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Shear and time‐dependent rheology of a fully nematic thermotropic liquid crystalline copolymer

Douglass S. Kalika, David W. Giles, and Morton M. Denn

J. Rheol. 34, 139 (1990); http://dx.doi.org/10.1122/1.550116 (16 pages) | Cited 2 times

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Rheological measurements are reported for a fully nematic thermotropic liquid crystalline copolyester composed of 80% p‐hydroxybenzoic acid/20% poly(ethylene terephthalate). The polymer displays shear thinning behavior with a constant power‐law index over eight decades of shear rate; no shear‐independent plateau (region II) is observed. Dynamic time sweeps indicate a high sensitivity of the rheological parameters to thermal history, apparently resulting from crystalline annealing. These annealing effects could be erased by appropriate thermal cycling. Torsional measurements (cone‐and‐plate) were limited at high shear rates by the occurrence of edge fracture. This instability was typically accompanied by an unusual sample texture composed of concentric rings, which was particularly distinct when offgassing had occurred in the polymer melt.

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46.40.-f	Vibrations and mechanical waves
83.50.-v	Deformation and flow

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The effect of surface tension on stretching of very thin highly elastic filaments

A. I. Leonov

J. Rheol. 34, 155 (1990); http://dx.doi.org/10.1122/1.550117 (13 pages)

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This paper deals with theoretical investigations of the extension of very thin highly elastic filaments as a function of fibrilar diameter. Some specific phenomena are predicted. If the diameter of the fibril is lower than a certain critical value, a nonmonotonous region appears on the stress–strain curve. In this region, a transition from slightly deformed to highly stretched (oriented) states occurs due to a special neck propagating along the fibril. A simple theoretical description of these phenomena is developed in terms of a given general high‐elastic dimensionless potential and two dimensionless parameters which characterize the external force and surface tension. These effects are illustrated by theoretical calculations using neo‐Hookean properties for the highly elastic material.

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68.70.+w	Whiskers and dendrites (growth, structure, and nonelectronic properties)
62.20.F-	Deformation and plasticity
81.40.Lm	Deformation, plasticity, and creep

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The motion of a ball oscillating in a bounded fluid: Inertial and wall effects

R. Tran‐Son‐Tay, B. E. Coffey, and R. M. Hochmuth

J. Rheol. 34, 169 (1990); http://dx.doi.org/10.1122/1.550122 (23 pages)

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Inertial and wall effects on the motion of a ball oscillating in a rigid container are investigated both experimentally and theoretically. Experiments are performed with an oscillating ball rheometer to determine the effects of inertia and of the wall on the motion of a rigid sphere oscillating within a Newtonian fluid in a vertically oriented cylindrical tube. It is found that under certain conditions the effect of inertia on the drag force acting on a ball oscillating inside a cylindrical tube is well described by the theory for a ball oscillating inside a spherical container. When the imaginary component of the total hydrodynamic force is negligible, this result allows a correction and the use of the Stokes drag equation to account for the boundary and frequency effects in the determination of the non‐Newtonian viscosity with a ball rheometer. Finally, it is shown that a simple study on Newtonian fluids can provide information to help understand the more complex effect of inertia in non‐Newtonian suspensions. As an application, rheological properties of concentrated red blood cell suspensions are studied in a ball rheometer at frequencies of oscillation where inertia is important. It is found that additional dependence of the storage modulus on inertia is not proportional to the square of the angular frequency of oscillation as stated by Sellers et al., and that terms in S of order higher than two are not negligible in the case of a ball rheometer.

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47.80.-v	Instrumentation and measurement methods in fluid dynamics
47.50.-d	Non-Newtonian fluid flows
87.19.rh	Fluid transport and rheology

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Rheological behavior of polydimethylsiloxane/polyoxyethylene blends in the melt. Emulsion model of two viscoelastic liquids

D. Graebling and R. Muller

J. Rheol. 34, 193 (1990); http://dx.doi.org/10.1122/1.550123 (13 pages) | Cited 8 times

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The linear viscoelastic behavior of two‐phase polymer blends in the melt is characterized by high values of storage modulus at low frequencies and by long relaxation times. The variation of dynamic moduli with frequency could be explained with an emulsion model as developed by Oldroyd. This model allows us to take in account the viscoelastic behavior of each phase, as well as characteristic parameters of the blends like volume fraction, interfacial tension, and size of inclusions. Experimental results on polydimethylsiloxane/polyoxyethylene‐diol blends are found to be in good accordance with Oldroyd’s emulsion law. The terminal relaxation process of the blend can be assigned to the geometric relaxation of the inclusions.

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62.60.+v

Acoustical properties of liquids

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Flow properties and electrical conductivity of carbon black–linseed oil suspension

Takeshi Amari and Koichiro Watanabe

J. Rheol. 34, 207 (1990); http://dx.doi.org/10.1122/1.550124 (15 pages)

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The electrical conductivity and apparent viscosity for suspensions of carbon black in linseed oil were measured at various volume fractions of carbon black as a function of rate of shear using a Couette type viscometer. The structural density may be reduced with increasing rate of shear and consequently the electrical conductivity and apparent viscosity decrease with rate of shear. The value of conductivity is proportional to the fourth power of concentration above a critical concentration. The viscosity also increases exponentially with increasing concentration. However, obvious threshold values of the concentration and of the power law index cannot be obtained. These phenomena are discussed in the framework of percolation theory. At intermediate structural density the electrical conductivity changes as the square of the viscosity. However this relationship is reversed when the denser structural networks are formed in the whole system. Since an oxidized boundary layer is gradually formed on the surface of the particles in the suspension of carbon black, the apparent viscosity and the electrical conductivity decrease with elapsed time. After reducing rate of shear, the conductivity and the viscosity increase with time due to growing flocculated structure. The value of conductivity reaches a maximum and then decreases, whereas the value of viscosity keeps increasing. These phenomena are discussed from a viewpoint of the kinetic processes of the formation and breakdown of the structural networks.

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47.15.-x	Laminar flows
66.20.-d	Viscosity of liquids; diffusive momentum transport
72.80.Ph	Liquid semiconductors

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Concentration dependent changes of apparent slip in polymer solution flow

H. Müller‐Mohnssen, D. Weiss, and A. Tippe

J. Rheol. 34, 223 (1990); http://dx.doi.org/10.1122/1.550125 (22 pages) | Cited 8 times

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In order to prove the depletion hypothesis of ‘‘apparent slip,’’ velocity profiles in ducted flow of aqueous polyacrylamide (PAM) solutions were measured to a distance of d=0.15 μm from the wall and the dependency of the slip velocity on the PAM concentration c_∞ was determined. As the slip velocity exhibited exceptionally high values when using glass surfaces all quantitative results were obtained with rectangular glass ducts. For c_∞ <0.05% (wt. %), the assumed slip layer lining the wall was identified by an experimental determination of the velocity profile within this layer, as well as of its width δ. Intersection of this profile with the wall position at zero velocity verified the slip as being ‘‘apparent.’’ The width δ decreased with increasing c_∞ from δ=0.3 μm at c_∞=0.005% to δ≤0.15 μm at c_∞ ≥0.05%; 0.15 μm represents the spatial resolution of the anemometer used. The ratio of the slip velocity to wall shear stress, i.e., the slip coefficient—which was constant for each concentration—decreased with increasing c_∞. For all PAM concentrations examined the average viscosity η_δ, as well as the concentration c_δ of the fluid within the slip layer, was determined to be smaller than the corresponding values in the bulk solution, thus indicating a depletion of polymer molecules in the slip layer. Further experimental results support the hypothesis that such depletion is largely (up to 80% of the slip velocity) the result of electrostatic interactions between charged PAM molecules and an electric double layer present at the wall surface.

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47.45.Gx

Slip flows and accommodation

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Correction factor for Leaderman’s formula

A. C. Pipkin

J. Rheol. 34, 245 (1990); http://dx.doi.org/10.1122/1.550126 (6 pages)

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Leaderman’s formula gives a simple approximate relation between the modulus and the compliance of a viscoelastic material, which is accurate when the log–log slopes of these functions are small and slowly varying. The first‐order correction due to variation of the slope is computed, and a table of numerical values of the correction factor is given.

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46.35.+z

Viscoelasticity, plasticity, viscoplasticity

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Extension of plane rubber films

Susumu Kase and Taro Nishimura

J. Rheol. 34, 251 (1990); http://dx.doi.org/10.1122/1.550127 (23 pages)

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Extension of thin plane films, uneven in initial thickness and obeying the constitutive equation of rubber‐like elasticity, was analyzed mathematically with the following results. (i) The plane extension of rubber films is governed by two simultaneous partial differential equations whose independent variables are (u,v) and dependent variables are ( f,g) where (u,v) is the position in Cartesian coordinates of a rubber particle constituting the film occupied before the extension and ( f,g) is the position of the same particle after the extension. (ii) The axisymmetrical stretching mode is governed by a single ordinary differential equation which can readily be solved analytically or numerically upon specification of film thickness known at any one radial position. (iii) Uniform thickness extension is possible only when the film is initially uniform in thickness and the mode of extension is uniform biaxial, i.e., the two principal strains in x and y directions, respectively, are independent of position (u,v). This is in marked difference from the case of the extension of flat Newtonian fluid films in which a complex mode of uniform thickness extension obeying the Cauchy–Riemann equations exists. (iv) The governing equations were solved numerically for the general case by means of the Newton iteration scheme used in a finite difference approximation.

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