Investigation of the relaxation process in polycarbonate film

The temperature relaxation of polycarbonate film and the accompanying change in the birefringence path difference are considered. It is shown that at a temperature of about 170°C intense crystallization takes place in the film. The deformation modulus is a function of the density of the network and its degree of orientation. The variation of these parameters with the stretch ratio and temperature is determined experimentally. The creep of polycarbonate film is considered and correlated with the curves representing the fall in the number of chains of the molecular network in pure relaxation.Mendeleev All-Union Scientific-Research Institute of Metrology, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 72–76, January–February, 1973.     

Effect of aggregation on population recovery modeled by a forward-backward pseudoparabolic equation

In this paper we study the equation

in a bounded domain of , , with homogeneous boundary conditions of the Neumann type, as a model of aggregating population with a migration rate determined by , and total birth and mortality rates characterized by . We will show that the aggregating mechanism induced by allows the survival of a species in danger of extinction. Numerical simulations suggest that the solutions stabilize asymptotically in time to a not necessarily homogeneous stationary solution. This is shown to be the case for a particular version of the function .

     

RETRACTED ARTICLE: Effect of electromagnetic field on the stability of viscoelastic fluid film flowing down an inclined plane

The stability of thin electrically conducting viscoelastic fluid film flowing down on a non-conducting inclined plane in the presence of electromagnetic field is investigated under induction-free approximation. Surface evolution equation is derived by long-wave expansion method. The stabilizing role of Hartman number M (magnetic field) and the destabilizing role of the viscoelastic property \({\varGamma}\) and the electric parameter E on such fluid film are established through the linear stability analysis of the surface evolution equation. Investigation shows that at small values of Hartman number (M), the influence of electric parameter (E) on the viscoelastic parameter \({(\varGamma)}\) is insignificant, while for large values of M, E introduces more destabilizing effect at low values of \({\varGamma}\) than that at high values of \({\varGamma }\). An interesting result also perceived from our analysis is that the stabilizing effect of Hartman number (M) is decreasing with the increase of the values of \({\varGamma}\) and E, even it gives destabilizing effect after a certain high value of the electric field depending on the high value of \({\varGamma}\). The weakly nonlinear study reveals that the increase of \({\varGamma}\) decreases the explosive and subcritical unstable zones but increases the supercritical stable zone keeping the unconditional zone almost constant.     

Effect of temperature on the chemical relaxation process in rubbers

The effect of temperature on the chemical relaxation of rubbers has been investigated. With reference to nine industrial rubbers it has been shown that during storage in the stressed state (at =const) chemical relaxation is chiefly determined by two processes proceeding at different rates. Furthermore, the chemical relaxation of rubbers is determined not only by the rate constants of these two processes but also by the pre-exponential constants C_0i, the relationship between which varies with increase in temperature. It is possible to extrapolate the rate constants (k_i) and pre-exponential constants (C_0i) from elevated temperatures (110–50° C) to temperatures in the range 20–25° C. An equation is proposed that makes it possible to calculate the change in the elastic properties of rubbers in the stressed state at storage temperatures (20–25° C) by means of results obtained at elevated temperatures.Mekhanika Polimerov, Vol. 3, No. 3, pp. 448–454, 1967     

Nonlinear stability of an axial electric field: Effect of interfacial charge relaxation

We introduce a nonlinear perturbation technique to third order, to study the stability between two cylindrical inviscid fluids, subjected to an axial electric field. The study takes into account the relaxation of electrical charges at the interface between the two fluids. At first order, a linear dispersion relation is obtained. Analytical and numerical results for the overstability and incipient instability conditions are given. For perfect dielectric fluids, the electric field has a stabilizing influence, while for leaky dielectric fluids, the electric field can have either a stabilizing or a destabilizing influence depending on the conductivity and permittivity ratios of the two fluids. At higher order, a nonlinear dispersion relation (nonlinear Ginzburg–Landau equation) is derived, describing the evolution of wave packets of the problem. For leaky dielectric fluids near the marginal state, a nonlinear diffusion equation (nonlinear incipient instability) is obtained. For perfect dielectric fluids, two cubic nonlinear Schrödinger equations are obtained. One of these equations to determine a nonlinear cutoff electric field separating stable and unstable disturbance, whereas the other is used to analyze the stability of the system. It is found that the nonlinear stability criterion depending on the ratio of permittivity, Such effects can only be explained successfully in the nonlinear sense, as the linear analysis unsuccessful to inform about them.     

Numerical simulation two phase flows of casting filling process using SOLA particle level set method

Mould filling process is a typical gas–liquid metal two phase flow phenomenon. Numerical simulation of the two phase flows of mould filling process can be used to properly predicate the back pressure effect, the gas entrapment defects, and better understand the complex motions of the gas phase and the liquid phase. In this paper, a novel sharp interface incompressible two phase numerical model for mould filling process is presented. A simple ghost fluid method like discretization method and a density evaluation method at face centers of finite difference staggered grid are proposed to overcome the difficulties when solving two phase Navier–Stokes equations with large-density ratio and large-viscosity ratio. A new mass conservation particle level set method is developed to capture the gas–liquid metal phase interface. The classical pressure-correction based SOLA algorithm is modified to solve the two phase Navier–Stokes equations. Two numerical tests including the Zalesak disk problem and the broken dam problem are used to demonstrate the accuracy of the present method. The numerical method is then adopted to simulate three mould filling examples including two high speed CCD camera imaging water filling experiments and an in situ X-ray imaging experiment of pure aluminum filling. The simulation results are in good agreement with the experiments.     

Galerkin discontinuous approximation of the transport equation and viscoelastic fluid flow on quadrilaterals

Numerical simulation of industrial processes involving viscoelastic liquids is often based on finite element methods on quadrilateral meshes. However, numerical analysis of these methods has so far been limited to triangular meshes. In this work, we consider quadrilateral meshes. We first study the approximation of the transport equation by a Galerkin discontinuous method and prove an 𝒪(h^k+1/2) error estimates for the Q_k finite element. Then we study a differential model for viscoelastic flow with unknowns u the velocity, p the pressure, and σ the viscoelastic part of the extra-stress tensor. The approximations are ((Q₁)² transforms of) Q_k+1 continuous for u, Q_k discontinuous for σ, and P_k discontinuous for p, with k ≥ 1. Upwinding for σ is obtained by the Galerkin discontinuous method. We show that an error estimate of order 𝒪(h^k+1/2) is valid in the energy norm for the three unknowns. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 97–114, 1998     

Dependence of stability of Nicholson's blowflies equation with maturation stage on parameters

The stability of Nicholson''s blowflies equation with maturation stage is investigated by reducing the number of parameters in the original model. We derive the condition on the stability of the positive equilibrium of the model, and discuss the dependence of the stability on the parameters by analyzing geometrically the dependence of real parts of eigenvalues of the characteristic equation with fewer parameters on the parameters. By restoring parameters, the condition on the stability of the positive equilibrium of the original model are formulated explicitly, and the corresponding regions are depicted for some different cases. The obtained result shows that the parameter determining the maximum reproductive success of the population affects only the size of the positive equilibrium, but plays no role in determining its stability.     

Effect of ultrasonic vibrations on the flow of a viscoelastic liquid

The rheological characteristics of a viscoelastic liquid flow, on which finite-amplitude ultrasonic shear vibrations have been superimposed, are investigated. It is shown that at periodic deformation amplitudes of 5 µ or more there is a thixotropic reduction of the viscosity and elasticity of the system owing to the destruction of certain types of structural bonds. The experimental apparatus is described.Moscow Institute of Chemical Machine Building. Translated from Mekhanika Polimerov, No. 6, pp. 1097–1099, November–December, 1971.     

Effect of moisture on the viscoelastic properties of an epoxy-clay nanocomposite

The results of a complex study on the viscoelastic behavior of an epoxy-clay nanocomposite after a long-term exposure to moisture are presented. The main laws of variation in the glass-transition temperature of the nanocomposite in relation to the different content of filler and absorbed moisture were determined by using a thermomechanical analysis. The loading levels in creep experiments were chosen according to the results of quasi-static tensile tests. The sets of creep and creep recovery curves obtained were approximated by the Boltzmann–Volterra linear integral equation with account of the principle of moisture-time analogy. The variation in the spectrum of retardation time of the epoxy resin with introduction of the nanofiller was estimated. It is shown that the moisture-time reduction function correlates with changes in the forced rubber-like elasticity and the volume of nanocomposite specimens upon their moistening.     

Effect of combined extrusion parameters on mechanical properties of basalt fiber-reinforced plastics based on polypropylene

Basalt fibers are efficient reinforcing fillers for polypropylene because they increase both the mechanical and the tribotechnical properties of composites. Basalt fibers can compete with traditional fillers (glass and asbestos fibers) of polypropylene with respect to technological, economic, and toxic properties. The effect of technological parameters of producing polypropylene-based basalt fiber-reinforced plastics (BFRPs) by combined extrusion on their mechanical properties has been investigated. The extrusion temperature was found to be the main parameter determining the mechanical properties of the BFRPs. With temperature growth from 180 to 240°C, the residual length of the basalt fibers in the composite, as well as the adhesive strength of the polymer-fiber system, increased, while the composite defectiveness decreased. The tensile strength and elastic modulus increased from 35 to 42 MPa and 3.2 to 4.2 GPa, respectively. At the same time, the growth in composite solidity led to its higher brittleness. Thus, a higher temperature of extrusion allows us to produce materials which can be subjected to tensile and bending loads, while the materials produced at a lower temperature of extrusion are impact stable. The effect of the gap size between the extruder body and moving disks on the mechanical properties of the BFRPs is less significant than that of temperature. An increase of the gap size from 2 to 8 mm improves the impregnation quality of the fibers, but the extruder productivity diminishes. The possibility of controling the properties of reinforced polypropylene by varying the technological parameters of combined extrusion is shown. The polypropylene-based BFRPs produced by the proposed method surpass the properties of glass and asbestos fiber-reinforced plastics.Submitted to the 10th International Conference on Mechanics of Composite Materials (Riga, April 20–23, 1998).Ukrainian State University of Chemical Technology, Dnepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 845–850, November–December, 1997.     

Effect of reinforcement on the stress relaxation and creep ofelasto-hereditary materials

The elastic moduli of a reinforced material are calculated. The reinforcing fibers are assumed to be elastic and isotropic and the polymer matrix isotropic and elasticoviscous. It is further assumed that in the latter case the hereditary properties are described by a linear integral shear modulus operator with a fractional-exponential kernel. The changes in the relaxation and retardation times due to the correlations between inhomogeneities are estimated.Moscow Institute of Electronics Engineering. Translated from Mekhanika Polimerov, No. 3, pp. 470–474, May–June, 1969.     

Effect of long-term exposure to water on the viscoelastic properties of an epoxy-based composition

For modeling the effect of volume change on the viscoelastic properties of a polymer, an equation underlying the concept of free volume is used. The parameters of the moisture–time reduction function, characterizing changes in the viscoelastic properties of an epoxy-based composition, are determined from tests results. To verify the approach suggested, results of long-term (up to one year) tests on stress relaxation under compression in an epoxy composition (COMFLOOR), both in the initial state and after a long-term (up to one year) exposure to water, are used. A satisfactory agreement between the reduction functions based on predictions and determined experimentally is found to exist. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 201–210, March–April, 2009.