Ordered fluids

Cladis PE, Finn PL, Goodby JW (1984) In Griffin AC, Johnson JF (eds) Liquid crystals and ordered fluids, vol 4. Plenum Press, New York, p 203... 

The relationship between film thickness of hexadecane with the addition of cholesteryl LCs and rolling speed under different pressures is shown in Fig. 25 [50], where the straight line is the theoretic film thickness calculated from the Hamrock-Dowson formula based on the bulk viscosity under the pressure of 0.174 GPa. It can be seen that for all lubricants, when speed is high, it is in the EHL regime and a speed index 4> about 0.67 is produced. When the rolling speed decreases and the film thickness falls to about 30 nm, the static adsorption film and ordered fluid film cannot be negligible, and the gradient reduces to less than 0.67 and the transition from EHL to TFL occurs. For pure hexadecane, due to the weak interaction between hexadecane molecules and metal surfaces, the static and ordered films are very thin. EHL... 

General Flow Properties for Nematic-like Ordered Fluids... 

Using this equation an attempt was made to find a critical Re-number which could be correlated to the onset of vortices observed with the naked eye, as has been done, for example, for Newtonian fluids [93], but no correlation could be found [88]. The reason is probably due to the fact that polymer solutions are viscoelastic fluids, also called second-order fluids. 

In a first-order fluid (Newtonian) only significant dimensionless groups can be derived which include elastic behaviour [88]. 

Lyotropic polymeric LC, formed by dissolving two aromatic polyamides in concentrated sulphuric acid, have been studied using variable-director 13C NMR experiments.324 The experimental line shapes at different angles w.r.t the external field were used to extract macromolecular order and dynamic in these ordered fluids. An interesting application of lyotropic LC is for the chiral discrimination of R- and S-enantiomers, and has recently been demonstrated by Courtieu and co-workers.325 The idea was to include a chiral compound 1-deutero-l-phenylethanol in a chiral cage (e.g., /1-cyclodextrin) which was dissolved and oriented by the nematic mean field in a cromolyn-water system. Proton-decoupled 2H NMR spectrum clearly showed the quad-rupolar splittings of the R- and S-enantiomers. The technique is applicable to water-soluble solutes. 

It may be desirable to define certain basic physical processes afresh, when we are dealing with systems essentially subject to two-dimensional conformations and hence two-dimensional constraints. This is the case for membranes, and also for a number of alkali salts of alkali -alkane carboxylates. These melt to give mesophases, in which the anions and cations are arranged in layerlike structures. At considerably higher temperatures the mesophases pass into isotropic ionic melts, but in the intervening temperature range they exhibit marked anisotropy of optical and physical properties. In these mesophases, which are ordered fluid... 

MD simulations, complete with ghost particle insertions (160, 161), may be used to obtain static and dynamic information. (These particle insertions were performed after the MD runs and do not affect the calculations they merely probe the insertion of particles into the system.) The MD simulations performed by Snurr et al. (155) were slightly more expensive than the GC-MC calculations, but they produced similar isotherms and also yielded important information about the structure of the adsorbed fluid. The methane molecules appeared to behave like an ordered fluid at all concentrations, although the structure does change. This change reflects the changing importance of sorbate-sorbate and zeolite-sorbate interactions as a function of loading. 

Coleman,B.D., Markovitz,H. Normal stress effects in second-order fluids. J. Appl. Phys. 35,1-9 (1964). 

This behaviour of the extinction angles is in accordance with eq. (1.3), if % = In fact, for a second order fluid the first normal stress difference increases with the square of the shear rate, whereas the shear stress increases with the first power of this rate (constant viscosity). As a consequence, it follows from eq. (1.3) that cot 2% increases linearly. From this fact the above mentioned linear behaviour of the extinction angle curve is deduced, since... 

Fig. 1.4 gives such a plot, which was prepared by Philippoff (8,9) from his early measurements on a 15 per cent solution of polyisobutylene (P-100) in decalin (measurement temperatures 30 and 50°C). From this figure it is clearly seen that An as a function of p21 is non-linear. In contrast to the above mentioned solution of S 111 in methyl 4-bromo-phenyl carbinol, the solution of the poly-isobutylene P-100 in decalin does not form a second order fluid. However, for the product A n sin 2%, one obtains a beautiful straight line. The stress-optical law seems to hold also for this more general type of fluid. ... 

There are some interesting points to be noted. First, it seems that also for polymer melts the normal stress differences (fin — fi22) and (fin—fi33) are practically equal. (Similar results have been obtained for melts of several polyethylenes.) Second, for the investigated polystyrene a practically quadratic dependence of nn — n33 on the shear stress is found up to the point of the inset of an extrusion defect. It is noteworthy that Fig. 1.9 shows no quadratic dependence of Pjd vs Ds, as would be expected for a second order fluid. Third, the measurements in the cone-and-plate apparatus have to be stopped at a shear stress at least one... 

As is well-known, this pair of expressions will not be valid for the most general case of a second order fluid, since p22 — tzi must not necessarily vanish for such a fluid. Eq. (2.9) states that the first normal stress difference is equal to twice the free energy stored per unit of volume in steady shear flow. In Section 2.6.2 it will be shown that the simultaneous validity of eqs. (2.9) and (2.10) can probably quite generally be explained as a consequence of the assumption that polymeric liquids consist of statistically coiled chain molecules (Gaussian chains). In this way, the experimental results shown in Figs. 1.7, 1.8 and 1.10, can be understood. 

The course of this curve suggests that the theoretical slope two, which should hold for a second order fluid, will be reached only at shear rates or angular frequencies considerably lower than the ones used in the experiments. It thus appears that the interrelations given by the above mentioned equations hold even outside the literal range of validity of the discussed theory. Similar results were obtained for two samples of linear polyethylene. 

The trouble is that, under transient conditions, the shear recovery vs. preceding shear deformation can be much more sensitive to deviations from the strict behaviour of a second order fluid than the shear viscosity or the normal stress difference. A few entanglements between extraordinarily long chain molecules may be responsible for a maximum in the shear recovery. If this is the case, a shear recovery higher than the one... 

As a final remark it may be mentioned that the discussed polypropylene melts do not at all behave like second-order fluids in the range of shear rates and angular frequencies accessible to measurement. This is shown in Fig. 4.6. In this figure the doubled extinction angle 2 is plotted... 

It is clearly seen that the validity of the stress-optical law is more general than that of the said relation for second order fluids. As the... 

Bueche-Ferry theory describes a very special second order fluid, the above statement means that a validity of this theory can only be expected at shear rates much lower than those, at which the measurements shown in Fig. 4.6 were possible. In fact, the course of the given experimental curves at low shear rates and frequencies is not known precisely enough. It is imaginable that the initial slope of these curves is, at extremely low shear rates or frequencies, still a factor two higher than the one estimated from the present measurements. This would be sufficient to explain the shift factor of Fig. 4.5, where has been calculated with the aid of the measured non-Newtonian viscosity of the melt. A similar argumentation may perhaps be valid with respect to the "too low /efi-values of the high molecular weight polystyrenes (Fig. 4.4). 

H. Finkelmann, B. Liihmann, G. Rehage, H. Stevens in Liquid Crystals and Ordered Fluids , eds. Johnson and Porter, Plenum Press, Vol. 4, in press... 

Despite their complexity, the dynamics in these systems is fast with the molecules flipping and changing their positions. In fact these are ordered fluids composed of distinct compartments. There are no fixed positions of the molecules but distinct spaces with a maximum time averaged probability for each of the segregated units to be located and these dynamic compartments are arranged periodically in space. The structures are in thermodynamic equilibrium as indicated... 

The self-organization of both thermotropic and lyotropic liquid crystals make these ordered fluids remarkable media for the dispersion and organization (alignment) of CNTs. This subject has been the focus of a recent excellent review by Scalia [231], theoretical work on anchoring at the liquid crystal/CNT interface by Popa-Nita and Kralj [458], and a number of earlier experimental reports on liquid crystal/CNT composites demonstrating that liquid crystal orientational order can be transferred to dispersed CNTs, which is commonly illustrated using polarized Raman spectroscopy [459 -62]. 

Here we have three parameters r/o the zero-shear-rate viscosity, Ai the relaxation time and A2 the retardation time. In the case of A2 = 0 the model reduces to the convected Maxwell model, for Ai = 0 the model simplifies to a second-order fluid with a vanishing second normal stress coefficient [6], and for Ai = A2 the model reduces to a Newtonian fluid with viscosity r/o. If we impose a shear flow,... 

In a complex, polymeric liquid, normal stresses as well as the shear stress can be present, and these contributions will influence the shape of the structure factor. The simplest rheological constitutive model that can account for normal stresses is the second-order fluid model [64], where the first and second normal stress differences are quadratic functions of the shear rate. Calculations using this model [92,93,94,90,60], indicate that the appearance of normal stresses can rotate the structure factor towards the direction of flow in the case of simple shear flow and can induce a four-fold symmetry in the case of exten-sional flow. 

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