Dynamic Theory of Die Swell for Entangled Polymeric Liquids in Tube Extrusions: New Set of Equations for the Growth and Ultimate Extrudate Swelling Ratios under the Free States

A new dynamic theory of die swell for entangled polymeric liquids in a steady simple shear °ow is proposed which can be used to predict the correlation of the time-dependent and time-independent extrudate swelling behaviors to the molecular parameters of polymers and the operational variables. The theory is based on the O-W-F constitutive equation and the free recovery from Poioeuille flow with different ratios. Experimentsshow that the magnitudes of the simple shear in the steady simple shear flow may be resolved into the free recoil resulting from the recoverable elastic strains and the viscous heating resulting from the unrecoverable viscoelastic strains. For distinguishing the recoil from the viscous heating, a partition function and twoexponential fractions of conformation for the recoil and the viscous heating were defined. Thus the instantaneous, delayed and ultimate recoverable strain, and recoil in the free recovery were correlated to the partition function, the fraction of recoverable conformation, the molecular parameters, and the operational variables. Also the dynamics of the growth equation on the delayed viscoelastic strain and the delayed recoil in freestate were deduced. After introducing the condition of uniform two dimensional extensions, the definition ofswell ratio and the operational variables into the above correlation expressions and growth equations, then the correlations of the delayed extrudate swelling effect and the ultimate extrudate swelling effects to the molecular parameters and the operational variables were derived. Finally, two new sets of equations on the growth variables and ultimate extrudate swelling ratios under the dynamic and equilibrium states were also deduced from this dynamic theory of die swell. The first set of equations on the ultimate extrudate swelling ratio under the free and equilibrium states was verified by HDPE experimental data at two temperatures and different operational variables. The second set of equations on the growth extrudate swelling ratios under free and dynamic states was verified by PBD experimental data with different molecular weights and different operational variables. An excellent agreement is obtained, which shows that the two sets of equations for the growth and ultimate extrudate swelling ratios can be used directly to predict the correlation of extrudate swelling ratios to the molecular parameters and the operational variables.     

碳酸盐岩自转向酸酸液流动模拟实验研究与评价

在自转向酸酸化机理研究的基础上,对实验所用酸液体系从增黏性能、破胶性能和转向性能等方面进行了评价。实验发现,残酸在80℃时黏度可达到1 128.2 mPa·s,具有良好的封堵增黏性能;5%的乙二醇可使残酸黏度降至2 mPa·s,破胶效果好。通过岩心流动实验分别对常规酸和自转向酸在地层中的反应流动进行模拟,绘制了水驱-酸化-水驱全压降曲线。单岩心流动实验表明,自转向酸对于较高渗透率岩心的处理效果优于常规酸液,而对于较低渗岩心改造效果不明显。双岩心流动实验发现,对于不同渗透率差异倍数的两块岩心,自转向酸对于其中的低渗岩心改造效果要好于常规酸,然而随着渗透率极差进一步增大,自转向酸增黏改造效果变差。     

Stability of the viscoelastic Rayleigh–Taylor problem with internal surface tension

We investigate the stability of the Rayleigh–Taylor (RT) problem for stratified viscoelastic fluids with internal surface tension. More precisely, under the stability condition $\mathrm{Dis}(\vartheta ,\kappa )<1$, we prove the existence of unique strong solution with exponential decay in time for the (stratified) viscoelastic RT (VRT) problem with proper initial data in Lagrangian coordinates. This shows that a sufficiently large elasticity coefficient or a sufficiently large surface tension coefficient has a stabilizing effect so that it can inhibit the development of (stratified) RT instability.     

Effect of filler content on the stress relaxation behavior of fly ash/polyurea composites

In this study, fly ash/polyurea (FA/PU) composites of various fly ash volume fractions were fabricated. The time-domain stress relaxation behaviors of pure polyurea and the FA/PU composites were measured by dynamic mechanical analysis (DMA) in tension mode at various temperatures. Both temperature and volume fraction of fly ash can affect the segmental motion of polyurea as well as the interaction between fly ash hollow spheres and polyurea matrix, which constitutes the intrinsic mechanism of stress relaxation. Master curves of relaxation modulus were constructed and compared for PU and FA/PU composites. A model was proposed to relate the relaxation modulus and volume fraction of fillers based on three-parameter fractional derivative model and Mori-Tanaka model. The numerical predictions obtained from the model are found to be in good agreement with the experimental results.     

A least squares finite element method for viscoelastic fluid flow problems

Viscoelastic flows remain a demanding class of problems for approximate analysis, particularly at increasing Weissenberg numbers. Part of the difficulty stems from the convective behavior and in the treatment of the stress field as a primary unknown. This latter aspect has led to the use of higher-order piecewise approximations for the stress approximation spaces in recent finite element research. The computational complexity of the discretized problem is increased significantly by this approach but at present it appears the most viable technique for solving these problems. Motivated by recent success in treating mixed systems and convective problems, we formulate here a least squares finite element method for the viscoelastic flow problem. Numerical experiments are conducted to test the method and examine its strengths and limitations. Some difficulties and open issues are identified through the numerical experiments. We consider the use of high degree elements (p refinement) to improve performance and accuracy.     

水解聚丙烯酰胺溶液粘弹特性的研究

通过锥板测量系统对水解聚丙烯酰胺(HPAM)溶液的粘弹性进行了研究.结果表明, 这种锥板测量系统能较灵敏地检测出溶液粘弹性结构的存在,并得到了聚合物溶液的弹性成份和粘性成份的关系.发现随着HPAM溶液浓度的增大,聚合物溶液的弹性成份起初迅速增大,随后增大的趋势变慢而趋于平缓,在经历一最大值后又略有下降.在剪切速率&#7773; =0.36 s－1下,超高分子量的HPAM(M=1.65×107)溶液(c = 1.5 g·L－1)具有明显的粘弹特性;随着盐的加入,溶液的粘弹性下降,当盐浓度达到一定值的时候,溶液内部的网络结构遭到破坏,其弹性行为完全消失.对于聚丙烯酰胺(PAAM, M=2.0×105)溶液(c = 2.0 g·L－1)在剪切速率(&#7773;=0.36～1.36 s－1)范围内没有观察到粘弹行为,只在&#7773;≥1.65 s－1时,才能观察到微弱的粘弹现象.     

Enhanced rheological properties and performance of viscoelastic surfactant fluids with embedded nanoparticles

A combination of viscoelastic surfactants with nanoparticles gives a new class of functional self-assembled materials promising for a large variety of applications. Nanoparticles improve the rheological properties of these systems because of the incorporation into the network of entangled wormlike micelles by linking to micellar end-caps, thus leading to elongation or cross-linking of the micelles. The present article reviews recent studies of these hybrid systems. Mechanisms of the interaction of nanoparticles with wormlike surfactant micelles as well as factors favoring the enhancement of rheological properties of viscoelastic surfactants by added nanoparticles are discussed, providing ways for proper design of such systems in the future. It is shown that viscoelastic surfactants modified with nanoparticles display very attractive features for practical applications, in particular, for fracturing fluids in oil recovery.     

Effect of magnetic field on electroosmotic flow of viscoelastic fluids in a microchannel

Electroosmotic flow is an efficient transportation technology driven by applying an external electric field across the microchannel, which has a great potential for future application. This work is presented to study the unsteady electroosmotic flow of viscoelastic fluids combined with a constant pressure gradient and a vertical magnetic field through a parallel plate microchannel. For the reason that the upper and bottom walls of the parallel plate microchannel in microfluidic devices can be made of different materials, this leads to different hydrophobic properties, asymmetric zeta wall potentials, and different slip boundary conditions. The Navier slip model with different slip coefficients at walls is considered. The generalized Maxwell fluid with fractional derivative is adopted for the constitutive equation of the fluid. The analytical and numerical solutions of velocity are derived by employing the integral transform method and finite difference method, respectively. Excellent agreement is found between the numerical solutions and analytical solutions. Finally, the effects of fractional parameter , relaxation time , slip coefficients and , the ratio of wall zeta potentials , Hartmann number , and electrical field strength parameter on velocity profiles are interpreted graphically in detail.     

Nonlinear vibration analysis of isotropic cantilever plate with viscoelastic laminate

The nonlinear vibration of an isotropic cantilever plate with viscoelastic laminate is investigated in this article. Based on the Von Karman’s nonlinear geometry and using the methods of multiple scales and finite difference, the dimensionless nonlinear equations of motion are analyzed and solved. The solvability condition of nonlinear equations is obtained by eliminating secular terms and, finally, nonlinear natural frequencies and mode-shapes are obtained. Knowing that the linear vibration of this type of plate does not have exact solution, Ritz method is employed to obtain semi-analytical nonlinear mode-shapes of transverse vibration of this plate. Airy stress function and Galerkin method are employed to reduce nonlinear PDEs into an ODE of duffing type. Stability of plate and chaotic behavior are investigated by Runge–Kutta method. Poincare section diagrams are in good agreement with results of Lyapunov criteria.