Showing papers in "Journal of Rheology in 1978"
TL;DR: In this paper, a nonlinear constitutive equation for polymer melts and concentrated solutions is derived from a Lodge-Yamamoto type of network theory, where the network junctions are postulated to move nonaffinely in a well-defined manner.
Abstract: A nonlinear constitutive equation for polymer melts and concentrated solutions is derived from a Lodge‐Yamamoto type of network theory. The network junctions are postulated to move nonaffinely in a well‐defined manner. The functional form of the creation and destruction rates of junctions is assumed to depend on the average extension of the network strand and the absolute temperature in such a way to allow for the time‐temperature superposition principle. The theory shows good agreement with all data examined. The paper concludes with a strong flow problem (melt spinning). The results indicate the validity of the model in this flow regime.
487 citations
TL;DR: It is speculated the conformation of xanthan in solution is rodlike, having some flexibility, and intrinsic viscosity data are modeled as a suspension of rods and found to be in agreement with existing theory.
Abstract: Rheology of aqueous solutions of xanthan gum was studied over a wide range of shear rate and concentration. At sufficient dilution and low shear rates xanthan solutions show a region of Newtonian viscosity behavior. More concentrated solutions appear to show a yield stress. These results with preliminary normal stress data and effects of salt concentration are discussed in terms of the structure of this polysaccharide in solution. Intrinsic viscosity data are modeled as a suspension of rods and found to be in agreement with existing theory. We speculate the conformation of xanthan in solution is rodlike, having some flexibility. A hydrodynamic length near 1.5 μm is estimated, assuming a diameter of 19 A.
225 citations
TL;DR: In this paper, shear viscosity, shear flow normal stresses, and elongational viscosities have been investigated for glass-fiber-filled high-density polyethylene and polystyrene melts.
Abstract: Shear viscosity, shear flow normal stresses, and elongational viscosity have been investigated for glass‐fiber‐filled high‐density polyethylene and polystyrene melts. Viscosity measurements are consistent in cone‐plate and capillary instruments Normal stress coefficients increase more rapidly with glass fiber content than the shear viscosity, especially at low deformation rates. Elongational viscosities are very high at low elongation rates but decrease rapidly with increasing deformation rate. Mechanisms are proposed to explain these observations.
161 citations
TL;DR: A transparent channel was constructed of Plexiglas and droplets of known volume were injected into the reservoir upstream of the channel, through which a suspending medium (i.e., continuous phase) was pumped at a constant flow rate.
Abstract: A transparent channel was constructed of Plexiglas and droplets of known volume were injected into the reservoir upstream of the channel, through which a suspending medium (i.e., continuous phase) was pumped at a constant flow rate. The deformation patterns of the droplets were recorded on still and movie films as they approached the die entrance and passed through the fully developed region of the channel. The suspending fluids were glycerin as Newtonian medium, and aqueous solutions of polyacrylamide (Separan AP30) at various concentrations (0.6, 2.0, 4.0, and 6.0 wt %) as viscoelastic medium. Droplets were formed of both viscoelastic and Newtonian fluids. For the viscoelastic droplets, polyisobutylene dissolved in decalin (0.6, 2.0, 6.0, and 10.0 wt %) was used, and for Newtonian droplets, low molecular weight polybutene (Indopols L50 and H25) was used. It was observed that at wall shear rates of a suspending medium below a certain critical value, the droplets, initially spherical when upstream in the ...
86 citations
TL;DR: In this paper, a wide gap viscometer is used to model non-Newtonian fluids and several approximate methods for calculating on the first derivative of the power law exponent are compared.
Abstract: Several of the more powerful approximate methods for calculating on the first derivative of the power‐law exponent are appreciably more shear rates for non‐Newtonian fluids in coaxial viscometers are compared. Each is applied to model fluids representing the two most common types of non‐Newtonian behavior, in a wide‐gap viscometer. Results with the power law are moderately accurate (ca. 1%) for fluids which do not display yield stresses, but much less accurate for those which do. Methods based on the first derivative of the power‐law exponent are appreciably more accurate, but a second‐derivative term may be needed for fluids which show yield stresses.
74 citations
TL;DR: In this article, the rheological behavior of PVC emulsion resin plastisols was investigated in steady shear flow and the shear rate dependence of the plastisol viscosity was influenced by Brownian diffusion, partial dissolution of the suspended resin, and particle-particle interactions.
Abstract: The rheological behavior of PVC emulsion resin plastisols was investigated in steady shear flow. The shear rate dependence of the plastisol viscosity was influenced by (1) Brownian diffusion, (2) partial dissolution of the suspended resin, and (3) particle‐particle interactions. Partial dissolution of polymer from the resin particle surface resulted in a particle‐size‐dependent increase in the continuous phase viscosity. At a disperse phase volume fraction of φ=0.02 a non‐Newtonian master curve was obtained for the relative viscosity of several plastisol systems as a function of Peclet number, independent of plasticizer or particle radius. These plastisols behaved (at φ=0.20) as suspensions of rigid spheres subject to Brownian motion. The magnitude of the deviation from Newtonian behavior appeared to be influenced also by the strength of particle‐particle interactions. Viscoelastic response was observed in concentrated plastisols. At φ=0.54 relaxation time versus shear rate was found to be independent of ...
58 citations
TL;DR: In this article, a multiple integral expansion of the Boltzmann superposition principle was applied to sinusoidal shear oscillations with hollow cylinders of polycarbonate and polymethylmethacrylate at 1 Hz from Tg to below their β transitions.
Abstract: A multiple integral expansion of the Boltzmann superposition principle when applied to sinusoidal shear oscillations becomes σ(t)=γ0[G1′ sinωt+G1″ cosωt]+γ03[G3′ sinωt+H3′ sin3ωt+G3″ cosωt+H3″ cos3ωt]+γ05[0]. We have evaluated this constitutive equation with hollow cylinders of polycarbonate and polymethylmethacrylate at 1 Hz from Tg to below their β transitions. Shear strain amplitude, γ0, was increased incrementally from the linear to the nonlinear region. Phase angles and harmonic content were determined with a Rheophasor digital cross correlator. At the maximum strain used, 2–4%, deformation was completely recoverable, after some time, upon returning to the linear region. G1′ and G1″ vs temperature compare excellently to the literature and our own small strain measurements of G′ and G″ on rectangular bars in free and forced torsion. H3′, H3″, and higher harmonic terms were found to be small. All nonlinearity in the range studied can be modeled by G3′ and G3″ is in the range 1010–1011 N/m2. G3′ is nega...
56 citations
41 citations
TL;DR: In this paper, the nonlinear n-measure of strain into the Boltzmann superposition integral allows accurate prediction of the viscoelastic behavior of soft (rubberlike) materials if the relaxation spectrum remains unchanged during the deformation.
Abstract: Introduction of the nonlinear n‐measure of strain into the Boltzmann superposition integral allows accurate prediction of the viscoelastic behavior of soft (rubberlike) materials if the relaxation spectrum remains unchanged during the deformation. This condition is generally satisfied in moderately large deformations (typically about 150% strain in simple tension). Apart from the strain parameter n, only the small deformation relaxation modulus is required by the theory. Both pieces of information are obtained from the response to a step of strain in simple tension. Data obtained in the temperature range −40 to 23°C on a dicumyl‐peroxide‐cured styrene‐butadiene rubber (SBR), lightly plasticized with silicone oil (1.5%), gave excellent agreement with the theory in various strain histories including sensitive tests in which small deformations were superposed on a finite stretch. Published data were used to corroborate the theory further. The temperature dependence of n was obtained from the authors' data on SBR and from published data on Viton A‐HV. The dependence of n on crosslink density and swelling ratio was also examined.
38 citations
TL;DR: In this paper, the nonlinear viscoelastic behavior of colloidal systems is studied experimentally and the applicability of a modified bead-spring model where the springs can be reversibly broken down is considered.
Abstract: The nonlinear viscoelastic behavior of colloidal systems is studied experimentally. Model systems are used that consist of carbon black particles, dispersed in mineral oil. The experimental techniques include dynamic measurements, steady state shear viscosity and normal force, parallel superposition, and nonlinear relaxation. The data are expressed in rate‐dependent spectra. The effect of shear on the spectra is compared with available results for polymeric systems. After cessation of flow a thixotropic recovery takes place in the dispersions. This recovery has been followed by measuring the changing relaxation spectrum. The effect of shear and time on the spectrum is discussed in terms of the variable, colloidal structure. The applicability of a modified bead‐spring model where the springs can be reversibly broken down is considered.
34 citations
TL;DR: In this article, the process of extracting time constants from shear-viscosity data was investigated, and it was found that the three and four-parameter models, while providing excellent fits to the data, did not provide time constants with as low an expected error as the better two-dimensional models.
Abstract: The process of extracting time constants from shear‐viscosity data was investigated. Fourteen viscosity functions were fitted to 12 diverse sets of experimental data using a Gauss‐Newton optimization technique. It was found that the three‐ and four‐parameter models, while providing excellent fits to the data, did not provide time constants with as low an expected error as the better two‐parameter models. An analysis of the sensitivity of the error in the time constant to error in the viscosity data showed that regions at very low shear rate and at shear rates near the reciprocal of the time constant were critical. Time constants from shear‐viscosity data for a set of low‐density polyethylenes correlated well with Rouse times based on the weight average molecular weight.
TL;DR: In this paper, a summary of theoretical predictions of tensile stress in suspensions of oriented rigid fibers in nonlinear materials exhibiting fluid-like power law shear behavior is given, compared with experimental creep data of Street (1971) for a lead matrix containing phosphor-bronze fibers, and also with extensional flow data of Chan et al. (1977) for polymer melts containing chopped glass fibers.
Abstract: A summary is given of certain theoretical predictions of the tensile stress in suspensions of oriented rigid fibers in nonlinear materials exhibiting fluidlike power law shear behavior. The theory is compared with experimental creep data of Street (1971) for a lead matrix containing phosphor‐bronze fibers, and also with the extensional flow data of Chan et al. (1977) for polymer melts containing chopped glass fibers. In the first instance, the agreement is satisfactory, whereas in the latter it is only qualitative, suggesting a need for further work.
TL;DR: In this paper, it was shown that the characteristic time necessary for these dimensionless groups may be obtained from the Carreau model B. The model time constants λ 1 and λ 2 are found to decrease with the concentration dependence of these parameters.
Abstract: It has been suggested that an extra dimensionless group such as the Weissenberg or the Deborah number is necessary to correlate the drag and heat transfer reductions of very dilute polymer solutions in turbulent flows. It is demonstrated in this study that the characteristic time necessary for these dimensionless groups may be obtained from the Carreau model B. To achieve this, rheological properties of nine concentrations (0.012–2.0% by weight) of aqueous polyacrylamide solutions (Separan AP‐273) were measured with the Weissenberg rheogoniometer (WRG). The measurements include the shear viscosity, the primary normal stress difference, the dynamic viscosity, and storage modulus. Parameters of the Carreau model B were then determined by simultaneously fitting all the experimental data. It is shown that the model adequately describes the experimental data and also that it is possible to establish the concentration dependence of these parameters. The model time constants λ1 and λ2 are found to decrease with ...
TL;DR: In this paper, the crosslinked particles were prepared by adding divinyl benzene in the emulsion-polymerization recipe, with the exception of the difunctional monomer.
Abstract: It is a common industrial practice to incorporate crosslinked polymer particles into raw elastomers. This results in decreased time and energy of mixing with carbon black. In the system studied, the gel is in the form of discrete particles in contrast to gels formed in bulk. Samples were butadiene‐acrylonitrile copolymer containing 33% acrylonitrile. The crosslinked particles were prepared by adding divinyl benzene in the emulsion‐polymerization recipe. With the exception of the difunctional monomer, the crosslinked particles and the noncrosslinked rubber were prepared in the same manner. The two latices were blended in different proportions. Gel contents of 100, 75, 50, 25, and 0% were examined. The flow behavior of these materials was examined with a capillary rheometer at 70, 100, and 125°C for the shear rate range of 3–3000 sec−1. In the shear rate range studied, the viscosity decreased with increasing gel content. This is contrary to the cases where crosslinking is formed in the bulk, where the visco...
TL;DR: In this paper, the authors review the state of existing knowledge concerning the linear viscoelastic properties of liquids, with particular reference to experiments on rolling contacts under conditions of elastohydrodynamic lubrication.
Abstract: It is now well established from experimental work on rolling contacts under conditions of elastohydrodynamic lubrication that the lubricant does not behave as a simple highly viscous liquid. Conflicting explanations have been put forward to explain how the observed effects are related to the properties of the lubricant at the high pressures and short contact times encountered under conditions where the elastic deformation of the contact surfaces is significant in comparison with the thickness of the film of lubricant. The majority of these approaches treat the lubricant as a viscoelastic material. Detailed knowledge of the properties which the lubricating fluid exhibits in shear and compression over wide ranges of time scale, pressure, and temperature is therefore essential for a clearer understanding of elastohydrodynamic lubrication. The purpose of this paper is to review the state of existing knowledge concerning the linear viscoelastic properties of liquids, with particular reference to experiments wh...
TL;DR: In this paper, steady-state solutions for the isothermal melt spinning of Newtonian, power-law, and Maxwell fluids have been obtained with respect to both the Lagrangian coordinate (threadline residence time) and the Eulerian coordinate(threadline spinning distance) to demonstrate the utility of the two coordinate systems in revealing different characteristics of the spinning process.
Abstract: Analytic steady‐state solutions for the isothermal melt spinning of Newtonian, power‐law, and Maxwell fluids have been obtained with respect to both the Lagrangian coordinate (threadline residence time) and the Eulerian coordinate (threadline spinning distance) to demonstrate the utility of the two coordinate systems in revealing different characteristics of the spinning process. Some of the findings for Maxwell fluids are as follows. The effect of the relaxation time of Maxwell fluids on the threadline deformation rate curve is quite dramatic in that, as the relaxation time is increased, the shape of the deformation rate curve is changed from concave upward to convex upward in both the Eulerian and Lagrangian representations. The Eulerian profiles agree quite well with the experimental results by Weinberger et al. [AIChE J., 22, 441–448 (1976)]. The threadline stress, divided by its corresponding Newtonian stress, exhibits a maximum in the Eulerian plots, whereas the same stress ratio monotonically increases with the Lagrangian coordinate. This Lagrangian plot of the stress ratio can be viewed as the constant force stretching analog to the constant rate stretching case derived by Denn and Marrucci [AIChE J., 17(1), 101 (1971)].
TL;DR: In this article, the viscosity and first normal stress difference functions were determined using a Weissenberg rheogoniometer over a shear rate range of approximately 10−2−1500'sec−1.
Abstract: Viscous and elastic rheological properties of three very dilute solutions (100 to 500 parts per million) of a polyacrylamide in distilled water which exhibit drag reduction in turbulent flow were determined. Apparent viscosity and first normal stress difference functions were determined using a Weissenberg rheogoniometer over a shear rate range of approximately 10−2–1500 sec−1. In addition, transient response characteristics were determined using a specially designed transient rheometer modified for increased resolution. A relatively simple five‐parameter nonlinear integral constitutive equation which was consistent with all steady and unsteady measurements was used to correlate the data. For comparison, Carreau's seven‐parameter model B, which has previously been found to be appropriate for such solutions, was also evaluated for its ability to represent the observed data. Although capable of a precise representation of the steady shear and normal stress data, this model is incapable of qualitative repres...
TL;DR: In this article, the authors modify the form of the previous constitutive equations slightly in order to extend the validity of the theory to the rubber region in which the medium behaves elastically.
Abstract: A nonisothermal theory of viscoelastic media, motivated by thermomechanical behaviour of polymeric materials in the transition zone between the rubber and glassy states, was developed previously by Crochet and Naghdi (1974) and included as a special case a theory with small deformation suitable for thermorheologically simple materials. The object of the present paper is to modify the form of the previous constitutive equations slightly in order to extend the validity of the theory to the rubber region in which the medium behaves elastically.
TL;DR: In this article, the Regularization-Quadratic Programming (RQP) method is used to circumvent the inherent illposedness of integral equations of the first kind found in the theory of linear viscoelasticity.
Abstract: The Regularization‐Quadratic Programming (RQP) method is used to circumvent the inherent ill‐posedness of integral equations of the first kind found in the theory of linear viscoelasticity. The ability of this method to detect sharp “cutoffs” in a relaxation spectrum is investigated. Finally, the method is applied to standard master curve polyisobutylene data in order to substantiate the ability to reliably predict sharp boundaries and the overall spectrum shape. The results are very encouraging since no prior assumptions were made as to the functional shape of the sought‐after relaxation spectrum.
TL;DR: In this paper, a fixture consisting of a bob and a special cup was developed to ease the charging of polymer melt to the gap of a concentric cylinder rheometer.
Abstract: A fixture consisting of a bob and a special cup was developed to ease the charging of polymer melt to the gap of a concentric‐cylinder rheometer Dynamic measurements with the improved rheometer for two polyolefins below melt temperatures were compared with results obtained on the Rheovibron and the torsion pendulum Shear moduli were generated for polypropylene, polyethylene,and poly(vinyl chloride) melts by oscillating the bob in the axial mode at amplitudes effecting relatively large strain Bob oscillations in the rotational mode were also investigated The phase angles and complex shear moduli differed slightly for different modes of oscillation At strains of 9%, the time‐temperature shift factor αT remained constant throughout the test‐frequency range for an isotactic polypropylene However, αT increased with increasing frequency for strains of 98% A time‐strain shift factor, αe, was found to satisfactorily superimpose polypropylene moduli data generated at high and low strain levels
TL;DR: In this article, the flow behavior of both highly flocculated and dispersed kaolin suspensions has been studied using a capillary tube viscometer and two horizontal pipeline test loops, which enabled wall shear rates to be varied from 30 to 11,000
Abstract: The flow behavior of both highly flocculated and dispersed kaolin suspensions has been studied using a capillary tube viscometer and two horizontal pipeline test loops. These facilities enabled wall shear rates to be varied from 30 to 11,000 sec−1. Experiments were carried out in which volumetric solids concentrations ranged from 8.6 to 23.4% for the flocculated suspensions, and from 23.4 to 38.7% for the dispersed suspensions. Over the shear rate range 30–1000 sec−1, the rheograms for laminar flow of the flocculated suspensions followed the Ostwald‐de Waele power law model, while for the higher shear rate range 2000–11,000 sec−1, the Bingham plastic model fitted slightly better. Since the high shear rate range was obtained using the capillary tube viscometer, it was concluded that great care must be exercised when scaling up from capillary tube data to pipeline installations, in which the wall shear rate rarely exceeds 500 sec−1. The dispersed kaolin suspensions were essentially Newtonian, but at the highest solids concentration a measurable degree of shear‐thickening behavior was observed. Results for turbulent flow of the flocculated material are in good agreement with those obtained for similar systems by Kemblowski and Kolodziejski (1973), who have already shown that Dodge and Metzner's equation (1959) for the friction factor of a power law material is not applicable.
TL;DR: In this article, a thin-walled tube of low-density polyethylene in torsion during increasing and decreasing temperature was reported, and it was shown that creep was dependent on temperature history.
Abstract: Nonlinear creep of a thin‐walled tube of low‐density polyethylene in torsion during increasing and decreasing temperature is reported. This material was selected after verifying that its thermal expansion was stable. Results showed that creep was dependent on temperature history for both increasing and decreasing temperature. Nonlinear creep was described reasonably well by employing the Morland‐Lee reduced time variable, together with a master creep curve. The master curve for a given stress was constructed from creep at different temperatures by horizontal shifts along the time axis. The temperature‐history independence of creep during rising temperature previously reported for polyurethane is attributed to changes in moisture content.
TL;DR: In this paper, the shape of the Fano column profile was best fit by the equation Di/D=C1/exp(C2z/L), where C1 and C2 are constants, Di is the inside diameter of Fano nozzle, L is the total height of the column, and D is the diameter of column at height z.
Abstract: A device for producing a Fano extensional flow with a total pressure drop of more than 1 atm has been designed and tested with Newtonian fluids. It was found that the shape of the Fano column profile was best fit by the equation Di/D=C1 exp(C2z/L), where C1 and C2 are constants, Di is the inside diameter of the Fano nozzle, L is the total height of the column, and D is the diameter of the column at height z. Extensional viscosity calculations for glycerine Fano columns produced values equal to approximately three times the shear viscosity.
TL;DR: In this article, a visual study of the dynamics of screw extrusion was undertaken by using a 1-in. diameter (L/D=20) extruder with a transparent barrel, where the extrudate consisted of frozen pellets of a 40% solution of polystyrene in diethylphthalate plasticizer.
Abstract: A visual study of the dynamics of plasticating screw extrusion was undertaken by using a 1‐in.‐diameter (L/D=20) extruder with a transparent barrel. The extrudate consisted of frozen pellets of a 40% solution of polystyrene in diethylphthalate plasticizer. Blue and red colored pellets of the same material were added in ratios of 1:120 and 1:40, respectively. This was done in order to mark the flow of material in the screw channel. The flow was recorded on color movie film taken at both 15 and 90 frames/sec. Films of the unsteady state as well as of the steady state, flow were obtained. Unsteady conditions in the flow were induced by introducing step changes in screw speed which were in the range of 60–75 rpm. Analysis of the steady state films revealed that the steady melting mechanism, as described by past workers, is valid. Under transient conditions involving a step‐up in screw speed, a rupture in the solid bed occurred. This phenomenon was related to the rheological characteristics of the viscoelastic liquid extrudate. It was hypothesized that this occurred because of a difference in the response times of the liquid polymer at various points along the screw axis. Variation in liquid polymer temperature was assumed to result from the near adiabatic mode of extruder operation employed, which in turn gave rise to the large differences in the liquid response time. Solid bed profiles of the extrudate in the melting zone under transient conditions were also constructed from the films. These profiles showed departures of the flow regime from that under steady state conditions. Defects in the solid bed were seen to propagate in the screw down‐channel direction. Those defects undoubtedly contributed to fluctuations in the flow rate and to the lack of good mixing observed in the product.
TL;DR: In this article, boundary and centerline injection of long hairlike fibers has been investigated to reduce the drag in turbulent pipe flow by means of boundary and centreline injection, and the results show that the reduction in the momentum transfer ability of the suspensions in the turbulent core can be attributed to a reduction of the velocity of the fibers.
Abstract: Drag reduction in turbulent pipe flow by means of boundary and centerline injection of long hairlike fibers has been investigated. Experiments have been conducted at various main flow Reynolds numbers as well as at various injection rates of the fiber suspensions. The occurrence of drag reduction was observed even with a trace quantity of the fibers. Comparison of the two modes of fiber injection indicates that elongated fibrous elements are more effective as drag reducers when they are present in the outer region of the turbulent core. Measurements of the mean velocity profiles with both modes of injection indicate that the drag reduction can be attributed to a reduction in the momentum transfer ability of the suspensions in the turbulent core.
TL;DR: In this paper, an anomalous styrene-butadiene rubber (SBR) was studied and it was shown that nonpreservation of time shift invariance is not linked with stress-strain nonlinearity.
Abstract: Emulsion polymerized compression molded dicumyl‐peroxide‐cured SBR does not obey Boltzmann's principle for the superposition of time effects at very small strains at which the true stress‐strain relation is linear. Normally, nonpreservation of time shift invariance is linked with stress‐strain nonlinearity. In this anomalous styrene‐butadiene rubber (SBR) the former effect can be studied independently of the latter.
TL;DR: In this paper, pigmented tracer elements, placed at precise locations in the tube, illustrated flow patterns which were recorded on 16 mm movie film and the diagonal components of the rate-of-deformation tensor were computed at several different positions in the flow channel.
Abstract: Velocity field rearrangement in tube flow followed by stagnation flow and diverging radial flow between parallel plates has been investigated with a polypropylene melt and composites of solid glass beads in a polypropylene melt. The tube axis was aligned normal to the parallel plates, creating a stagnation flow at the inlet to the diverging flow channel. Pigmented tracer elements, placed at precise locations in the tube, illustrated flow patterns which were recorded on 16 mm movie film. After an analysis of the film, the diagonal components of the rate‐of‐deformation tensor were computed at several different positions in the flow channel. From the sign and relative magnitude of the diagonal components the basic types of extensional flow were identified. The flow behavior of the polypropylene and the bead‐filled polypropylene in the complex channels is essentially the same despite large differences in the rheological and physical properties of the composites. Although the tracer technique needs to be refin...
TL;DR: In this article, the authors measured flow rates of gases, liquids, suspensions, and particulate solids through right cylindrical capillaries (microopenings) having diameters from 0.5 to 60 μm and lengths in the range of 100-4000 diameter.
Abstract: Fluid flow rates of gases, liquids, suspensions, and particulate solids were measured through right cylindrical capillaries (microopenings) having diameters from 0.5 to 60 μm and lengths in the range of 100–4000 diameter. The results showed that gases passing through microopenings with diameters from 5 through 60 μm and lengths of 100 times the diameter or more obey Darcy's Equation. For microopenings with diameters from 0.6 to 1.7 μm and lengths of at least 200 times the diameter, the measured flow rates of gases exceed those predicted by the Darcy Equation by a factor of approximately three. Water and low‐viscosity aqueous solutions flowing in 1 μm diameter or larger microopenings having lengths of at least 100 diameter appeared generally to follow Poiseuille's Law, although at low pressure drops in the smaller sizes, the flow rates suddenly became considerably lower than those predicted. Polystyrene latex suspensions flowing in microopenings from 25 through 50 μm in diameter flowed as predicted by the ...
TL;DR: In this article, the authors considered the problem of determining the relaxation functions of a linear viscoelastic material over an extended time domain using data other than those from step response, and applied the Lagrange-type multipliers to derive the relaxation function of low-density polyethylene.
Abstract: The problem of determining the relaxation functions of a linear viscoelastic material over an extended time domain using data other than those from step response is considered. It is assumed that two or more longitudinal stress, longitudinal strain, and transverse strain data history triples are available for use in this determination. It is further assumed that the durations of all triples are related progressively by the same multiplicative parameter. Instabilities which arise in the normal form inversion scheme are countered by minimizing a curvature functional while constraining the matrix system to a maximum squared error through a matrix of Lagrange‐type multipliers. The technique is applied to the constitutive characterization of a commercial grade, low‐density polyethylene using five data history triples. These data histories are sinusoidal in character with periods ranging from 0.002 to 20.0 hr in multiples of 10. Owing to the nearly incompressible nature of low‐density polyethylene, attempts at ...