Particle resistance

Particle surface characteristics Type of solid (in terms of internal liquid content) gel, flocculated, hard particle Strength of particle (resistance to deformation under pressure) compressibility over time expressed cake... 

In filters etc. the particles become largely static in a bed or cake and in such cases the fluid therefore passes through a fixed array of particles or a porous solid and experiences drag as it does so (Figure 2.9). The particles resist the flow, reduce the velocity and give rise to an enhanced pressure drop compared with that in open channel flow. 

Provide protection against alpha particles and low-energy beta particles resists some chemicals (depends on the type selected) relatively inexpensive Latex gloves tear easily... 

The influence of the decomposing atmosphere on the final species obtained has been studied for an oxygen-free carbon-supported Ru3(CO),2 [106]. A DRIFT study showed that under H2 the fast formation of H4Ru4(CO),2 species results under He, Ru3(CO),2 decomposes via a progressive decarbonylation and fragmentation. Complete decarbonylation under both H2 or He produced well-dispersed Ru particles resistant to sintering under CO hydrogenation conditions [106]. 

In some cases, microbial cell fragments may arise and can be particularly problematic. For example, the disc centrifuges often used to remove yeast after brewery fermentations are known to produce shearing forces that break off yeast cell wall fragments (Siebert et ah, 1987). Agitation of yeast by other means is also problematic (Lewis and Poerwantaro, 1991 Stoupis et ah, 2003). In beer, the resulting particles resist sedimentation and impair filtration. 

To avoid the difficulties associated with the spherical diffusion equation, a useful hypothesis is the linear-driving-force concept. This arises when a parabolic concentration profile within the spherical particles is supposed - which is a good approximation in cases where there is a Thiele modulus of a maximum volume of 2-5 (that is, with some intra--particle resistance [50]). In these conditions, the volume-averaged intra-particle concentration is defined as ... 

X-ray diffraction studies of the spent catalysts in the absence of sulfur, indicate that after 1 h the oxycarbide and oxynitride particles resist significant agglomeration. XPS analysis of the spent catalysts indicates that... 

Each particle is considered as a center to which other particles diffuse by Browian motion. Thus the rate of flocculation is proportional to the square of the number of particles. The original treatment assumed that all interparticle collisions were effective in causing flocculation. Later modifications (6) assumed that the potential energy barrier between particles resists flocculation and that only those collisions with sufficient energy to overcome this barrier will cause flocculation. The agitation-induced flocculation has also been analyzed theoretically (7). 

In evaluating the particle resistance due to relative motion to the fluid, it is convenient to begin with the constant velocity case and work to the time-dependent case. Consider the case of a sphere moving in a gravitational field and assume that the gravitational acceleration is in the same direction as the sphere motion. Denote Fz as the resistance. Since the total resistance is due to the surface shear and surface pressure, and the flow is axisymmetric, Fz can be postulated as... 

The lipid-soluble antioxidants present in the LDL particle are responsible for the LDL particle resistance to oxidation [3]. LDL copper-mediated oxidability in vitro, has been used by several researchers to evaluate oxidation resistance of LDL. LDL oxidation is evaluated by following in vitro copper-mediated oxidation of LDL [3,49]. Duration of the lag phase determines the resistance of LDL to oxidation and depends on the content of antioxidants in the LDL molecule. During the lag period, the alpha-tocopherol and other antioxidants are lost from LDLs. The length of the lag phase reflects the protective effects of chain-breaking antioxidants, especially alpha-tocopherol. When LDL particles, isolated from subjects who have consumed vitamin E supplements, or are enriched with vitamin E, the length of lag period is significantly increased [3]. 

Particle resistivity decreases as gas temperature increases due to enhanced volume conductivity. Resistivity may also decrease as gas temperature decreases if surface conditioning agents such as moisture or acid gases are present in the gas stream. Adsorption of these on the particle surface is favored at lower temperatures and provides a conductive path on the particle surface. 

Uniform collection efficiency independent of particle resistivity... 

Internal forces. A fluid particle exhibits an internal pressure due to surface forces, the Laplace pressure, which is inversely proportional to its diameter (Section 10.5.1). This means that the particle resists deformation, the more so the smaller it is. The colloidal forces that may act between particles, keeping them aggregated, often are about proportional to d (Chapter 12). This means that the stress (force over area) involved would, again, be inversely proportional to d. 

Pb removal from water by means of a Na-exchanged phillipsite-rich tuff was studied, using a diffusional model. The model is based on the linear driving force (LDF) approximation and takes into account both fluid-particle and intra-particle resistances to diffusion, making no specific assumption on their relative magnitude or on the form of the ion exchange isotherm. 

A nonspherical particle is generally anisotropic with respect to its hydro-dynamic resistance that is, its resistance depends upon its orientation relative to its direction of motion through the fluid. A complete investigation of particle resistance would therefore seem to require experimental data or theoretical analysis for each of the infinitely many relative orientations possible. It turns out, however, at least at small Reynolds numbers, that particle resistance has a tensorial character and, hence, that the resistance of a solid particle of any shape can be represented for all orientations by a few tensors. And the components of these tensors can be determined from either theoretical or experimental knowledge of the resistance of the particle for a finite number of relative orientations. The tensors themselves are intrinsic geometric properties of the particle alone, depending only on its size and shape. These observations and various generalizations thereof furnish most, but not all, of the subject matter of this section. 

Use of symbolic drag coefficients (Section I1,C,2) and symbolic heat-and mass-transfer coefficients (Section IV, A) furnishes a unique method for describing the intrinsic, interphase transport properties of particles for a wide variety of boundary conditions. Here, the particle resistance is characterized by a partial differential operator that represents its intrinsic resistance to vector or scalar transfer, independently of the physical properties of the fluid, the state of motion of the particle, or of the unperturbed velocity or temperature fields at infinity. Though restricted as yet in applicability, the general ideas underlying the existence of these operators appear capable of extension in a variety of ways. 

---