Viscosity particle shape from

Having determined cp experimentally, one may roughly (to the first approximation) evaluate the viscosity of the plastisol. The real plastisols of course are not ideal dispersed systems, and their viscosity as a rule is essentially different from that given in Eq. (3.1). This results not only from the low accuracy of

particle shape from the ideal sphere (K / 2.5), but also from the strong influence of a number of factors which will be discussed below on the basis of the available published data. 

B. Determination of Particle Shape from Intrinsic Viscosity. 333... 

We conducted cold flow model experiments in a air-water/glycerin system to investigate a cause of maldistribution in a catalyst bed. The apparatus used was a 30 cm I.D. acrylic column equipped with a liquid distributor at the top and a liquid collector with 33 compartments at the bottom. Bed depth can be varied by combining the pipes. Liquid distribution at a given depth of the bed was estimated by measuring the liquid flow from each compartment of the collector. We examined effects of gas and liquid velocity, liquid viscosity, particle shapes, and ways of catalyst loading on liquid distribution in the bed. An increase in liquid velocity or viscosity slightly improved liquid distribution. However, gas flow rate did not affect liquid distribution. 

The diffusion coefficient D (at c 0) is related to the frictional coefficient /d [see equation (7-21). The coefficient fjy and, thus, D depend on a series of molecular quantities, as can be seen from the following reasoning. According to Stokes law, the frictional coefficient /sphere of an unsolvated sphere of homogeneous density is /sphere = Tif/iTsphere where is the solvent viscosity. In a solvated sphere, the hydrodynamically effective radius takes the place of the radius Tsphere- The deviation of the particle shape from that of an unsolvated sphere is described by an asymmetry factor /a = /nZ/sphere- Thus, the frictional coefficient fjj of a solvated particle of any given shape is, for c 0,... 

Note that, apart from the filler particle shape and size, the molecular mass of the base polymer may also have a marked effect on the viscosity of molten composites [182,183]. The higher the MM of the matrix the less apparent are the variations of relative viscosity with varying filler content. In Fig. 2, borrowed from [183], one can see that the effect of the matrix MM on the viscosity of filled systems decreases with the increasing filler activity. In the quoted reference it has also been shown that the lg r 0 — lg (MM)W relationships for filled and unfilled systems may intersect. The more branches the polymer has, the stronger is the filler effect on its viscosity. The data for filled high- (HDPE) and low-density polyethylene (LDPE) [164,182] may serve as an example the decrease of the molecular mass of LDPE causes a more rapid increase of the relative viscosity of filled systems than in case of HDPE. When the values (MM)W and (MM)W (MM) 1 are close, the increased degree of branching results in increase of the relative viscosity of filled system [184]. 

From the above expressions it can be seen that reduced and intrinsic viscosities have the unit of reciprocal concentration. When one considers particle shape and solvation, however, concentration is generally expressed in terms of the volume fraction of the particles (i.e. volume of particles/total volume) and the corresponding reduced and intrinsic viscosities are, therefore, dimensionless. 

Apart from the important effect of mass velocity, summarised in Table II, the particle size and, to a greater extent, the particle shape were also found to be important. The salt bath temperature gave an effect on U which could not be explained by the induced changes in the conductivity and viscosity of air alone. Particle conductivity and tube diameter, within their range of variation, have only marginal effects on the overall heat transfer coefficient. 

Figure 6.14 Intrinsic viscosity versus Peclet numberfor dilute suspensions of spheroidal particles of (a) oblate shape and (b) prolate shape, (From Macosko 1994, adapted from Brenner 1974, with permission from Pergamon Press.)...

Solids concentrations can vary from a few percent to well over 50% in a typical stirred tank. Solids concentration, particle shape, and the viscosity of the suspending phase are the main factors affecting the rheology and settling characteristics of the slurry. Cubic- and spherical-shaped solids tend to form Newtonian slurries, while needle-, oblong-, and plate-shaped solids form thixotropic slurries. Such slurries exhibit yield stresses even at quite low solids concentrations. This can lead to the development of caverns, as shown in Section 9.4. Proper design can usually overcome these stagnation problems. 

The intrinsic viscosity is increased from Galahad-7 to Classic. Assuming a spherical shape the relative sizes for Galahad-7, Caprimus, Soissons and Classic are 1 8 12 15. This again points at considerable differences between the four varieties. Physical theory states that the rheological properties of a gel are related to the size and concentration of the contained particles. Although it is not yet possible to quantify this, the differences in G plateau values are clearly reflected... 

Particle Shape Effect. To this point, we have been dealing only with spherical particle suspensions. When the particles have irregular shapes, the rheological properties are expected to be very different from those of the spherical particle suspensions. Consider, for example, a simple system of cylindrical fibre suspensions. Because the particles are expected to align in the direction of the flow or shear, the viscosity needs to be treated as a second-order tensor, that is, the values of the viscosity under the same condition are different when different directions are referred. Only at the low (zero) shear limit may the particles be randomly distributed and have an isotropic rheological behavior. 

Particle shape, size, and density polymer gelling-agent concentration solids concentration test temperature and fracture shear rate affect viscosity increase that results from the addition of a solid in the fracturing fluid. 

The viscosity of slurries is a function of the solution and solid involved, as well as the slurry density. The viscosity can also be significantly affected by the particle size, size distribution, and particle shape. As a general rule, as particle shape varies from spheres to needles, the viscosity moves further from Newtonian behavior. A detailed discussion of factors affecting the viscosity of suspensions can be found in Sherman (1970). 

If/m is the maximum packing density of the particles, which is defined as the volume fraction at which the particles touch one another, so that flow is not possible, then the actual particle volume firaction/used in injection molding is lower than/m by 5-10 vol%. This means that in a well-dispersed suspension, the particles are separated from one another by a thin layer of polymer with a thickness of about 50 nm dming the molding, so that the mixture is able to flow. Therefore, the volume fraction of particles / is determined by the particle size and distribution and the particle shape. In practice, the volume firaction of ceramic powders is determined from viscosity measurements by using a capillary rheometer. Data for the relative viscosity, i.e., the viscosity of the mixture divided by the viscosity of the unfilled polymer versus particle concentration can be well fitted by the following equation [209] ... 

From the practical point of view, the change of filtration pressure, filtration area, filter medium, filtrate viscosity and solids loading is limited . To increase the filterability of the cake, most practical way, therefore, is to decrease the average specific cake resistance a. This could be accomplished by changing the particle shape, increasing the particles size and narrowing the size distribution of the particles in the cake. The latter two factors can be manipulated by polymer flocculation. 

Viscosity studies showed that polymer consisted of units of spherical rather than elongated shape. From the composition it can be calculated that the ratio of hydroxyl plus butoxy groups to silicon is 0.95, which would be the OH Si ratio in the corresponding silicic acid. Referring to the formula in Chapter 1 relating particle size to composition of surface-hydroxylated silica particles. OH Si = 24.6 p/ll.5cP, the particle diameter is estimated to be 2.3 nm. 

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