Volume 41, Issue 1, January 1997
Index of content:
41(1997); http://dx.doi.org/10.1122/1.550881View Description Hide Description
Rupture is one of the least investigated and least understood features of the rheological behaviour of polymeric liquids. Some key experimental results on the rupture of polymer melts in uniaxial extension are discussed. Three features of experimental results for narrow molecular weight distribution (MWD) polymers may be highlighted. Firstly, steady elongational flow becomes impossible and rupture of the liquid filament occurs when and if the stored elastic (Hencky) strain reaches 0.5 units. This can be interpreted in terms of a critical Weissenberg number. Secondly, at higher rates of strain (when the elastic strain becomes more than 0.5) the relationship between limiting stress and elastic strain (at the breaking point) is linear. In this case the limiting elastic strain can become at least as high as 2. Thirdly, the strength of a fluid polymer is not a constant but may be characterised by the lifetime, or durability, of the filament. This leads to an empirical criterion for rupture: M MJ/m, where η is the shear viscosity, σ is the stress at rupture, and M has the dimension of specific energy. This criterion also predicts conditions of rupture for various complicated deformation histories. These results are compared with results for broad MWD polymers. Theoretical criteria based on the results are related to rheological ideas and hypotheses concerning rupture, highlighting areas where further work is required.
41(1997); http://dx.doi.org/10.1122/1.550879View Description Hide Description
Blends of polystyrene (PS) and poly(methylmethacrylate) (PMMA) have been investigated in elongation at 170 °C. The melts of the pure PS and PMMA have only a small difference in their viscosities. Consequently, with 8–12–16–20 weight % PS in PMMA, the elongational viscosities of the melts show only small differences and are similar to that of PMMA. However, when the maximum elongation of 3.5 Hencky units (corresponding to a stretch λ=33 and obtained at a strain rate of 0.1 s−1) is followed by recovery, the recoverable strain strongly depends on the PS concentration and shows very large values with a maximum that corresponds to a recoverable stretch of λ R =14.5 (for the 20% PS blend). The morphology obtained by quenching the samples shows that the originally spherical PSdroplets in the continuous PMMA are stretched into ellipsoids and finally into long needles. During recovery, the viscoelastic deformation (molecular orientation) recovers and the stretched needles change backwards into spheres. But these two procedures occur with different time scales. The driving force for the second procedure is the interfacial tension α. An analysis is given for the determination of α from the measured transient recovery. Conversely, the transient recovery can be predicted when α, the droplet size, and the equilibrium value λ R are known. Resulting from the different blends the interfacial tension between the melts of PS and PMMA is between α=1.5 and 2.2 mN/m. This range covers previously published results for the same blends measured by a very different method, viz. shear oscillations.
41(1997); http://dx.doi.org/10.1122/1.550858View Description Hide Description
Two nominally identical pure bitumens, commonly employed for pavement construction in the United Kingdom, were tested in uniaxial tension, compression, and shear, over a wide range of temperatures, stresses, and strain rates. The bitumens were found to exhibit linear viscous behavior at low stress levels, and power-law creeping behavior at higher stress levels. The temperature dependence was found to follow the Arrhenius relationship at temperatures immediately above the glass transition and the Williams, Landel, and Ferry (WLF) equation at higher temperatures. Below the glass transition temperature, the Eyring plasticity model was found to hold. Constitutive models that reflect the physical mechanisms of steady state and transient deformation are proposed. The fracture properties of the bitumens are also discussed.
41(1997); http://dx.doi.org/10.1122/1.550854View Description Hide Description
We examine the rheological response of zeolite-based electrorheological (ER) suspensions in silicone oil, mineral oil, and N-(4-methoxybenzylidine)-4 butylaniline, a low molecular weight, nematic liquid crystal. The carriers were selected to explore the effects of fluidviscosity and dielectricpermittivity on the ER properties of the suspensions. A particular form of the White–Metzner constitutive equation correctly reproduces the main, qualitative features of the experiments, with only three parameters. When used in conjunction with an equation describing rheometer dynamics, the rheological model satisfactorily captures artifacts caused by the coupling of inertia and elastic compliance of the instrument with the nonlinear material response.
41(1997); http://dx.doi.org/10.1122/1.550802View Description Hide Description
The steady flow of an incompressible material of the Bingham viscoplastic type along a rectangular duct is calculated. This flow has importance in a number of geophysical problems. A numerical solution to the problem is found using finite differencing of the partial differential equation governing the fluid motion. The flow is seen to consist of a plug in the center of the duct with dead regions of “no-flow’’ at the corners, due to the rectangular cross section. The variation of this flow pattern as a function of two nondimensional parameters, the yield stress and the aspect ratio, is investigated.
41(1997); http://dx.doi.org/10.1122/1.550803View Description Hide Description
We present the first quantitative experimental measurements of the transient motion of a sphere as it accelerates from rest along the centerline of a tube containing a highly elastic,shear-thinning, aqueous polyacrylamide solution. For all shear-rate-dependent Deborah numbers and sphere-to-tube ratios investigated, transient oscillations in the velocity of the sphere are observed, often causing the sphere to “rebound,” or reverse directions during the first oscillation. These measurements are in qualitative agreement with the analysis of King and Waters (1972) who presented an analytic solution for the transient motion of a sphere through an unbounded domain of fluid described by the linear Jeffreys model. We also show a similar response in one-dimensional creepexperiments which are described quantitatively by a multimode formulation of the upper-convected Maxwell model including a solvent retardation term. Such experiments isolate the shear kinematics from the combined shear and extensional flow around a sphere and indicate that because of the slow quadratic growth of the elastic normal stresses in the fluid at short times and small fluid strains, the initial transient motion of the sphere is governed primarily by a balance of linear viscoelastic stresses and the inertia of the sphere.
Determination of the molecular weight between crosslinks of waxy maize starches using the theory of rubber elasticity41(1997); http://dx.doi.org/10.1122/1.550804View Description Hide Description
The theory of elasticity for solvent swollen rubbers was used to calculate the average molecular weight of chain between crosslinks, Mc , of five waxy maize starches with different degrees of crosslinking. Above a critical starch concentration (%w/w), maximum packing of granules occurs, and the interior of the granules controls the rheological behavior of the starch suspensions. A rubbery plateau, characterized by a storage modulus, G, independent of frequency, is related to the average Mc by the equation: Mc=c1/3ρ2/3RT/G. Mc values determined (g/mol) for lightly crosslinked starch were 2.7×106 and 2.6×106; for moderately crosslinked, 2.5×106; and, 1.2×106 and 1.2×106 for highly crosslinked starches. As expected, a lower degree of crosslinking results in a higher molecular weight between the covalent bonds.
41(1997); http://dx.doi.org/10.1122/1.550852View Description Hide Description
A scaling analysis of the relative viscosity of two-phase liquid-liquid emulsions is presented. According to the analysis, the relative viscosity of two oil-in-water emulsions at the same oil concentration and particle Reynolds number is the same, even if the emulsions differ greatly in droplet size. Experimental results are presented to confirm the validity of the proposed scaling relations.
Rheological and rheo-optical characterization of shear-induced structure formation in a nonionic drag-reducing surfactant solution41(1997); http://dx.doi.org/10.1122/1.550839View Description Hide Description
We know of only a few rheological studies of nonionic surfactant solutions, and these did not show clear evidence of shear-induced structures (SIS) formation. This paper reports, however, some rheological and rheo-optical results for nonionic surfactant solutions at different concentrations and temperatures that do show clear evidence of such SIS formation. For example, in a 0.3% SPE 95285 solution at 5 °C, the shear viscosity, N, and flowbirefringence start from a low level and takes tens of seconds to grow to a high plateau region upon the application of a 100 shear. The re-application of the same shear after rest following a preshear indicates that the effect of the shear persists for a very long time (hundreds of seconds). These transient flow results resemble those exhibited by cationic surfactants or associating polymer solutions. The time needed for the viscosity and , to reach plateau values generally decrease with increasing shear rate and temperature. At moderate shear rates, the N and viscosity decrease monotonically with increasing temperature, whereas at low shear rate the viscosity increases with temperature up to the cloud point, and then decreases. The steady state and viscosity levels increase with the surfactant concentration. Both the transient and steady state behavior appear rather insensitive to the addition of contaminants.
41(1997); http://dx.doi.org/10.1122/1.550813View Description Hide Description
The viscosity measurements of four Carbopol solutions at various temperatures and concentrations show shear thinning effects. However, an unexpected viscosity-temperature behavior according to the concentrations of Carbopol solutions has been found. The viscosities of 3500 and 5000 wppm of Carbopol solutions decreased with increasing temperature. However, the viscosities of the 7500 and 10 000 wppm solutions increased with increasing temperature.