Transient viscoelastic flow

J. Baranger and S. Wardi, Numerical analysis of a finite element method for a transient viscoelastic flow, Comput. Meth. Appl. Mech. Engrg., 125 (1995) 171-185. 

Kokini, J. L. and Dickie, A. 1981. An attempt to identify and model transient viscoelastic flow in foods. J. Texture Stud. 12 539-557,... 

Leppard, W. R. and Christiansen, E. B. 1975. Transient viscoelastic flow of polymer solutions. Am. Inst. Chem. Engrs. J. 21 999-1006. 

Einstein A (1906) A new determination of molecular dimensions. Annu Physik 19 289-306. Corrections, ibid. (1911) 34 591-592. hr Ftirth R ( 1956) (ed) Investigations on the TheOTy of the Brownian Movement (Translated by Cowper AD). Dover, New York Ellero M, Tanner RI (2005) SPH simulations of transient viscoelastic flows at low Reynolds number. J Non-Newtonian Fluid Meeh 132 61-72 Ericksen JL (1960) Anistropic fluids. Arch Rat Mech Anal 4 231-237... 

Wapperom, P., Keunings, R., and Legat, V. (2000) The backward-tracking Lagrangian particle method for transient viscoelastic flows./. Non-Newtonian Fluid Mech., 91, 273-295. 

Currently, the CVFEM and CONNFFESSIT methods are decoupled. We will combine them together to carry out the transient viscoelastic flow simulation in the micro-injection molding. 

The experimental ranges of strain rates (or strains) are summarized in Table 2 for the various types of experiments. Time-temperatiire superposition was successfully applied on the various steady shear flow and transient shear flow data. The shift factors were foimd to be exactly the same as those obtained for the dynamic data in the linear viscoelastic domain. Moreover, these were found to be also applicable in the case of entrance pressure losses leading to an implicit appUcation to elongational values. 

In transient shear flows starting from an isotropic distribution of fiber orientations, considerably higher viscosities will be initially observed, until the fibers become oriented. In Bibbo s experiments, t]r for isotropically oriented fibers is around 3.5 for v = 75. These viscosities can also be predicted reasonably well by semidilute theory and by simulations (Mackaplow and Shaqfeh 1996). Figure 6-25 shows the shear stress as a function of strain for a polyamide 6 melt with 30% by weight glass fibers of various aspect ratios, where the fibers were initially oriented in the flow-gradient direction. Notice the occurrence of a stress overshoot (presumably due to polymer viscoelasticity), followed by a decrease in viscosity, as the fibers are reoriented into the flow direction. 

Pang JN, Owens RG, Tacher L, Parriaux A (2006) A numerical study of the SPH method for simulating transient viscoelastic free surface flow. J Non-Newtonian Fluid Mech 139 68-84 Feng J, Leal LG (1997) Simulating complex flows of liquid crystalline polymer using the Doi theory. J Rheol 41 1317—1335... 

Our simulations of the above viscoelastic nematodynamics theory require the reliable and representative rheological data for LCPs, obtained for steady and transient shear flows and relaxation. We chose literature rheological data for two commercial LCPs, Titan and Zenith 6000 [49], as well as for two model polymers, a main-chain LCP, PSHQ9, and a side-chain LCP, PI-14-5CN [53]. 

The Larson-Doi theory predicts qualitatively the essential features of transient shear flow of some model TLCPs (Ugaz 1999). It is, however, not clear to what extent the Larson-Doi theory can describe the dynamics of TLCPs that do not exhibit tumbling. This is because the Larson-Doi theory is based on the Ericksen-Leslie theory, which determines structural responses through the tumbling parameter A,. As will be presented later in this chapter, the experimental data available to date suggest that TLCPs are flow aligning. It is fair to state that the theoretical attempts reported thus far contain, understandably, many crude approximations, and so do not warrant quantitative comparison with experimental results for textured LCPs, particularly TLCPs. Thus the development of a molecular viscoelastic theory for textured LCPs is still in its infancy. 

With regard to constitutive equations, White (13) notes that, in view of the short residence time of the polymer in the nip region (of the order of magnitude of seconds), it would be far more realistic to use a constitutive equation that includes viscoelastic transient effects such as stress overshoot, a situation comparable to that of squeezing flows discussed in Section 6.6. 

The purpose of this paper is to explore various aspects of the rheological behaviour of lyotropic liquid crystalline systems. Lyotropics are often used as model systems for thermotropics because their viscoelastic behaviour seems to be quite similar (1) and solutions are much more easier to handle and can be studied more accurately than melts. The emphasis is on transient data as these are essential for verifying viscoelastic models but are hardly available in the literature. Transient experiments can also provide insight in the development of flow—induced orientation and structure. The reported experiments include relaxation of the shear stress and evolution of... 

Keywords Colloidal dispersion Flow curve Glass transition Integration through transients approach Linear viscoelasticity Mode coupling theory Nonlinear rheology Non-equilibrium stationary state Shear modulus Steady shear... 

Calendering takes place at a transient temperature between the polymer viscoelastic and viscous-flow states. Thermoplastic materials displaying a wide range of the flow temperatures and sufficient melt viscosity (e.g. PVC)... 

The attempts to model the hydrodynamics of mbdng devices were made only in Refs. [20] and [21] concerning the estimate of the role of viscoelastic effects. In Ref. [20], the stream-lines for a model agitator in the form of a sphere are studied the flow patterns are defined (a) typical for viscous liquid, (P) transient, (y) typical for elastic liquid. The most important result of RdF. [20] is the finding that the transition from one type of the flow to another is defined by the ratio of Weissenberg and Reynolds Numbers ... 

So, the mixtures show a viscoelastic behavior which is very different from neat PPS. Strong solid-like responses in the small amplitude oscillatory shear flow are observed. After quiescent annealing, a strainscaling transient stress behavior is observed in the mixtures in the reverse flow [61]. 

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