Relative viscosity, calculation

Calculations. For determination of the intrinsic viscosity [ti] the prepared pectins were solved in an 0.1 M phosphate buffer with pH 6.0. The relative viscosity was determined by a glass. Ubbelhode viscometer at 25 0.1 °C. The flow time of solvent (L) was 81.8 seconds. At least six pectin solutions with different concentrations were measured in a way that their flow times (ts) comply the order 1.2to[Pg.528]

Table 3.4 Calculation of the Relative Viscosity, Specific Viscosity, and Plotting Parameters for the Data in Table 3.3...

The following is a brief review of the viscosity pareimeters that are commonly used in polymer analyses. The relative viscosity (ripgi) of a polymer saitple solution as defined in Equation 1 can be determined experimentally from the measured viscosity value for the polymer saitple solution (h) and that of the solvent (h )- From the h -1 value and the polymer sanple concentration (c), tne calculations for the other viscosity parameters are possible in accordance to Equations 2 through 5 ... 

Relative viscosities are calculated from viscosities for the individual components at 0° (II7), weighting them on a mole fraction basis. The change in diffusivities and viscosities with temperature and pressure is assumed to be independent of gas mixture. If desired, more accurate calculations of diffusivities and viscosities of gas mixtures can be made using the approaches of Wilke (IIS) and Bromley and Wilke (II0), respectively. Table V presents relative values for Dfree, m, and p across the stagnant film for the gas-carbon reactions. Substituting these values in Equation (42), the relative reaction rates in Zone III for the gas-carbon reactions are calculated and also presented in Table V. Qualitatively, the rates of the carbon-oxygen and carbon-steam reactions are predicted to be about twice the rate... 

The numerical correlations given by the direct BEM simulations are similar to the expressions given earlier. In fact, the first coefficient in the power expansion is close to the one predicted by Einstein [15]. The second coefficient in the power expansion is between the value suggested by Guth and Simha [25] and one suggested by Vand [65, 66], In Figure 10.29, the calculated BEM relative viscosity is collapsed for all cases. 

It has been a common practice to measure the viscosities in a multigradient viscometer. The relative viscosities at each concentration are then plotted against the rates of shear, followed by extrapolation to zero rate of shear and the intrinsic viscosity is calculated from these intercepts for various concentrations in the customary Huggins plot. From both theoretical and experimental considerations, however, the shearing stress rather than the rate of shear should be preferred, although tradition has emphasized the latter (Section IV, C). 

They reported values of A in the range 2.50-3.82 for dispersions of rigid solids, and 1.70-1.85 for red blood suspensions. For gelatinized 2.6% tapioca STDs, the relative viscosity was calculated using Equation 2.30 ... 

Yoo and Rao (1996) studied the influence of two different sizes of tomato pulp particles (TP4 and TP6) at a pulp weight fraction of 17% in terms of Peclet number and relative viscosity (Krieger, 1985 Tsai and Zammouri, 1988). The Peclet numbers (Pe) were calculated using the equation ... 

The relative viscosity of the gelatinized 2.6% tapioca SDs was calculated using Equation 4.45 ... 

Figure 6.29 Zero-shear relative viscosity versus particle volume fraction for aqueous suspensions of charged polystyrene spheres (a = 34 nm) in 5 x lO " M NaCl ( ) (Buscall et al. 1982a). The line is calculated by using Eq. (6-66) for the viscosity, with 0eff given by Eq. (6-64), and d ff by Eq. (6-67a) or (6-67b). The potential 1T(/ ) is given by Eq. (6-58) or (6-59) with k given by Eq. (6-61) the constant K is 0.10, and is in the range 50-90 mV. (From Buscall 1991, reproduced with permission of the Royal Society of Chemistry.)...

Figure 11 shows the relative-viscosity-concentration behavior for a variety of hard-sphere suspensions of uniform-size glass beads. Even though the particle size was varied substantially (0.1 to 440 xm), the relative viscosity is independent of the particle size. However, when the particle diameter was small ( 1 fJLm), the relative viscosity was calculated at high shear rates, so that the effect of Brownian motion was negligible. Figure 8 shows that becomes independent of the particle size at high shear stress (or shear rate). 

On the basis of the analogy with the influence of variable pressure on a material that obeys Hooke s law, Richardson 44) calculated the compressibility of an emulsion whose dispersed-phase volume concentration is increased from + A. From this calculation he derived the following expression for the relative viscosity of concentrated emulsions ... 

As the size ratio of the sand particle to the oil droplets d d increases to about 2, there is less dependence on the oil concentration, as shown in Figure 21b. When the size ratio increases to about 3, as shown in Figure 21c, the relative viscosity becomes independent of the oil concentration this result indicates that the emulsions act as a continuous phase toward the solids. Under this condition, the solids and the droplets behave independently, and no interparticle interaction occurs between the solids and the droplets. Yan et al. (64) showed that when the emulsions behave as a continuous phase toward the solids, the viscosity of the mixtures can be predicted quite accurately from the viscosity data of the pure emulsions and the pure solids suspensions. The viscosity of an emulsion-solids mixture having an oil concentration of Pq (solids-free basis) and a solids volume fraction of 0s (based on the total volume) can be calculated from the following equation ... 

Table 7. Relative viscosity values for povidone in water for calculating the K-value according to Ph.Eur. and USP (capillary viscometer, 25 °C)...

The average molecular weight of povidone is expressed in terms of the K-value in the pharmacopoeias valid in Europe, the USA and Japan [13]. It is calculated from the relative viscosity in water and always forms a part of the commercial name. The K-values specified in Section 2.2.1.2 are the ranges specified in the European Pharmacopoeia (Ph.Eur.). As can be seen from Table 9, the K-value ranges specified in the USP are identical. The USP and Ph.Eur. specify harmonized limits of 85-115% for nominal (= stated) K-values up to 15, while for nominal K-values... 

A simpler method for determining the intrinsic viscosity is to calculate it from the relative viscosity at a single concentration [16] ... 

Pharmacopoeia (e. g. Jap.Ph. XII). It is based on the relative viscosity of a 1% solution of povidone in water and is calculated with the following equation ... 

The viscosity-average of the molecular weight, Mv has attracted greater interest recently, as it can be calculated direct from the relative viscosity, the intrinsic viscosity or the K-value (see Section 2.3.2.2). Table 18 shows typical viscosity-average values for the different povidone types. 

Table 28. The effect of sterilization (20 min at 120 -121 °C) on the relative viscosity and the average molecular weight of aqueous solutions of Kollidon 12 PF and Kollidon 17 PF (calculated according to Section 2.3.2.2)...

Table 30. Calculation of the K-value from the relative viscosity...

The K-value is calculated from the relative viscosity, r rel with the aid of the equation given in Table 30. 

Calculation of M v from the relative viscosity via the intrinsic viscosity... 

The average molecular weight of povidone and copovidone is expressed in terms of the K-value, in accordance with the Pharmacopoeias that apply in Europe and the USA [13]. It is calculated from the relative viscosity in water. The same methods can be applied to copovidone, and they give K-values between the limits given in Section 4.2.I.2. They are based on the relative viscosity of a 1% solution in water at 25°C. The relationship between the K-value and the relative viscosity is shown in Fig. 91. The curve was obtained using the method of determination and calculation described in Section 2.3.2.1. 

It has been known since the work of Einstein (relative viscosity of a dilute solution of large spherical molecules should depend only on the volume fraction occupied by the spheres, and not by their absolute size. The presence of the spheres distorts the stream, lines, as compared with the flow in the pure solvent which would occur at the same velocity gradient. Thereby, the amount of work required to maintain the flow, and hence the viscosity, is increased. In 1922, Jeffery (55) extended Einstein s method of calculation, and applied... 

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