Rheological properties of polymers in the fluid state

The possibilities and conditions of correlation are determined for the principal rheological characteristics of single-phase polymer systems measured for one-dimensional shear deformation in steady-state flow regimes, on transition from rest to steady-state flow, and in harmonic vibration regimes. Special significance attaches to the quantitative results of measuring the high-elastic properties of the polymer systems. It is shown that the Lodge theory, describing the flow behavior of high-elastic media, is well-founded in the linear region of deformation, i.e., for the limiting case of shear rates and shear stresses tending to zero, whereas the Mooney-Rivlin-Weissenberg theories are not in accord with the experimental data even in this limiting deformation regime.Topcheiv Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, Vol. 5, No. 1, pp. 164–181, January–February, 1969.     

Effect of steady-state flow of a polyisobutylene solution on its dynamic characteristics measured in the direction of flow

The effect of steady-state flow on the linear dynamic characteristics of a 10% solution of polyisobutylene in cetane, measured in the direction of flow, is investigated. The material characteristics in steady-state flow quantitatively describe the dynamic viscosity and elasticity at deformation frequencies small as compared with the steady-state shear rate.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 913–919, September–October, 1970.     

On determining current profiles in oscillatory flows

The time dependency of the linear three-dimensional hydrodynamic equations which describe oscillatory flow, is removed by expressing the horizontal components of current in terms of rotary components at a prescribed frequency. By this means two time independent equations (one for each rotary component) are derived, which can be readily solved using the Galerkin method, in a manner analogous to that developed by the author for steady-state wind-induced flow. The method is used to examine the influence of eddy viscosity on tidal current profiles. Two distinct flow regimes are identified. In one the water depth exceeds the thickness of the bottom stress layer, in the other, water depth is less than the thickness of this layer. The influence of these two depth regimes, and the magnitude and vertical variation of eddy viscosity on tidal current profiles is examined. The possibility of using the method to give tidal profiles from vertically integrated models is discussed.     

Flow of a nonlinear viscoelastic liquid in cylindrical channels

The problem of nonrectilinear steady-state flow of a nonlinear viscoelastic liquid in an arbitrary cylindrical channel is examined. On the assumption that the cross flows are insignificant as compared with the longitudinal flows an equation of state is derived for the flow regime in question. A variational principle established for steady-state flows of the investigated media is proposed as the basis of a method of solving problems of the flow of polymer materials in arbitrary cylindrical channels. The flow of a polymer solution in rectangular channels is investigated.Institute of Mechanics, AS UkrSSR, Kiev. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1103–1111, November–December, 1968.     

Multicritical phenomena in flow of viscoelastic liquids. 1. Zaremba-Fromm-De Witt liquid

It has been shown that multicritical phenomena caused by nonlinearity of viscosity and high elasticity, and forced anisotropy at finite shear rates take place during flow of viscoelastic polymer melts which are isotropic in the resting state. The sign of the low-frequency asymptotic values of the dynamic viscosity and elasticity measured during steady flow is a criterion of the appearance of instability. These arguments are illustrated by the solution and analysis of the complex reaction to low-amplitude, periodic shear of a steady-flowing, very simple viscoelastic liquid — ZFD liquid. It was shown that the instability of viscoelastic liquids for a given steady shear rate is due to the effect of perturbations lasting for no less than some limiting value and its manifestations are caused by superposition of different types of instability — multicritical phenomena.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 555–572, July–August, 1995.The study was conducted based on Topic 93,177 of the Latvian Science Council.     

Dynamic deformation of a stationary rubber flow

The effect of dynamic deformation on the stationary flow of a rubber composition has been experimentally investigated for comparable values of the stationary and dynamic strain rates. The dependence of the effective viscosity on the stationary shear rate is not equivalent to its dependence on the periodic shear rate amplitude. An expression is given for calculating the effective viscosity in the case of combined stationary and dynamic shear deformation. The effectiveness of the dynamic deformation, estimated in terms of the effective viscosity, depends on whether it is superimposed on the stationary flow at constant stationary shear rate or at constant stress. It is proposed to estimate the effectiveness of dynamic deformation of a stationary non-Newtonian flow in terms of the change in the power of the stationary forces. When the effective viscosity is reduced by dynamic deformation of the stationary flow, the power of the stationary forces increases at constant shear stress and falls at constant stationary shear rate.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 489–496, May–June, 1971.     

Normal stresses in non-Newtonian polymer flows

The calculation of the normal stresses from the flow curve is considered on the basis of the method of correlation of the frequency and stationary characteristics of flowing polymer systems. Simple expressions are given for finding the initial normal stress coefficient and the high-elastic modulus from the point corresponding to the beginning of non-Newtonian flow. A necessary condition for the appearance of normal stresses is a viscosity anomaly. It is shown that for a bounded value of the initial normal stress coefficient to exist the derivative of the effective viscosity with respect to shear rate must be zero at the initial point.Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 506–514, May–June, 1971.     

Calculation of the resistance to the flow of polymeric systems through short channels

A method is proposed for calculating the pressure drop associated with the flow of polymeric systems (solutions, melts, and rubber blends) through short capillaries in which the steady-state flow regime is not established. The method is based on the assumption that the duration of deformation in the prestationary stage plays a decisive role. The results of the calculations are in good agreement with the experimental data.All-Union Scientific-Research and Design-Engineering Institute of the Rubber Industry, Volzhskii. Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Volgograd Polytechnic Institute. Translated from Mekhanika Polimerov, No. 1, pp. 171–174, January–February, 1973.     

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.     

Rheological Properties of Nanosized AlN Powder Suspensions for Advanced Ceramics

The rheological properties (flow curves and viscoelastic behavior) of injection molding suspensions of a plasma-processed AlN nanosized powder (nanopowder) in paraffin are investigated over a broad range of shear rates (0.07–1350 s^–1). Two viscosity plateaux are observed on the flow curves and two values of the yield stress are obtained. The lower value of the strain amplitude (0.66%), exceeding the linearity limit of periodic shear, is restricted by the rheometer resolution. The ultrasound treatment and shear deformation of suspensions affect the structure of particle packing, which is responsible for the dependence of their rheological properties on the prehistory of mechanical actions.     

On the theory of non-Newtonian polymer flow

The Eyring-Frenkel theory of viscosity of low-molecular liquids has been extended to solutions of high-molecular compounds. It is shown that there are flow units of different sizes in the system, their mean size being proportional to the molecular weight of the polymer. An expression is obtained for the non-Newtonian viscosity of polymer solutions. In the limiting case of high shear rates the viscosity of the solution coincides with that of the solvent. At low shear rates Flory's empirical relation for the viscosity of polymer solutions is theoretically obtained.Mekhanika Polimerov, Vol. 2, No. 5, pp. 779–784, 1966     

The attractor on viscosity Degasperis–Procesi equation

In this paper the dynamical behaviors of a dispersive shallow water equation with viscosity, viscosity Degasperis–Procesi equation, are investigated. The existence of global solution to viscosity Degasperis–Procesi equation in L² under the periodical boundary condition is studied and the existence of the global attractor of semi-group to solution on viscosity Degasperis–Procesi equation in H² is obtained.     

Forced viscosity anisotropy of polymers

For two-dimensional flow the viscosity of an anisotropic medium is determined by two quantities. In relation to polymer melts, one of these corresponds to the viscosity for tension in the direction of orientation and the other to viscosity for shear in planes parallel to the orientation. By solving the problem of the flow of such a medium in a plane convergent channel and making optical-polarization measurements we were able to observe and quantitatively describe this phenomenon.Mekhanika Polimerov, Vol. 1, No. 5, pp. 13–18, 1965     

Theory of flow of concentrated polymer solutions and melts

Starting from the concept of a polymer system as a collection of macromolecules forming an effective network, an expression is obtained for the stress tensor of a flowing concentrated polymer solution or melt. It is shown that the variation of the effective viscosity of polymer systems is associated with the orientation of the macromolecules and changes in the equilibrium number of nodes during flow. A system of equations describing the flow of polymer systems characterized by a gradient dependence of the effective viscosity and normal stresses in shear is written in the single relaxation time approximation.Institute of Chemical Physics, Moscow Region, Academy of Sciences of the USSR. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 724–730, July–August, 1968.     

On the theory of non-Newtonian polymer flow

Shear flow of polymers is examined on the assumption that the main contribution to polymer viscosity is made by the dissipation of energy in the destruction of the fluctuation network. A simple physicomechanical model of the flow process is proposed and used to obtain an expression for the polymer viscosity in terms of certain functions reflecting the influence of the molecular structure.Mekhanika Polimerov, Vol. 2, No. 3, pp. 429–434, 1966     

Nonreflecting Boundary Conditions for Nonlinear Problems of Fluid Dynamics

External problems of fluid dynamics are modeled on artificially bounded regions. A method is proposed for applying nonreflecting boundary conditions to the linearized Euler equations obtained from the original nonlinear problem. The nonreflecting conditions are modified to allow for viscosity and nonhomogeneity of unperturbed background flow in linear Euler, Navier–Stokes, and quasi-fluid-dynamic models. One-dimensional test problems are computed in the linear and nonlinear cases.     

Non-newtonian viscosity of certain precopolymers of n-butyl methacrylate

The viscous flow of precopolymers of n-butyl methacrylate and triethylene glycol dimethacrylate at various shear rates is considered. The dynamic viscosity of the precopolymers is shown to depend on the conversion ratio.Kiev Branch, All-Union Scientific-Research Institute of Complex Problems of Polygraphy in Special Types of Printing. Institute of Chemistry of High-Molecular-Weight Compounds, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 6, pp. 1096–1097, November–December, 1971.     

Optimal control of non-isothermal viscous fluid flow

For flow inside a four-to-one contraction domain, we minimize the vortex that occurs in the corner region by controlling the heat flux along the corner boundary. The problem of matching a desired temperature along the outflow boundary is also considered. The energy equation is coupled with the mass, momentum, and constitutive equations through the assumption that viscosity depends on temperature. The latter three equations are a non-isothermal version of the three-field Stokes–Oldroyd model, formulated to have the same dependent variable set as the equations governing viscoelastic flow. The state and adjoint equations are solved using the finite element method. Previous efforts in optimal control of fluid flows assume a temperature-dependent Newtonian viscosity when describing the model equations, but make the simplifying assumption of a constant Newtonian viscosity when carrying out computations. This assumption is not made in the current work.     

High-frequency periodic deformation of polymers in the viscous-flow state

The propagation of high-frequency periodic vibrations in melts and solutions is considered in the case where the acoustic characteristics of the material are determined by the deformation amplitude. It is shown that in sufficiently large specimens the consequences of periodic deformation are concentrated near the vibration source, as a result of which a layer of material with strongly modified mechanical characteristics develops. It is suggested that when periodic high-frequency deformation is superimposed on steady-state flow, owing to the presence of a boundary layer there is effective slippages of the material at the vibration-emitting surfaces.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 722–728, July–August, 1973.     

stresses and reversible deformations during shear flow of polymer solutions and melts

The influence of the accumulated elastic energy on the relationships between tangential stresses, the first difference between the normal stresses and the reversible deformations during isothermal shearing steady-state flow of polymer solutions and melts, is analyzed. It is shown that the reversible deformation in the non-Newtonian flow region is related to the tangential and normal stresses by Lodge's formula, if the thixotropic disruption of the structural flow units is accompanied by the dissipation of the elastic energy accumulated in them; the conservation of the elastic energy accumulated during the flow causes exceeding of the reversible deformation values as compared with the values calculated by Lodge's formula.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 886–895, September–October, 1972.