Power Law Dependence Of Viscosity Research Articles

Long-time solutions for some mixed boundary value problems depicting motions of a class of Maxwell fluids with pressure dependent viscosity

Closed-form expressions are established for dimensionless long-tome solutions of some mixed initial-boundary value problems. They correspond to three isothermal unsteady motions of a class of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure. The fluid motion, between infinite horizontal parallel flat plates, is induced by the lower plate that applies time-dependent shear stresses to the fluid. As a check of the obtained results, the similar solutions corresponding to the classical incompressible Maxwell fluids performing same motions are recovered as limiting cases of present solutions. Finally, some characteristics of fluid motion as well as the influence of pressure-viscosity coefficient on the fluid motion are graphically presented and discussed.

Steady-state solutions for modified Stokes’ second problem of Maxwell fluids with power-law dependence of viscosity on the pressure

Analytical expressions for the steady-state solutions of modified Stokes’ second problem of a class of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure are determined when the gravity effects are considered. Fluid motion is generated by a flat plate that oscillates in its plane. We discuss similar solutions for the simple Couette flow of the same fluids. Obtained results can be used by the experimentalists who want to know the required time to reach the steady or permanent state. Furthermore, we discuss the accuracy of results by graphical comparisons between the solutions corresponding to the motion due to cosine oscillations of the plate and simple Couette flow. Similar solutions for incompressible Newtonian fluids with power-law dependence of viscosity on the pressure performing the same motions and some known solutions from the literature are obtained as limiting cases of the present results. The influence of pertinent parameters on fluid motion is graphically underlined and discussed.

English

Two isothermal motions of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure are investigated when gravity effects are taken into account. The fluid motion, between two infinite horizontal parallel plates, is generated by the lower plate that applies a time-dependent shear stress to the fluid. Exact expressions are established for the steady-state components of the dimensionless start-up velocity, shear stress, and normal stress. They are used to find the needed time to touch the steady-state and to provide corresponding solutions for the motion of the same fluids induced by an exponential shear stress on the boundary. This time is useful for experimentalists who want to eliminate transients from their experiments. It is higher for motions of ordinary fluids as compared to fluids with pressure-dependent viscosity. The variation of starting solutions (numerical solutions) in time and space is graphically represented and some characteristics of the fluid motion are brought to light.

"Permanent solutions for some motions of UCM fluids with power-law dependence of viscosity on the pressure"

Steady motion of two types of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure is analytically studied between infinite horizontal parallel plates when the gravity effects are taken into consideration. Simple and exact expressions are established for the permanent components of starting solutions corresponding to two oscillatory motions induced by the lower plate that oscillates in its plane. Such solutions are very important for the experimentalists who want to eliminate the transients from their experiments. The similar solutions for the simple Couette flow of the same fluids, as well as the permanent solutions corresponding to ordinary incompressible Maxwell fluids performing the same motions, are obtained as limiting cases of general solutions. The convergence of starting solutions to their permanent components as well as the influence of physical parameters on the fluid motion is graphically underlined and discussed.

Permanent solutions for some oscillatory motions of fluids with power-law dependence of viscosity on the pressure and shear stress on the boundary

Abstract In this paper, we provide simple expressions for the permanent solutions corresponding to some oscillatory motions of two classes of Newtonian fluids with power-law dependence of viscosity on the pressure between two infinite horizontal parallel plates. The fluid motion is generated by the lower plate that applies an oscillatory shear stress to the fluid. Such solutions, which are lack in the existing literature, can be useful both for those who want to eliminate the transients from their experiments and as tests to verify numerical schemes that are developed to study complex unsteady flow problems of these fluids. The similar solutions corresponding to the motion due to a constant shear stress on the boundary are also determined and, contrary to our expectations, the shear stresses are constant on the whole flow domain although the associated velocity fields depend both of the spatial variable and the dimensionless pressure-viscosity coefficient. Finally, for validation, some comparative graphical illustrations are included and the convergence of starting solutions to the permanent solutions is graphically proved. Spatial profiles of starting solutions are also provided.

Exact solutions for unsteady motion between parallel plates of some fluids with power-law dependence of viscosity on the pressure

Unsteady motion between two infinite horizontal parallel plates of incompressible viscous fluids with a power-law dependence of viscosity on the pressure is studied analytically. The fluid motion is generated by the lower plate that is moving in its plane with a time dependent velocity. General solutions for dimensionless velocity and shear stress fields are established using suitable changes of independent variable and unknown function. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any motion of this kind of respective fluids. Consequently, the problem in discussion is completely solved. For illustration, three particular cases with engineering applications are considered and graphical representations are presented and discussed. The solutions corresponding to some motions due to an accelerated plate are connected to those of the simple Couette flow by means of Riemann-Liouville fractional integral operator. The solutions corresponding to oscillating motions are presented as sums of steady-state and transient components and, for the validation of results that have been obtained, the steady-state solutions are presented in different forms whose equivalence is graphically proved. The required time to reach the steady-state is graphically determined both for oscillating motions and the simple Couette flow.

EXACT SOLUTIONS FOR OSCILLATING MOTIONS OF SOME FLUIDS WITH POWER-LAW DEPENDENCE OF VISCOSITY ON THE PRESSURE

Analytical expressions for the steady-state components of the dimensionless starting solutions corresponding to some oscillatory motions through a horizontal rectangular channel of two classes of incompressible Newtonian fluids with power-law dependence of viscosity on the pressure are established in the simplest forms. The fluid motion is generated by the lower plate that oscillates in its plane. For validation, three limiting cases are considered and interesting graphical representations are provided. It is worth pointing out the fact that such solutions are important in practice for those who want to eliminate the transients from their experiments. In addition, the dimensionless steady shear stresses corresponding to the simple Couette flow of such fluids are constants on the whole flow domain although the adequate velocity fields are functions of y

РЕШЕНИЕ ЛИНЕАРИЗОВАННОЙ ПО СКОРОСТИ СИСТЕМЫ УРАВНЕНИЙ НАВЬЕ–СТОКСА С УЧЕТОМ СТЕПЕННОГО ВИДА ЗАВИСИМОСТИ ВЯЗКОСТИ, ТЕПЛОПРОВОДНОСТИ И ПЛОТНОСТИ ГАЗООБРАЗНОЙ СРЕДЫ ОТ ТЕМПЕРАТУРЫ

We received the solution of the system of Navier–Stokes equations linearized with respect to the velocity in the spheroidal coordinate system with regard of a power-law dependence of viscosity, thermal conductivity and the gaseous medium density on the temperature by means of generalized power series.

Rheological Properties of Starch‐Based Materials and Starch/Poly(lactic acid) Blends

AbstractThe rheological properties of pure starch and blends of gelatinized starch/poly(lactic acid) (PLA) were studied using a rheometer incorporating a twin‐roll mixer and a single‐screw extruder. The mixer provides a useful and convenient tool to study the rheological properties and gelatinization processes of starch. The single‐screw extruder with a slit capillary die was used to measure shear stress and viscosity under different shear rates at different temperatures. Starch was shown to increase the shear viscosity of PLA. Methylenediphenyl diisocyanate (MDI) was used as a compatibilizer, and was distributed in different phases through controlled processing. The addition of MDI showed a stronger effect on rheological properties when it was distributed in the PLA phase prior to blending. Both the pure starch and blends showed a power law dependence of viscosity on shear rate.

Effect of Compatibilizer Distribution on Thermal and Rheological Properties of Gelatinized Starch/Biodegradable Polyesters Blends

Abstract Thermal and rheological properties of various blends of gelatinized starch and biodegradable polyester, polycaprolactone (PCL) or poly(butylene succinate adipate) (PBSA), were studied by DSC, TGA and rheometry. Methylenediphenyl diisocyanate (MDI) was used as a compatibilizer and was distributed in different phases through controlled processing. The addition of MDI showed a stronger effect on thermal and rheological properties when it was mainly distributed in the polyester phase prior to blending. Starch was shown to increase the shear viscosity of both types of polyesters. The two blends, starch/PCL and starch/PBSA, showed a similar pattern of a power law dependence of viscosity on shear rate. MDI was shown to enhance the effect of starch on the melting and decomposition temperatures, especially when distributed in the polyester phase.

Ablation of crystalline polymers

The author gives an approximate solution for determining the temperature of the working surface and the rate of ablation of thermoplastics in a hot gas stream. The flow parameters have been isolated from the properties of the melt, which is characterized only by ropiness and the exponent of the power-law dependence of viscosity on temperature.