Browsing by Subject "Viscoelasticity"

Now showing 1 - 5 of 5
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    Atomization of Non-Newtonian Fluids by Counterflow Atomizer
    (2022-05) Band, Chinmayi
    The effects of shear-thinning non-Newtonian liquid on droplet diameter distributionsgenerated using a Counterflow atomizer were studied. Aqueous solutions of Sodium Carboxymethyl cellulose (SCMC) salt of 0.5%, 1%, 1.5% and 2% by weight were considered for experiments, with corresponding zero shear viscosity values of 13.8 mPas, 28.2 mPas, 508 mPas and 1280 mPas. Droplet diameters were measured using a Particle Digital Image Analysis technique combined with diffuse back illuminated shadowgraphs. Flow visualization in the near-field of the nozzle exit was used to gain insight into the flow patterns inside the nozzle near the exit plane, and to explain far-field droplet distribution statistics. Tree-like spray structure similar to effervescent atomization was observed for test solutions with higher weight concentrations. During secondary atomization, droplets connected with thin filaments were observed, indicating a probable existence of extensional stresses in the fluid. At lower concentrations of solutions, the spray emerged as a plume of droplets that are shed from a liquid film on the inner wall of the nozzle discharge tube, accompanied by a gas core. The variation of the Sauter Mean Diameter in the axial and radial directions indicated that the filaments in the near field are sheared by the gas flow, and undergo secondary atomization, leading to small droplet diameters and a more uniform distribution as we proceed downstream.
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    Cure induced stress generation and viscoelasticity in polymer coatings.
    (2010-01) O’Neal, Daniel Jeffrey
    Coatings solidified by free-radical polymerization and crosslinking (curing) reactions initiated with ultraviolet (UV) light do so quickly and at room temperature. Low viscosity monomer or oligiomer makes the use of volatile solvent unnecessary, decreasing energy use and making the process more environmentally friendly but photoinitiators can be toxic, limiting certain applications. Stress may be generated by a changing specific volume during cure, and stress-induced defects are undesirable. The goal of this research is to understand stress generation in UV irradiated coatings and to model stress generation and viscoelasticity seen during curing. Two new mathematical models were created to accomplish viscoelastic stress modeling. The first, a network model, uses a two-dimensional network of one-dimensional elements to replicate deformation in the coating. The second uses continuum momentum conservation and linear viscoelastic equations. Inertial forces can be neglected and a substitution performed, making the solution more rapid and simple with standard finite element methods. Stress generation in uniformly cured coatings depends on how quickly the specific volume and physical properties change. Reaction kinetics, volume, and stress are calculated simultaneously. Rapid initiation from high initiator concentration or UV light intensity delays volume change, generating more stress because the volume changes with a higher modulus. An optimum curing schedule would insure the actual specific volume and its equilibrium value remain the same. Inhomogeneities in the substrate or the presence of defects change the stress field. Knowing forces on the coating boundaries suggests defect locations and types. Probing the types of geometries and surface roughnesses seen in different types of coatings shows that restricted deformation increases stress concentrations and surface forces seen. Also, avenues for reducing stress via relaxation are discussed. The two-dimensional stress profiles used in these analyses are not possible to measure experimentally, making computational modeling essential. The models developed and methodology presented may be extended to other UV cured coatings or to other methods of coating solidification. Process windows of allowable final conversion-stress-energy-time states suggest what tradeoffs must be made to meet constraints.
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    Evaluation of local fields and effective behavior of viscoelastic heterogeneous materials
    (2010-07) Pyatigorets, Andrey V.
    The dissertation is concerned with the study of the mechanical time-dependent behavior of viscoelastic composite materials and structures. The analysis of such materials should not only take into account their complex structure, but also the time-varying properties of one or more constituents. The first part of the dissertation is concerned with the calculation of local time-varying fields in the viscoelastic fiber-reinforced composites and porous media. A two-dimensional model that represents a section perpendicular to the axes of the fibers is employed. The analysis adopts the correspondence principle based on the Laplace transform, and the problem is treated with the use of a direct boundary integral approach. The unknown boundary parameters are approximated by the truncated Fourier series. The procedures of the analytical (for the case of porous viscoelastic media) and numerical (for the case of fiber-reinforced composites) inversion of the Laplace transform are used to obtain time-varying fields anywhere in the matrix or inside the inclusions. The developed approach possesses several advantages in regard to computational efficiency and accuracy if compared with conventional methods based on the use of collocation and discretization techniques. The second part of the dissertation is concerned with the evaluation of the effective transverse properties of the viscoelastic fiber-reinforced composites. The developed approach relies on the knowledge of local stress fields and adopts the equivalent inhomogeneity technique modified for the case of viscoelastic composite's matrix. The solution is obtained in the Laplace domain, and the Laplace inversion is required to arrive at the time-varying effective properties. The developed approach directly takes into account the interactions between the inhomogeneities. The final part of the dissertation is dealing with the problem of thermal stress evolution in viscoelastic composite structures. These stresses are due to mismatch between the coefficients of thermal expansion of the composite's constituents. The proposed approach employs the Volterra correspondence principle and relies on the ability to obtain the analytical solution for the corresponding elastic problem. The approach adopts the discrete (matrix) representation of Volterra type operators. Particular attention is devoted to the analysis of thermal stress evolution in viscoelastic asphalt binders at low temperatures.
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    Mixed methods with weak symmetry for time dependent problems of elasticity and viscoelasticity.
    (2012-07) Lee, Jeonghun
    In this dissertation, we study numerical algorithms for time dependent problems in continuum mechanics using mixed finite element methods. We are particularly interested in linear elastodynamics and the Kelvin--Voigt, Maxwell, and generalized Zener models in linear viscoelasticity. We use mixed finite elements for elasticity with weak symmetry of stress, and show the a priori error analysis. A main contribution of our analysis is proving existence of a new elliptic projection map, called a weakly symmetric elliptic projection. In our analysis we prove that a priori error estimates for elastodynamics and viscoelasticity problems are as good as that of stationary elasticity problems. We present numerical results supporting our error analysis. We also present some basic numerical simulations which are more involved in physical situations.
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    Uniaxial Extensional Behavior of A–B–A Thermoplastic Elastomers: Structure-Properties Relationship and Modeling
    (2015-05) Martinetti, Luca
    At service temperatures, A–B–A thermoplastic elastomers (TPEs) behave similarly to filled (and often entangled) B-rich rubbers since B block ends are anchored on rigid A domains. Therefore, their viscoelastic behavior is largely dictated by chain mobility of the B block rather than by microstructural order. Relating the small- and large-strain response of undiluted A–B–A triblocks to molecular parameters is a prerequisite for designing associated TPE-based systems that can meet the desired linear and nonlinear rheological criteria. This dissertation was aimed at connecting the chemical and topological structure of A–B–A TPEs with their viscoelastic properties, both in the linear and in the nonlinear regime. Since extensional deformations are relevant for the processing and often the end-use applications of thermoplastic elastomers, the behavior was investigated predominantly in uniaxial extension. The conceptual basis of the theories underlying each topical area was explained while the emphasis was kept on fundamental principles and the molecular viewpoint. The analysis herein is independent from the specific choice of the constituent blocks and thus applies to any microphase-segregated thermoplastic elastomer of the A–B–A type. The unperturbed size of polymer coils is one of the most fundamental properties in polymer physics, affecting both the thermodynamics of macromolecules and their viscoelastic properties. Literature results on poly(D,L-lactide) (PLA) unperturbed chain dimensions, plateau modulus, and critical molar mass for entanglement effect in viscosity were reviewed and discussed in the framework of the coil packing model. Self-consistency between experimental estimates of melt chain dimensions and viscoelastic properties was discussed, and the scaling behaviors predicted by the coil packing model were identified. Contrary to the widespread belief that amorphous polylactide must be intrinsically stiff, the coil packing model and accurate experimental measurements undoubtedly support the flexible nature of PLA. The apparent brittleness of PLA in mechanical testing was attributed to a potentially severe physical aging occurring at room temperature and to the limited extensibility of the PLA tube statistical segment. The linear viscoelastic response of A–B–A TPEs was first examined at temperatures where the A domains are glassy. Characteristic length scales and tube model parameters were determined, and the role of the glassy A domains on the entangled rubbery B network was assessed. Thermo-rheological complexity, observed near and below Tg,A, was attributed to augmented motional freedom of the B block ends at the corresponding A/B interfaces, in harmony with the theoretical treatment of thermo-rheological complexity for two-phase materials developed by Fesko and Tschoegl. When the magnitude of the steepness index was taken into account, the shift behavior was analogous to the response measured for pure B melts. Building upon the procedure proposed by Ferry and co-workers for entangled and unfilled polymer melts, a new method was developed to extract the matrix monomeric friction coefficient ζ0 from the linear response behavior of a filled system in the rubber-glass transition region, and to estimate the size of Gaussian submolecules. Stress relaxation beyond the path equilibration time was found qualitatively and quantitatively compatible with dynamically undiluted arm retraction dynamics of entangled dangling structures (originating either from a fraction of triblock chains having one end residing outside A domains or from diblock impurities). By employing tube models and rubber elasticity theories, suitably modified to account for microphase-segregation, the linear elastic behavior across the rubbery plateau and up to the entanglement time was modeled, and a simple analytical expression relating the Langley trapping factor with the fraction of entangled and unentangled dangling structures of the material was obtained. The critical-gel-like behavior typical of A–B–A TPEs at service temperatures approaching Tg,A was analyzed in terms of a power-law distribution of relaxation times derived from the wedge distribution, shown to be equivalent to Chambon–Winter's critical gel model and to the mechanical behavior of a fractional element. A relation between the observed power-law exponent and molecular structure was established. The measured low-frequency response, originating from the incipient glass transition of the A domains, was exploited and extrapolated to lower frequencies via a sequential application of the fractional Maxwell model and the fractional Zener model. With only a few, physically meaningful material parameters a realistic description of the A–B–A self-similar relaxation was obtained over a frequency range much broader than the experimental window and not accessible via time-temperature superposition. The relationship between large-strain response and network structure of A–B–A triblocks was investigated, by examining (1) the effect of linear relaxation mechanisms on the tensile behavior, (2) the sources of elastic and viscoelastic nonlinearities, and (3) the strain rate dependence of the ultimate properties. Because of the numerous typos that appear in the original papers as well as in a recent Macromolecules review, a detailed analysis of the Edwards–Vilgis slip-link model was performed and the main steps leading to the determination of the chemical and topological contributions to the reduced stress were outlined. After establishing an operational definition of initial modulus for critical-gel-like materials subjected to start-up extensional tests, it was possible to determine the relationship between the dimensionless stress in tensile tests at constant strain rate and the step-strain extensional damping function. Based on the molecular picture of the strain-induced structural changes gained from exposing time and strain effects, the governing mechanism of rupture was identified with ductile/fragile rupture of A domains. To the best of our knowledge, this is the first experimental evidence linking the strain rate dependence of ultimate properties of triblock TPEs to the strain-induced glass-rubber transition of the domains. In addition, experimental results on the ultimate properties of A–B–A/B–A blends were consistent with this mechanism of rupture. For the first time in the literature, the complex high-dimensional rheological signature of chewing gum was analyzed, especially in response to nonlinear and unsteady deformations in both shear and extension. A unique rheological fingerprint was obtained that is sufficient to provide a new robust definition of chewing gum that is independent of specific molecular composition.