Mathematical and numerical analysis of a simplified time-dependent viscoelastic flow

A time-dependent model corresponding to an Oldroyd-B viscoelastic fluid is considered, the convective terms being disregarded. Global existence in time is proved in Banach spaces provided the data are small enough, using the implicit function theorem and a maximum regularity property for a three fields Stokes problem. A finite element discretization in space is then proposed. Existence of the numerical solution is proved for small data, so as a priori error estimates, using again an implicit function theorem. Supported by the Swiss National Science Foundation. Fellowship PBEL2–114311.     

Leray–Hopf solutions to a viscoelastoplastic fluid model with nonsmooth stress–strain relation

We consider a fluid model including viscoelastic and viscoplastic effects. The state is given by the fluid velocity and an internal stress tensor that is transported along the flow with the Zaremba–Jaumann derivative. Moreover, the stress tensor obeys a nonlinear and nonsmooth dissipation law as well as stress diffusion. We prove the existence of global-in-time weak solutions satisfying an energy inequality under general Dirichlet conditions for the velocity field and Neumann conditions for the stress tensor.     

Influence of isotacticity and molecular weight on the properties of metallocenic isotactic polypropylene

The relationships between structure and properties have been established for isotactic polypropylene, iPP, homopolymers synthesized by metallocene catalyst systems. These iPPs exhibit different isotacticity degrees and molecular weights, and several thermal treatments during their processing have been applied. The most important factor affecting the structure and properties of these polymers is the isotacticity content. The thermal treatment, i.e., the rate of cooling from the melt, is also important and a clear molecular weight effect has been also found for the sample with lowest M_w. These factors affect the thermal properties, the degree of crystallinity and, therefore, the structural parameters and the viscoelastic behavior. A slow cooling from melt favors the formation of the γ phase instead of the α modification. The storage modulus, Young modulus and microhardness values increase as crystallinity does, independently of the origin of this increase: higher isotacticity or application of a slow crystallization from the melt.     

Molecular mechanism of physical gelation of hydrocarbons by fatty acid amides of natural amino acids

A variety of fatty acid amides of different naturally occurring l-amino acids have been synthesized and they are found to form gels with various hydrocarbons. The gelation properties of these compounds were studied by a number of physical methods including FTIR spectroscopy, X-ray diffraction, scanning electron microscopy, differential scanning calorimetry, rheology, and it was found that gelation depended critically on the fatty acid chain length and the nature of the amino acid. Among them l-alanine based gelators were found to be the most efficient and versatile gelators as they self-assemble into a layered structure to form the gel network. Mechanisms for the assembly and formation of gels from these molecules are discussed.     

Viscoelastic and thermal characterization of crosslinked PVC

Soft PVC is employed for the manufacturing of a wide range of products with different properties and a relatively low cost. The utilization of soft PVC is restricted by the poor thermal, chemical and mechanical resistance properties. Also, plasticizer migration can modify the properties or can make useless the materials for some applications because of toxicity or a general loss of properties. PVC crosslinking is the most effective way to improve mechanical and transport properties of rigid or flexible PVC at high temperatures, but at the same time the thermal stability of PVC may be significantly reduced. In this work, the crosslinking reaction of plasticized poly(vinyl chloride) (PVC) through difunctional amines was studied. The mechanisms involved in the crosslinking reaction were explained by Fourier transform infrared (FTIR) analysis. The thermal activated crosslinking reaction was studied by cone and plate rheometry, analyzing the evolution of viscoelastic properties of the suspension as a function of time and temperature. The effect of the addition of crosslinking agents on the thermal stability of the polymer was studied by thermogravimetric analysis (TGA), which revealed that crosslinking reactions promote thermal degradation phenomena in the polymer matrix. This is attributed to the formation of HCl and other species promoting polymer degradation during crosslinking, thus leading to higher weight loss during thermal treatment with respect to unmodified PVC plastisols. This was also confirmed by an evident yellowing after crosslinking, especially at higher temperatures.     

Sloshing waves in a heated viscoelastic fluid layer in an excited rectangular tank

In this paper, we have investigated the motion of a heated viscoelastic fluid layer in a rectangular tank that is subjected to a horizontal periodic oscillation. The mathematical model of the current problem is communicated with the linearized Navier–Stokes equation of the viscoelastic fluid and heat equation together with the boundary conditions that are solved by means of Laplace transform. Time domain solutions are consequently computed by using Durbin's numerical inverse Laplace transform scheme. Various numerical results are provided and thereby illustrated graphically to show the effects of the physical parameters on the free-surface elevation time histories and heat distribution. The numerical applications revealed that increasing the Reynolds number as well as the relaxation time parameter leads to a wider range of variation of the free-surface elevation, especially for the short time history.     

A reduced simulation applied to the viscoelastic fatigue of polymers

The paper extends the use of the PGD method to viscoelastic evolution problems described by a large number of internal variables and with a large spectrum of relaxation times. The internal variables evolution is described by a set of linear differential equations that involve many time scales. The feasibility and the robustness of the method are discussed in the case of a polymer in a non-equilibrium state under creep and cyclic loading. The relationships between different time scales (loading and internal variables) are also discussed.     

Existence and uniqueness of maximal strong solution of a 1D blood flow in a network of vessels

We study the well-posedness of a system of one-dimensional partial differential equations modeling blood flows in a network of vessels with viscoelastic walls. We prove the existence and uniqueness of maximal strong solution for this type of hyperbolic/parabolic model. We also prove a stability estimate under suitable nonlinear Robin boundary conditions.     

Viscoelastic wave propagation in the viscoelastic single walled carbon nanotubes based on nonlocal strain gradient theory

In this paper, the viscoelastic wave propagation in an embedded viscoelastic single-walled carbon nanotube (SWCNT) is studied based on the nonlocal strain gradient theory. The characteristic equation for the viscoelastic wave in SWCNTs is derived. The emphasis is placed on the influence of the tube diameter on the viscoelastic wave dispersion. A blocking diameter is observed, above which the wave could not propagate in SWCNTs. The results show that the blocking diameter is greatly dependent on the damping coefficient, the nonlocal and the strain gradient length scale parameters, as well as the Winkler modulus of the surrounding elastic medium. These findings may provide a prospective application of SWCNTs in nanodevices and nanocomposites.     

Numerical study for the electrified instability of viscoelastic cylindrical dielectric fluid film surrounded by a conducting gas

The linear electrohydrodynamic cylindrical instability of annular Walters B^′${\mathrm{B}}^{\prime }$ viscoelastic dielectric fluid layer surrounded by a conducting gas in the presence of radial electric field is investigated. The obtained dispersion relation is found to be complicated and cannot be treated theoretically easily. Two limiting cases of interest are investigated, when the inertia is dominant, and when both the kinematic viscosity and viscoelasticity are high, and the corresponding new stability conditions are obtained for both cases. We solve the eigenvalue problem numerically using the continuation method which gives better results than the classical non-linear solvers such as Newton and Secant methods. It is found that the applied radial electric field has a dual role on the stability of the considered system, depending of the chosen wavenumbers range. Both the kinematic viscoelasticity and liquid depth are found to have stabilizing effects, while both the kinematic viscosity and surface tension have destabilizing effects on the considered system. The stability or instability breaks down for critical wavenumber values at which the growth rate vanishes. The behaviors of both the maximum growth rate and the corresponding dominant wavenumber are discussed in detail corresponding to the effect of all physical parameters. Finally a comparison between the results obtained here for Walters B^′${\mathrm{B}}^{\prime }$ viscoelastic fluids, and those obtained here too if the fluid is replaced by a Rivlin–Ericksen viscoelastic one is achieved. The limiting cases of absence of electric field and/or kinematic viscoelasticity are also investigated in detail.