Semi-analytical solution for the problem of extended Pom-Pom fluid flow in a round pipe

A semi-analytical solution to the problem of the steady flow of viscoelastic single equation eXended Pom-Pom (XPP) fluid in a round pipe using the four-mode rheological equation of state of XPP is presented. An original parametric method for solving the set problem is used. The resulting method is applicable for solving a similar problem in a flat slit. The developed solution method is tested by comparing it with numerical results and experimental data. Using a polyacrylamide solution as an example, the influence of the Weissenberg number on the axial velocity profiles and the components of normal stresses is studied.

Features of the Behavior of a Polymer Solution Jet in Electrospinning

Using the numerical analysis of the force balance equation and the rheological equation of the model of finitely extensible chains, the dynamics of a charged jet during the electrospinning of a polymer solution and the orientation of macromolecules in the jet are studied. In fairly weak electric fields, the jet always remains rectilinear, while in strong fields the straight section of the jet has a finite length, after which the motion of the jet becomes unstable. This behavior is due to the competition between inertial and viscoelastic forces, with viscoelasticity dominating in strong fields. It is found that polymer chains in the jet are strongly stretched along the flow direction.

Mathematical Model of Fluids Motion in Poroelastic Snow-ice Cover

The dynamics of a snow-ice cover is considered within the theory of poroelasticity. The snow-ice cover is modeled by a three-phase medium consisting of water, air and ice. The governing equations are the equations of mass conservation for each phase with phase transitions, the equations of conservation of phase momentum in the form of Darcy’s law, the equation of conservation of momentum of the whole system, the rheological equation for porosity and the equation of heat balance of snow. In the full formulation the liquid and air pressures are functions of the temperature and the corresponding densities, and the viscosity and compressibility coefficients of ice are functions of the temperature. The problem of two-dimensional nonstationary filtration of water in a thin poroelastic ice plate is considered in the model case. The solution is obtained in quadratures

Experience of determining the parameters of the elastoviscoplastic soil model

Rheological studies of soils were carried out by S.S. Vyalov, M.N. Gol’dshtejn, N.N. Maslov, G.I. Ter-Stepanyan, S.R. Meschyan, A.L. Gol’din, Z.G. Ter-Martirosyan and many others. On the basis of existing rheological soil models, a new universal rheological equation was proposed in Ter-Martirosyan’s dissertation, which allows describing kinematic shear, creep and stress relaxation at the same parameters. Experimental studies of the soil were carried out in a simple shear device in a kinematic loading mode at a shear displacement rate u̇= 0.05 mm/min and at two values of compaction loads (σ1 < σ2). Based on the results of the experimental studies, the parameters of the elastoviscoplastic model were determined and graphs of the dependence of shear stresses on time were plotted, which clearly show the high convergence of the experimental and theoretical curves.

THERMOHYDRODYNAMIC ANALYSIS OF THE WORK ROLL FORMING MACHINE CONFECTIONERY PRODUCTION BASED ON THE CFD APPROACH

On the basis of the equations of conservation of mass, energy and momentum, a mathematical model of the steady non–isothermal laminar flow of a nonlinear viscous medium in the gap between two rotating rolls of the forming machine of confectionery production is compiled. As a rheological equation, a modified four–parameter Carro model is used, which includes a temperature correction to the viscosity. The model takes into account the geometric parameters of the roll gap of the forming machine, the kinematic modes of its operation, the rheological and thermophysical parameters of the candy mass and their temperature dependences. A computational experiment was carried out using the Comsol Multiphysics multiphysics computational modeling package, which made it possible to estimate the temperature, velocity, and viscosity fields of the candy mass that characterize the flow of hydrodynamic and heat exchange processes during the molding of candy masses on roller machines. It is established that at a certain kinematic mode of operation of the rolls in the inter–roll gap, a region of circulating flow with significant and multidirectional shear deformations is formed, which allows the use of roll machines for mixing, plasticizing and dispersing.

Study on Penetration Grouting Mechanism Based on Newton Fluid of Time-Dependent Behavior of Rheological Parameters

Grouting mechanism is one of the important factors on the grouting effects of practical projects. At present, the vast majority of Newton fluid penetration grouting mechanisms are considering that the viscosity of Newton fluid during the grouting whole process was constant, so the theoretical diffusion radius calculated by them is far greater than the actual measurements in the grouting engineering. Carrying out theoretical analysis and experimental research, the rheological equation and seepage motion equation for Newton fluid of time-dependent behavior of rheological parameters were established; then, the penetration grouting mechanism of them was deduced. What is more, they were validated by means of designing the grouting verifying experiments. Experiment results show that the theoretical diffusion radius calculated by the formula of diffusion radius of penetration grouting mechanism based on Newton fluid of time-dependent behavior of rheological parameters was in accordance with the change regulation of the actual measurement diffusion radius by grouting experiments. Their difference within the range of 15% is far less than about 80% change between the theoretical diffusion radius calculated by the Maag formula and the actual measurement radius. In general, it can reflect the grout infiltration laws that Newton fluid changes with time. Therefore, research achievements may not only be able to provide a strong theoretical basis for perfecting the penetration grouting mechanism but also play a reference guiding role for the theoretical research, design, and construction in the grouting technique.

Orientation and Aggregation of Polymer Chains in the Straight Electrospinning Jet

The dynamics of a straight section of a jet arising during the electrospinning of a polymer solution without entanglements, and the orientation of polymer chains in the jet were explored based on the analysis of the forces balance equation and the rheological equation of the finitely extensible nonlinear elastic model. Two modes of the jet behavior were predicted. At relatively low volumetric flow rates, the straight jet has a limited length, after that, its rectilinear motion becomes impossible, while at higher flow rates, the jet always remains straightforward. It is shown that polymer chains in a jet can be strongly stretched, which leads to phase separation in a spinning solution. Aggregation of the stretched chains was also studied and the parameters of the emerging inhomogeneous structure were predicted.

Numerical Modeling of p-v-T Rheological Equation Coefficients for Polypropylene with Variable Chalk Content

The paper reports the experimental results of a study investigating the effect of different contents of a mineral filler on the rheological properties, p-v-T, of polypropylene. Using the pvT100 apparatus, we measured specific volume under isobaric cooling at different pressures for pure polypropylene and chalk-filled polypropylene (10 wt%, 20 wt% and 30 wt%). Next, we employed computer methods to determine the coefficients of a mathematical model describing the variations in specific volume in a function of temperature and pressure. The model was used in the numerical simulations of injection molding and shrinkage processes.