Rigid Particles

Filter pore size, /Ltm Maximum rigid particle to penetrate, /itm Filter pore size, /Ltm Maximum rigid particle to penetrate, /itm... 

For solutions of rigid particles, then, the intrinsic viscosity exceeds 2.5 as a result of some combination of the following effects ... 

The effect of ellipticity also increases [77] above the 2.5 value obtained for spheres. Analytical functions as well as graphical representations like Fig. 9.3 are available to describe this effect in terms of the axial ratios of the particles. In principle, therefore, a/b values for nonsolvated, rigid particles can be estimated from experimental [77] values. 

Rigid particles other than unsolvated spheres. It is easy to conclude qualitatively that either solvation or ellipticity (or both) produces a friction factor which is larger than that obtained for a nonsolvated sphere of the same mass. This conclusion is illustrated in Fig. 9.10, which shows the swelling of a sphere due to solvation and also the spherical excluded volume that an ellipsoidal particle requires to rotate through all possible orientations. 

Solution Filtration. The polymer solution, free of unacetylated ceUulose, rigid particle contaminants, and dirt, must pass through spinnerets with holes of 30—80 ]lni diameter. Multistage filtration, usuaUy through plate-and-frame filter presses with fabric and paper filter media, removes the extraneous matter before extmsion. Undesirable gelatinous particles, such as the hemiceUulose acetates from ceUulose impurities, tend to be sheared into smaller particles rather than removed. The solution is also aUowed to degas in hoi ding tanks after each state of filtration. 

Nonsplierical Rigid Particles The drag on a nonspherical particle depends upon its shape and orientation with respect to the direction of motion. The orientation in free fall as a function of Reynolds number is given in Table 6-8. 

Compaction of the filter bed over time will result in gas channeling and pressure-drop increases. This can be avoided by adding large, rigid particles such as plastic spheres, ceramics, or wood/bark chips to provide additional support to the filter substrate. 

However, for the case of the rigid particle indenting a compliant substrate, the change in area, which arises from the stretching of the surface of the substrate, is given by the expansion in size of a spherical cap. 

Fixed rigid media are available in the forms of disks, pads and cartridges. They are composed of firm, rigid particles set in permanent contact with one another. The media formed have excellent void uniformity, resistance to wear and ease in handling as piece units. Depending on the particle size forming the filter media, temperature, pressure and time for caking, it is possible to manufacture media with... 

Suppose we have a physical system with small rigid particles immersed in an atomic solvent. We assume that the densities of the solvent and the colloid material are roughly equal. Then the particles will not settle to the bottom of their container due to gravity. As theorists, we have to model the interactions present in the system. The obvious interaction is the excluded-volume effect caused by the finite volume of the particles. Experimental realizations are suspensions of sterically stabilized PMMA particles, (Fig. 4). Formally, the interaction potential can be written as... 

The packings used in modern HPLC consist of small, rigid particles having a narrow particle-size distribution. The types of packing may conveniently be divided into the following three general categories. 

The simplest indicator of conformation comes not from but the sedimentation concentration dependence coefficient, ks. Wales and Van Holde [106] were the first to show that the ratio of fcs to the intrinsic viscosity, [/ ] was a measure of particle conformation. It was shown empirically by Creeth and Knight [107] that this has a value of 1.6 for compact spheres and non-draining coils, and adopted lower values for more extended structures. Rowe [36,37] subsequently provided a derivation for rigid particles, a derivation later supported by Lavrenko and coworkers [10]. The Rowe theory assumed there were no free-draining effects and also that the solvent had suf-... 

Most biological polymers, such as proteins and nucleic acids and some synthetic polymers, have relatively inflexible chains. For rigid particles, the size is no longer of predominant importance, because the polymer chain is no longer in the form of a flexible random coil instead, shape becomes an important parameter. Following are some theoretical proposals for the estimation of the shape factor p from the viscosity measurement (table 4). The term f/fo is sometimes denoted as p, Perrin constant. 

There is currently considerable interest in processing polymeric composite materials filled with nanosized rigid particles. This class of material called "nanocomposites" describes two-phase materials where one of the phases has at least one dimension lower than 100 nm [13]. Because the building blocks of nanocomposites are of nanoscale, they have an enormous interface area. Due to this there are a lot of interfaces between two intermixed phases compared to usual microcomposites. In addition to this, the mean distance between the particles is also smaller due to their small size which favors filler-filler interactions [14]. Nanomaterials not only include metallic, bimetallic and metal oxide but also polymeric nanoparticles as well as advanced materials like carbon nanotubes and dendrimers. However considering environmetal hazards, research has been focused on various means which form the basis of green nanotechnology. 

The effective viscosity is also affected by the microrotation of the rigid particles. If the gap is much larger than the molecular dimensions, the boundary walls will have little influence on the microrotation motion. This means that if the gap between the solid walls is sufficiently large, the micropolarity can be reasonably taken out of consideration without losing precision. The microrotation in thin film lubrication will result in viscosity-enhancements and consequently higher film thicknesses, which contribute to a better performance of lubrication. 

Slurry packing techniques are required for the preparation of efficient columns with rigid particles of less than 20 micrometers in diameter. The same general packing apparatus. Figure 4.8, can be used to pack columns by the balanced-density slurry, liquid slurry, or the viscous slurry techniques. Down-fill slurry packing is the method of choice for small bore columns and packed capillary columns. 

Rigid particles with diameters greater than 20 micrometers can be dry-packed efficiently with relatively simple apparatus using the tap-fill method [149]. The empty column. is held... 

The influence of K on g is caused by the so-called wall effect and an increase of void volume that is accessible for small particles with K. Both of these effects correspond to the appearance of the excluded volume in the places of contact of rigid particles between themselves (Figure 9.18) or a rigid wall (Figure 9.20). 

This latter case is the same result as Einstein calculated for the situation where slip occurred at the rigid particle-liquid interface. Cox15 has extended the analysis of drop shape and orientation to a wider range of conditions, but for typical colloidal systems the deformation remains small at shear rates normally accessible in the rheometer. The data shown in Figure 3.11 was calculated from Cox s analysis. His results have been confirmed by Torza et al.16 with optical measurements. The ratio of the viscous to interfacial tension forces, Rf, was given as ... 

The rotational mobility of human low-density (LDL) and very-low-density (VLDL) lipoproteins was studied as a function of viscosity and temperature in the range of —90 to — 50°C.(86)The rotational behavior for LDL is represented by a single correlation time, consistent with the overall rotation of a spherical rigid particle as the source of the phosphorescence depolarization. For VLDL, internal peptide motions dominate the depolarization profile. 

The reorientational correlation time can be predicted for spherical rigid particles, according to the Stokes Einstein equation (75-77) ... 

Several such failure mechanisms may take place simultaneously in a toughened resin, depending on the type of particles, whether liquid rubber or rigid particles, and the matrix material. Each of these mechanisms contributes to the energy absorption of the whole structure. 

For a rigid particle consisting of mass elements of mass mt, each located at a distance r from the centre of mass, the radius of gyration, s, is defined as the square root of the mass-average of r for all the mass elements, i.e.. 

For a non-rigid particle, an average over all conformations is considered, i.e.. 

Equation (3-33) shows how the inertia term changes the pressure distribution at the surface of a rigid particle. The same general conclusion applies for fluid spheres, so that the normal stress boundary condition, Eq. (3-6), is no longer satisfied. As a result, increasing Re causes a fluid particle to distort towards an oblate ellipsoidal shape (Tl). The onset of deformation of fluid particles is discussed in Chapter 7. 

---