Viscosity coefficients experimental determination

Experimental Determination of the Viscosity and Normal Stress Difference Coefficients, 94... 

EXPERIMENTAL DETERMINATION OF THE VISCOSITY AND NORMAL STRESS DIFFERENCE COEFFICIENTS... 

At the comparison of concentration dependencies of the characteristic quantities (6.61) with experimental determinations, one has to remember that effect of excluded volume was not taken into account in equations (6.61), which allow us to say only about qualitative correspondence. The behaviour of the initial viscosity is the most widely studied (Poh and Ong 1984, Takahashi et al. 1985). The concentration dependence of the viscosity coefficient in the melt-like region can be represented by a power law (Phillies 1995). The index can be found to be approximately 25 + 1, in accordance with (6.61). There are some differences in the behaviour of polymer solutions, which are connected with different behaviour of macromolecular coils at dilution. 

Experimental determination of viscosity and normal stress coefficients Since the range of rj may extend from 10 2 to 1011 N s/m2 and the normal stress coefficients, Tj and Tj, cover also a wide range of values, a number of different experimental techniques have been developed to cover this wide range. Some methods are listed in Table 15.2. 

Abstract—Gas-liquid interfacial areas a and volumetric liquid-side mass-transfer coefficients kLa are experimentally determined in a high pressure trickle-bed reactor up to 3.2 MPa. Fast and slow absorption of carbon dioxide in aqueous and organic diethanolamine solutions are employed as model reactions for the evaluation of a and kLa at high pressure, and various liquid viscosities and packing characteristics. A simple model to estimate a and kLa for the low interaction regime in high pressure trickle-bed reactors is proposed. 

For ellipsoids of revolution the numerical values of va and vb have been tabulated by Scheraga (1955), and the sum of va and vb (i.e., vr at oj = 0) is identical with the viscosity increment from Simha s equation. Thus Eq. (43) provides an alternative method to that of the non-Newtonian viscosity for the determination of the rotary diffusion coefficient, 0. Cerf has also pointed out that 0 is determinable from the slope at the inflection point (I.P.) of the vr versus w-curve, i.e., w(I.P.) = 2 /30. At present, however, no experimental test of Eq. (43) has as yet been reported. 

The extraction (and hence the transport) efficiency depends on several diluent factors such as Schmidt empirical diluent parameter [124,125], the Swain s acity and basity parameters along with the Dimroth and Reichardt polarity indices [126], dielectric constant [127], refractive index [127] and viscosity [127], and the Hildebrand s solubility parameter [128]. The permeability coefficients (Paio) were computed from the Wlke-Chang, Scheibel, and Ratcliff [129,130] equations, which compared reasonably well with the experimentally determined values as shown in Table 31.10. Efiiassadi and Do [131] have, on the other hand, taken into account only the viscosity and solubility effect of the diluent and the carrier immobilized in SLM. They have reported that these two factors influenced the transport rates significantly. 

The coefficients fco and kj, have been experimentally determined for many mass transfer systems and correlated with gas and liquid flow rates, liquid density and viscosity, the diffusivity of A in the gas and the liquid, and the physical dimensions of the systems. Dimensional analysis suggests that dimensionless quantities of the form... 

Figure 1.24 shows experimental determinations of the intrinsic viscosity. When both the Huggins and Kraemer equations provide the same intrinsic viscosity and Huggins coefficient, the higher-order terms in these equations can be safely ignored. On the other hand, if the Huggins and Kraemer plots are curved and do not give the same intercept, viscosity measurements need... 

We could use a simplified form of rj z) = ri f z). Here is the bulk viscosity, and /(z) can be experimentally determined. Here, z is the distance normal to the solid surface. A partial justification for the above functional form can be drawn from the temperature dependence of the surface diffusion coefficient and the bulk viscosity,or the fly stiction correlation with the bulk viscosity. To develop a rigorous hydro-dynamic model, we need better rheological data and more details are given in the following section on Rheology Measurement. 

The experimentally determined frictional coefficient was 5.93X10-10 g/sec and leads to some minor improvement in the above calculated viscosity coefficients. 

Experimental determination of the diffusion coefficients D is enough complicated and labor intensive process, whereas the experimental determination of the coefficients of viscosity doesn t strike the great eomplieations. Established long ago the empirical Walden s rule... 

Application of the Smoluchowski equation (1.3) requires a knowledge of the sizes and diffusion coefficients of molecules. An estimate of the effective values of r can usually be made from molecular volumes. Diffusion coefficients present more of a problem, since not very many have been experimentally determined over a range of temperature. They may, however, be eliminated from Equation (1.3) by using the Stokes-Einstein relation, which is theoretically derived from the same molecular model and is often in fairly good accord with experimental data it expresses D in terms of the viscosity of the solvent (t)) and the... 

To apply this relation we need to know the diffusion coefficients but for many systems of interest these have not been measured, and it would be very convenient to have expressions relating Dab to molecular sizes (which can usually be estimated) along with the viscosity of the solvent, so that values of Dab could be estimated. Such relations, of which the Stokes-Einstein equations are the best known, can be obtained by applying classical hydrodynamics on the assumption that the motions of molecules can be treated like those of macroscopic particles of simple shapes. Comparisons with the experimental values show how far these hydrodynamic values are reliable. The result is that, for many reactions in solution, fairly good estimates of diffusion coefficients and their temperature coefficients can be made, but that for special cases such as high-viscosity solvents it is important to use experimentally-determined values. 

In order to apply the Smoluchowski equation (Equations (1.3), (2.1), (3.29)), we need values for the least distance of approach (rAn) and the diffusion coefficient (Dab)- The value of tab can be estimated from molecular volumes (Section 2.5.1.2). The diffusion coefficient can be determined by various methods, but experimental values are available only for a minority of the myriad possible situations. A common practice is to use the Stokes-Einstein relation (Section 1.2.3), which rests on the assumption that solute molecules in motion behave like macroscopic particles to which classical hydrodynamic theory can be applied. We shall first outline (a) the relation between the diffusion coefficient D and the mechanics of motion of particles in fluids, leading to the Stokes-Einstein equation relating D to solute size and solvent viscosity and (b) the direct experimental determination of D. We shall then (c) compare the results and note the reservations that are required in relying on the Stokes-Einstein estimates of D in various cases. 

The transverse pressure gradient passes through a maximum at approximately =45°. A transverse pressure for this case and an angle dependence according to Eq. (57) has been experimentally confirmed [41]. In principle this experiment can be used for the determination of viscosity coefficient ratios. Because of experimental difficulties it should only be used to demonstrate the tensor property of the viscosity of nematic liquid crystals. 

The six Leslie coefficients can not be measured directly. They can only be determined with the aid of several experimental methods which ususally lead to combinations of these coefficients. Taking into account the Parodi equation, the six coefficients can be obtained from five linear independent viscosity coefficients. Thus, the four viscosity coefficients rji, rj2 and t/j2 and the rotational viscosity coefficient /] give a, = r)i2... 

The flow properties of a SmC phase with fixed director orientation and a flow parallel to the layers can, therefore, be described by seven independent viscosity coefficients. The experimental determination of these coefficients should be connected with a series of problems. If the coefficients 774 or 775 are determined in a capillary with a rectangular cross section with T< W and the layer parallel to one of the plates as in Fig. 20 I. The thickness has to be constant over the whole sample with an accuracy that is not easy achieved [63,64]. There are similar problems in the measurement of the other coefficients. Minor difficulties should occur in a shear experiment with a small lateral movement of one of the plates. 

This section covers experimental methods for the determination of shear and rotational viscosity coefficients of monomeric nematic liquid crystals and experimental results on this topic. Polymeric nematic liquid crystals are dealt with in Chap. V in Vol. 3 of this Handbook. 

A discussion of the influence of molecular form and structure on the shear viscosity coefficients is desirable but impossible on the basis of the available experimental data. The number of liquid crystals that have been investigated is small and the coefficients determined with different methods show different accuracies. The following list summarizes the most important investigations ... 

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