Viscosity isotropic

Eddy kinematic viscosity, isotropic turbulence 702 penetration of laminar sub-layer 701... 

The greater the extent of the fluorophore s rotation, as in low-viscosity isotropic media, the greater the rotational correlation time for the probe s motion, and the greater the perpendicular fluorescence intensity component will be, resulting in... 

A particularly interesting test of the above rule of thumb would be blends containing the HIQ polymer described in Section 5.4.2 in which the unusual positive thermal coefficient of viscosity was attributed to the coexistence of isotropic and anisotropic domains of the coploymer, as determined by the distribution of copolymer ratios and therefore local chain stiffness. As temperature increased, the fraction of the high viscosity isotropic phase increases at the expense of the low-viscosity anisotropic phase. This polymer by itself as the LCP component would open a degree of freedom in varying the viscosity ratio. Furthermore, blending this HIQ LCP with more conventional LCPs with which it is misdble would expand the window of control of the LCP component. 

We call the correlation time it is equal to 1/6 Dj, where Dj is the rotational diffusion coefficient. The correlation time increases with increasing molecular size and with increasing solvent viscosity, equation Bl.13.11 and equation B 1.13.12 describe the rotational Brownian motion of a rigid sphere in a continuous and isotropic medium. With the Lorentzian spectral densities of equation B 1.13.12. it is simple to calculate the relevant transition probabilities. In this way, we can use e.g. equation B 1.13.5 to obtain for a carbon-13... 

Flow behaviour of polymer melts is still difficult to predict in detail. Here, we only mention two aspects. The viscosity of a polymer melt decreases with increasing shear rate. This phenomenon is called shear thinning [48]. Another particularity of the flow of non-Newtonian liquids is the appearance of stress nonnal to the shear direction [48]. This type of stress is responsible for the expansion of a polymer melt at the exit of a tube that it was forced tlirough. Shear thinning and nonnal stress are both due to the change of the chain confonnation under large shear. On the one hand, the compressed coil cross section leads to a smaller viscosity. On the other hand, when the stress is released, as for example at the exit of a tube, the coils fold back to their isotropic confonnation and, thus, give rise to the lateral expansion of the melt. 

In packed beds of particles possessing small pores, dilute aqueous solutions of hydroly2ed polyacrylamide will sometimes exhibit dilatant behavior iastead of the usual shear thinning behavior seen ia simple shear or Couette flow. In elongational flow, such as flow through porous sandstone, flow resistance can iacrease with flow rate due to iacreases ia elongational viscosity and normal stress differences. The iacrease ia normal stress differences with shear rate is typical of isotropic polymer solutions. Normal stress differences of anisotropic polymers, such as xanthan ia water, are shear rate iadependent (25,26). 

Reynolds Stress Models. Eddy viscosity is a useful concept from a computational perspective, but it has questionable physical basis. Models employing eddy viscosity assume that the turbulence is isotropic, ie, u u = u u = and u[ u = u u = u[ = 0. Another limitation is that the... 

Molecules of nematic Hquid crystals also are aligned in flow fields which results in a viscosity that is lower than that of the isotropic Hquid the rod-shaped molecules easily stream past one another when oriented. Flow may be impeded if an electric or magnetic field is appHed to counter the flow orientation the viscosity then becomes an anisotropic property. 

The load or stress has another effect on the creep behavior of most plastics. The volume of isotropic or amorphous plastic increases as it is stretched unless it has a Poisson ratio of 0.50. At least part of this increase in volume manifests itself as an increase in free volume and a simultaneous decrease in viscosity. This decrease in turn shifts the retardation times to being shorter. 

Continuous transition of state is possible only between isotropic states it may thus occur between amorphous glass (i.e., supercooled liquid of great viscosity) and liquid ( sealing-wax type of fusion ), or between liquid and vapour, but probably never between anisotropic forms, or between these and isotropic states. This conclusion, derived from purely thermodynamic considerations, is also supported by molecular theory. 

Characterization439 Inherent viscosity before and after solid-sate polymerization is 0.46 and 3.20 dL/g, respectively (0.5 g/dL in pentafluorophenol at 25°C). DSC Tg = 135°C, Tm = 317°C. A copolyester of similar composition440 exhibited a liquid crystalline behavior with crystal-nematic and nematic-isotropic transition temperatures at 307 and 410°C, respectively (measured by DSC and hot-stage polarizing microscopy). The high-resolution solid-state 13C NMR study of a copolyester with a composition corresponding to z2/zi = 1-35 has been reported.441... 

In formulating liquid detergent products with LAS, the carbon chain distribution, phenyl isomer distribution, and DATS level can all contribute to the solubility and viscosity characteristics. Hydrotrope requirements for isotropic liquid detergents can vary widely for different types of commercial LAS. 

Benzene is an isotropic solvent its viscosity is the same in every direction. However, a liquid crystal solvent is an anisotropic solvent its viscosity is smaller in the direction parallel to the long axis of the molecule than the perpendicular direction. Methylhenzene is a small, spherical molecule, so its interactions with either solvent are similar in all directions. 

A review of the literature demonstrates some trends concerning the effect of the polymer backbone on the thermotropic behavior of side-chain liquid crystalline polymers. In comparison to low molar mass liquid crystals, the thermal stability of the mesophase increases upon polymerization (3,5,18). However, due to increasing viscosity as the degree of polymerization increases, structural rearrangements are slowed down. Perhaps this is why the isotropization temperature increases up to a critical value as the degree of polymerization increases (18). 

Usually, however, the stresses are modeled with the help of a single turbulent viscosity coefficient that presumes isotropic turbulent transport. In the RANS-approach, a turbulent or eddy viscosity coefficient, vt, covers the momentum transport by the full spectrum of turbulent scales (eddies). Frisch (1995) recollects that as early as 1870 Boussinesq stressed turbulence greatly increases viscosity and proposed an expression for the eddy viscosity. The eventual set of equations runs as... 

The (isotropic) eddy viscosity concept and the use of a k i model are known to be inappropriate in rotating and/or strongly 3-D flows (see, e.g., Wilcox, 1993). This issue will be addressed in more detail in Section IV. Some researchers prefer different models for the eddy viscosity, such as the k o> model (where o> denotes vorticity) that performs better in regions closer to walls. For this latter reason, the k-e model and the k-co model are often blended into the so-called Shear-Stress-Transport (SST) model (Menter, 1994) with the view of using these two models in those regions of the flow domain where they perform best. In spite of these objections, however, RANS simulations mostly exploit the eddy viscosity concept rather than the more delicate and time-consuming RSM turbulence model. They deliver simulation results of in many cases reasonable or sufficient accuracy in a cost-effective way. 

The Reynolds-averaged approach is widely used for engineering calculations, and typically includes models such as Spalart-Allmaras, k-e and its variants, k-co, and the Reynolds stress model (RSM). The Boussinesq hypothesis, which assumes pt to be an isotropic scalar quantity, is used in the Spalart-Allmaras model, the k-s models, and the k-co models. The advantage of this approach is the relatively low computational cost associated with the computation of the turbulent viscosity, fit. For the Spalart-Allmaras model, one additional transport equation representing turbulent viscosity is solved. In the case of the k-e and k-co models, two additional transport equations for the turbulence kinetic energy, k, and either the turbulence dissipation rate, s, or the specific dissipation rate, co, are solved, and pt is computed as a function of k and either e or co. Alternatively, in the RSM approach, transport equations can be solved for each of the terms in the Reynolds stress tensor. An additional scale-determining equation (usually for s) is also required. This means that seven additional transport equations must be solved in 3D flows. 

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