Barry Bernstein

Analysis of diffusion-induced bubble growth in viscoelastic liquids

Abstract Transport models of diffusion-induced bubble growth in viscoelastic liquids are developed and evaluated. A rigorous model is formulated that can be used to describe bubble growth or collapse in a non-linear viscoelastic fluid, and takes into account convective and diffusive mass transport as well as surface tension and inertial effects. Predictions for bubble growth dynamics demonstrating the importance of fluid elasticity are presented. These predictions indicate that for diffusion-induced bubble growth in viscoelastic liquids, the lower bound for growth rate is given by growth in a Newtonian fluid and the upper bound by diffusion-controlled growth. The influence of non-linear fluid rheology on bubble growth dynamics is examined and found to be relatively minor in comparison to fluid elasticity. It is shown how previously published models employing various approximations can be derived from the rigorous model. Comparisons of predicted bubble growth dynamics from the rigorous and approximate models are used to establish the ranges of applicability for two commonly-used approximations. These comparisons indicate that models using a thin boundary layer approximation have a rather limited range of applicability. An analysis of published experimental bubble growth data is also carried out using appropriate transport models.

Pulverization of rubber granulates using the solid state shear extrusion process. Part II. Powder characterization

Abstract Rubber powder obtained from the solid state shear extrusion (SSSE) process and the unprocessed rubber granulates were analyzed using physical, thermal, and chemical characterization methods. A portion of the granulates and two different size fractions of the powder produced by several passes of the rubber through the extruder were sampled by sieves and then characterized. Particle size distribution of the samples was determined using a laser diffraction technique. The shape of the particles was observed with an optical microscope, and the details of the particle surfaces were visualized using a scanning electron microscope. The total surface area was obtained using a BET method. Thermal analysis techniques were used to determine the composition, thermal, and thermo-oxidative degradation characteristics. The cross-link density and gel fraction of the rubber were determined using swelling and Soxhlet extraction methods, respectively. The microscopy study revealed that the particles generally had irregular shapes with rough surfaces, whereas the granulates had angular shapes with smooth surfaces. The larger particles produced by the SSSE process were mainly agglomerates of smaller particles. The total and external surface areas of the particles produced by the SSSE process were significantly greater than those of a cryogenically ground rubber of a similar size range. The extent of thermo-oxidation depended on the external and total surface areas of the samples. However, characteristic temperatures and kinetic parameters of the thermal degradation in the nitrogen environment were not affected by the size or surface area. The composition of the granulates was the same as that of the particles. However, the cross-link density and gel fraction of the rubber particles were smaller than those of the granulates suggesting the cleavage of chemical bonds due to the high mechanical stresses and possible oxidation during the SSSE process. The particle agglomeration during the reprocessing was instrumental in the alteration of the rubber properties.

Pulverization of rubber granulates using the solid-state shear extrusion (SSSE) process:: Part I. Process concepts and characteristics

A single screw extruder was used to pulverize rubber granulates at high shear and compression without using cryogenic fluid for cooling. This process, solid-state shear extrusion (SSSE), is based on the large compressive shear deformation of rubber granulates, which results in the storage of a large amount of strain energy and the formation of cracks. When the stored energy reaches a critical level, the granulate cannot sustain itself. As a result, the stored elastic energy is converted into surface energy through the formation of new surfaces and, in turn, pulverization occurs. The stored elastic energy is dependent on the viscoelastic response of rubber granulates to the processing condition. The independent variables of the process were identified as the degree of compression of the rubber, number of extruder passes, barrel wall temperatures, rotation rate of the extruder screw, and feed rate of the granulates. The effects of these variables on the dependent variables, such as material and screw temperatures, particle size distribution (PSD), torque, and mechanical power consumption at steady state, were systematically studied. Fine rubber particles were obtained when the granulates were compressed sufficiently, and loss of strain energy due to viscoelastic stress relaxation was minimized by significant cooling in the pulverization zone. Agglomeration of rubber particles was found to be competing with the pulverization process.

A New Recycling Technology: Compression Molding of Pulverized Rubber Waste in the Absence of Virgin Rubber

Recycling of rubber waste poses a challenging environmental, economical, and social problem. In the present study, we propose a new two-stage recycling process to reuse a rubber waste. First, the granulates of the waste were pulverized into small particles using a single screw extruder in the Solid State Shear Extrusion (SSSE) process. Then, the produced powder was compression molded in the absence of virgin rubber. The slabs prepared at various molding conditions were subjected to mechanical, chemical, and microscopic tests. It is found that the slabs have high extensibility with low-medium tensile strength. Compressive creep of the powder, self-adhesion of rubber molecules, and interchange reactions of polysulfidic crosslinks are proposed as the basis of particle bonding.

Steady flows of viscoelastic fluids in axisymmetric abrupt contraction geometry: A comparison of numerical results

Recently two groups of researchers have reported numerical results simulating the steady flow of a KBKZ fluid in torsion free axisymmetric abrupt contraction geometry. The fluid model used in both cases was a constitutive equation chosen to match laboratory behavior of LDPE. In both cases, quadratic finite elements were used. Large corner vortices were observed in the simulations, similar to those observed in laboratory experiments. The agreement between the results in the two papers is good. We repeat the experiment, using linear finite elements. Tracking is performed via an artificial time method, and a novel ‘‘reduced velocity’’ variable is used in our finite element simulation. There is good qualitative and quantitative agreement between the results reported here and the results previously reported by others. Quantitative measures used in the comparison—vortex opening angle, Couette correction, and vortex intensity—are analyzed.

Flow of a curtiss-bird fluid over a transverse slot using the finite element drift-function method

Abstract A finite element method for incompressible flows of a memory fluid is described which is based on macroelements of crossed linear triangels. This allows virtually exact computations of strains in trial velocity fields. Memory is handled by construction of special Gaussian quadrature formulas. The problem of plane flows over slots is studied numerically using the reptational constitutive equation proposed by Curtiss and Bird. With this constitutive equation and an improved nonlinear iteration scheme, convergence difficulties which plagued earlier attempts at modelling viscoelastic flow seem to be avoided. Particular attention is paid to the relationship between first normal-stress difference and pressure difference across the slot as a function of Deborah and Reynolds number. The model predicts that there is a strong correlation between hole-pressure and first normal-stress difference if the inertial contribution to the hole-pressure is accounted for. Nevertheless the correlation differs to some extent from the Higashitani-Pritchard prediction. In our model this is traceable to specific violations of Higashitani and Pritchards assumptions related to fluid-memory effects.

Analysis of rubber particles produced by the solid state shear extrusion pulverization process

Abstract Vulcanized natural rubber was pulverized using a single screw extruder in a non-cryogenic Solid State Shear Extrusion (SSSE) process where rubber granulates were subjected to high compressive and shear stresses. The produced particles had diameters ranging from 40 to 1700 µm. Reprocessing of the produced powder resulted in a narrower particle size distribution. Considerable heat generated in the extruder due to friction caused surface oxidation of the fine rubber particles and, in turn, initiation of agglomeration of a portion of the produced particles. Physical, chemical, and thermal analyses were performed on the produced rubber particles and the rubber granulates to determine the effects of the pulverization process. The produced particles had irregular shapes with rough surfaces. The external surfaces of the particles were porous, but no microporosity was detected by nitrogen BET analysis. Swelling and extraction experiments showed that both the crosslink density and gel fraction of the parti...

Small shearing oscillations superposed on large steady shear of the BKZ fluid

Abstract This is a theoretical discussion of methods which could be used to determine, according to the BKZ elastic fluid theory, the shearing stress and normal stress responses of a non-Newtonian fluid to simple shearing histories for which the rate of shear varies arbitrarily with time. In order to do this for any given fluid, certain information is needed about the fluid. It is shown how this information could be obtained if one knew merely the shearing stress responses to simple shearing motions of any one of the following types; stress relaxation, suddenly imposed steady shear, or small oscillations superposed on steady shearing flow. For each such type of flow some rheological relations are derived. These are relations between directly measurable quantities and do not involve material properties, but hold only for given classes of motions. It is also shown how, according to the BKZ perfect elastic fluid theory, a change in temperature affects the results. Thence it is argued how a variation in temperature could be used to supplement data obtained when the range of mechanical parameters is limited.

Effect of material non-homogeneity on the inhomogeneous shearing deformation of a Gent slab subjected to a temperature gradient

Abstract It is well known that most rubber-like materials are non-homogeneous due to either imperfect manufacturing conditions or the action of severe thermo-oxidative environments in many practical applications. In this study, within the context of finite thermoelasticity, we theoretically analyze the inhomogeneous shearing deformation of a non-homogeneous rubber-like slab subjected to a thermal gradient across its thickness. The major objective of this study is to investigate the effect of the material non-homogeneity, which is the material-coordinate dependence of the material response functions, on the stress–strain fields for a given temperature gradient. First, we show the existence of a simple shearing deformation from which the generalized shear modulus and the generalized thermal conductivity of the slab could be obtained. Based on this information, the Gent material model is generalized to take the material non-homogeneity and the temperature dependence of the stress into account. To analyze the inhomogeneous shearing deformation of the non-homogeneous slab, deformation and temperature fields are postulated; then the decoupled temperature field is obtained analytically by solving the local energy balance equation. Finally, the static equilibrium equations are solved considering the linear temperature field. Our results show that the spatial pattern and the degree of the material non-homogeneity have profound effects on the stress–strain fields. The shear strain becomes nearly homogeneous and the stresses are relatively small for a certain spatial variation of the material non-homogeneity. This result suggests the possibility of designing a novel class of materials: functionally graded rubber-elastic materials (FGREMs).

Pulverization of rubber under high compression and shear

Non-cryogenic pulverization of rubber material was obtained under high compression and shear using a modified Bridgman Anvil apparatus. The effects of operating variables, such as temperature, normal and shear forces, shear rate, and residence time were examined, and optimum conditions for obtaining desired particle size distribution with minimum agglomeration were identified. Based on our strain energy storage theory, a criterion of pulverization was obtained and computational analysis of deformation of rubber using a Mooney-type equation for stored energy was performed. The numerical values for strain energy distribution in a rubber disk, which indicate potential pulverization under different compression and shear forces, were obtained using the ANSYS computer program. This information was used as a guide to obtain optimum operating conditions and design parameters for optimum design of the solid state shear extrusion (SSSE) pulverization process [H. Arastoopour, Single Screw Extruder for Solid State Shear Extrusion Pulverization, U.S. Patent No. 8,101,468 (1998)].