
a)
Differential models
: Initial theoretical work on rheology after its formal inception was largely concerned with continuum mechanics formulations to enable characterization and description of material flow behavior for commercial applications. A major advancement was J. G. Oldroyd’s work in 1950 on convected derivatives based on application of “the invariance of material properties with respect to the frame of reference;” this represented the culmination of a number of earlier efforts relating to complex derivatives of the stress. Some notable differential models are the “retarded-motion expansions” (e. g., Rivlin and Ericksen (1955) and Giesekus (1962)) in which the stress is expressed as a power series
1
The first official meeting of The Society of Rheology was held at the National Bureau of Standards on December 19, 1929 at which a formal committee was appointed on definitions and action was taken for securing an improved absolute viscosity standard; the Journal of Rheology was also started as a quarterly.
4
Table 2: Rheology since its inception in 1929
# AREA OF ACTIVITY REPRESENTATIVE WORKS
a) Differential models Oldroyd (1950), Truesdell (1952), Rivlin and Ericksen (1955), Giesekus (1962), White-Metzner (1963) b) Integral models Green & Rivlin (1957), Coleman & Noll (1961) c) Network models Green & Tobolsky (1946), Lodge(1956), Yamamoto (1956), Kaye (1962) - Bernstein et al. (1963) d) Reptation models Edwards (1967), De Gennes (1971), Doi & Edwards (1978, 1986) 1 Constitu-tive equations e) Molecular models Kuhn (1934), Rouse (1953), Zimm (1956), Kirkwood (1967), Bird et al. (1987) a) Shear flows and the no-slip boundary condition Eisenschitz et al. (1929), Mooney (1931,1936), Schofield & Blair (1930), Pearson & Petrie (1968), Graessley (1977), Ramamurthy (1986) b) Normal stresses and rod-climbing effects Lander (1945), Weissenberg (1947), Markowitz (1957), Philippoff (1957), Ginn & Metzner (1969), Binnington & Boger (1985) c) Dynamic studies Eisenschitz & Philippoff (1933), Schofield & Scott Blair (1932), Leaderman (1943), Cox-Merz (1958), Doraiswamy et al. (1991) d) Thixotropy Freundlich & Bircumshaw (1926), Cheng & Evans (1965), Mewis (1979), Barnes (1997) e) Flow Instabilities Nason (1945), Tordella (1958), Petrie & Denn (1976), Bousfield et al. (1986) f) Turbulent drag reduction Toms (1949), Agoston et al. (1954), Hershey & Zakin (1967), Seyer & Metzner (1967) g) Optical studies/ birefringence Adams et al. (1965), Carothers & Hill (1932), Hermans & Platzek (1939), Janeschitz-Kriegl (1983), Fuller (1985) h) Time-temp. superposition Williams et al. (1955), Ferry (1970) 2 Experi-mental advances and rheolog-ical descrip-tions i) Extensional behavior Merrington (1943), Treolar (1944), Ballman (1965), Cogswell (1969), Metzner (1968), Meissner (1969), Dealy et al. (1976), Spearot & Metzner (1972), Laun & Munstedt (1978), Sridhar & Gupta (1985) a) LCPs Leslie (1968)-Ericksen (1961),Doi (1981), Wissbrun (1985), Doraiswamy & Metzner (1986), Marrucci & Greco (1992) b) Composites and two-phase systems Taylor (1934), Krieger-Dougherty (1959), Rumscheidt & Mason (1961), Leal (1975), Batchelor (1977), Folgar & Tucker (1984), Heller & Kuntamukkula (1987), Khan & Armstrong (1986), Acrivos & Shaqfeh (1988), Mewis et al. (1989), Dennis et al. (2001) 3 Advanced materials c) ER/MR fluids Winslow (1949), Parthasarthy & Klingenberg (1996) a) Continuum simulations Turner et al. (1956), Gottlieb & Orzag (1977), Cruse & Risso (1968), Yoo & Joseph (1985), Beris et al. (1987), Walters & Tanner (1992), Crochet & Walters (1993) 4 Computa-tional rheology b) Molecular dynamic simulations Adler & Wainright (1957), Ashurst & Hoover, (1975), Evans & Morriss (1988), Davis & Todd (1998)
involving increasing powers of the rate-of-strain tensor and increasing orders of partial time derivatives. b)
Integral-type models
: Another slightly later development was the complementary effort of Green and Rivlin (1957), and Coleman and Noll (1961) who used integral formulations whereby the stress at any location and time depended on the entire past history of the local deformation. The entire subject of constitutive equations and their development have been discussed in great detail by Bird et al (1987a,b), Larson (1988) and more recently by Tanner (2001). c)
Network theories
: The early work by Green and Tobolsky (1946) was one of the first attempts to describe relaxation processes in networked polymers. The network theory for rubber-like fluids developed independently by Lodge (1956) and Yamamoto (1956) was the next major advance in the field. The permanent chemical junctions in rubber are assumed to be replaced by temporary physical junctions whose kinetics have to be described. An extension of the Lodge model is the K-BKZ model (Kaye (1962), Bernstein, Kearsley and Zapas (1963)) whereby a more general form was sought by redefining the kernel function in the Lodge integral formulation. d)
Reptation theories
: A “tube model” was first proposed by Edwards (1967) for rubbers. The Doi-Edwards model (1978, 1986) based on the reptation theory of de Gennes (1971) was another significant advancement in the field whereby the tube model was extended to melts and concentrated solutions. The polymer chain is constrained to move in a “tube” because of the presence of neighbouring molecules and the tube itself evolves in time as the chain crawls or “reptates.” e)
Molecular models
: Kuhn (1934) first addressed the characterization of the configuration of polymer molecules using a random coil model. Starting with this work and progressing with the landmark kinetic theory papers of Kramers (1944), Rouse (1953), Zimm (1956) and Kirkwood (1967), it was becoming increasingly apparent that material equations should reflect the polymer structure to facilitate processing and development of new materials. This approach culminated in the major effort by Bird et al. (1987b) which summarized the state-of the-art in the field (this work includes the so-called generalized phase-space kinetic theory which incorporates both the velocities and positions of the “beads” in the bead-spring models).
2) Experimental advances and rheological characterizations
The early decades of rheology were marked by investigations into a number of experimental phenomena. a)
Shear flows and the no-slip boundary condition
: Stokes (1845) was the first to establish the no-slip boundary condition

We Need Your Support

Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks