Dynamic shear flow

The most Important commercial blends of PE are those of LLDPE with LDPE (25, 26). The capillary flow data n (012) and B 8(012), Indicated (similar to HDPE/LDPE) PDB-type behavior (27-29). The latter authors also reported a PDB relation between melt strength and composition. Kecently (14, 15) these blende were studied under the steady state and dynamic shear flow as well as in uniaxial extension. A more detailed review of these results will be given in part 3 of this chapter. Like HDPE/LDPE blends, those of LLDPE/LDPE type are also consistently reported as immiscible. 

A standard commercial film blowing LLDPE resin, LPX-30, was blended at different ratios with either other LLDPE s or a LDPE polymer. The characteristic properties of these materials are listed In Table II. The resins were generously donated to the project by Esso Chem., Canada. Prior to blending the polymers were thoroughly characterized by SEC, SEC/LALLS, solution viscosity, CNMR, Atomic Absorbance, and their rheological behavior was characterized In steady state and dynamic shear flow as well as In the uniaxial extenslonal deformation (44-46). 

PS/PVME thermodynamic influence, dynamic shear flow Schneider Brekner, 1985 Brekner et a/., 1985 Yang et al., 1986... 

Dynamic shear flow within the linear viscoelastic region was used to determine binodal and spinodal temperatures (Tb and T, respectively) in LCST-type... 

Small-amplitude oscillatory flow is often referred to as dynamic shear flow. Fluid deformation under d)mamic simple shear flow can be described by considering ttie fluid wiflun a small gap dX2 between two large parallel plates of which the upper one undergoes small amplitude oscillations in its own plane with a frequency velocity field within the gap can be given by d , = ydxj but y is not a constant as in steady simple shear. Instead it varies sinusoidally and is given by... 

The shear stress in simple dynamic shear flow is expressed in terms of the amplitude and phase shift functions of the frequency as,... 

The Prandtl mixing length concept is useful for shear flows parallel to walls, but is inadequate for more general three-dimensional flows. A more complicated semiempirical model commonly used in numerical computations, and found in most commercial software for computational fluid dynamics (CFD see the following subsection), is the A — model described by Launder and Spaulding (Lectures in Mathematical Models of Turbulence, Academic, London, 1972). In this model the eddy viscosity is assumed proportional to the ratio /cVe. 

David.son, L, Large eddy simulation A dynamic one-equation subgrid model for three-dimensional recirculating flow. In llth Int. Symp. on Turbulent Shear Flow, vol. 3, pp. 26.1-26.6, Grenoble, 1997. 

Molecular dynamics, in contrast to MC simulations, is a typical model in which hydrodynamic effects are incorporated in the behavior of polymer solutions and may be properly accounted for. In the so-called nonequilibrium molecular dynamics method [54], Newton s equations of a (classical) many-particle problem are iteratively solved whereby quantities of both macroscopic and microscopic interest are expressed in terms of the configurational quantities such as the space coordinates or velocities of all particles. In addition, shear flow may be imposed by the homogeneous shear flow algorithm of Evans [56]. 

M. Kroger, R. Makhloufi. Wormlike micelles under shear flow A microscopic model studied by nonequihbrium molecular dynamics computer simulations. Phys Rev E 55 2531-2536, 1996. 

During dynamic measurements frequency dependences of the components of a complex modulus G or dynamic viscosity T (r = G"/es) are determined. Due to the existence of a well-known analogy between the functions r(y) or G"(co) as well as between G and normal stresses at shear flow a, seemingly, we may expect that dynamic measurements in principle will give the same information as measurements of the flow curve [1],... 

The rheological behavior of storage XGs was characterized by steady and dynamic shear rheometry [104,266]. Tamarind seed XG [266] showed a marked dependence of zero-shear viscosity on concentration in the semi-dilute region, which was similar to that of other stiff neutral polysaccharides, and ascribed to hyper-entanglements. In a later paper [292], the flow properties of XGs from different plant species, namely, suspension-cultured tobacco cells, apple pomace, and tamarind seed, were compared. The three XGs differed in composition and structural features (as mentioned in the former section) and... 

Bentley, B. J., and Leal, L. G., A computer-controlled four-roll mill for investigations of particle and drop dynamics in two-dimensional linear shear flows. J. Fluid Mech. 167, 219-240 (1986). 

H. Noguchi and G. Gompper, Dynamics of fluid vesicles in shear flow effect of membrane viscosity and thermal fluctuations, Phys. Rev. E 72, 011901 (2005). 

R. G. Winkler, K. Mussawisade, M. Ripoll, and G. Gompper, Rod-like colloids and polymers in shear flow a multi-particle-collision dynamics study, J. Phys. Condens. Matter 16, S3941 (2004). 

We have now to go one step further and to build stellar evolution models where the transport of angular momentum will be followed self-consistently under the action of meridional circulation, shear turbulence, and internal gravity waves. In this path some important aspects still need to be clarified Can we better describe the excitation mechanisms and evaluate in a more reliable way the quantitative properties of the wave spectra What is the direct contribution of 1GW to the transport of chemicals, especially in the dynamical shear layer produced just below the convective envelope by the wave-mean flow interaction What is the influence of the Coriolis force on IGW How do 1GW interact with a magnetic field Work is in progress in this direction. 

Viscosity, defined as the resistance of a liquid to flow under an applied stress, is not only a property of bulk liquids but of interfacial systems as well. The viscosity of an insoluble monolayer in a fluid-like state may be measured quantitatively by the viscous traction method (Manheimer and Schechter, 1970), wave-damping (Langmuir and Schaefer, 1937), dynamic light scattering (Sauer et al, 1988) or surface canal viscometry (Harkins and Kirkwood, 1938 Washburn and Wakeham, 1938). Of these, the last is the most sensitive and experimentally feasible, and allows for the determination of Newtonian versus non-Newtonian shear flow. 

Control in Non-Equilibrium-Molecular-Dynamics Simulations of the Shear Flow of Dense Liquids. 

The phase angle changes with frequency and this is shown in Figure 4.7. As the frequency increases the sample becomes more elastic. Thus the phase difference between the stress and the strain reduces. There is an important feature that we can obtain from the dynamic response of a viscoelastic model and that is the dynamic viscosity. In oscillatory flow there is an analogue to the viscosity measured in continuous shear flow. We can illustrate this by considering the relationship between the stress and the strain. This defines the complex modulus ... 

Chang, E. J., and K. Kailasanath. 1996. Simulations of particle dynamics in a confined shear flow. AIAA J. 34 1160-66. 

Grinstein, F.F., and K. Kailasanath. 1992. Chemical energy release and dynamics of transitional reactive, free shear flows. J. Physics Fluids A 4 2207. 

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