Relation between particle diameter

Figure 7.6b also demonstrates the effect of decreasing the reaction rate (by reducing the reaction rate constant, k) on the relation between particle diameter and the concentration A of reactive group. At constant A, decreasing k from kitoki/... 

Fig. 4. Relation between particle diameter and elution volume for gel permeation columns. Column A, G5000PW B, G4000SW C, G4000SW+G3000SW D, G3000SW+ G3000SW+G3000SW. Eluent 0.15 M NaCl. Flow rate 0.40 ml/min. Samples Standard lipoproteins (, v,n), standard proteins (a,v,b, ). Vq Void volume. Vt total permeation.

This equation shows that R is given by the ratio of particle displacement velocity V to average carrier velocity , or equivalently to the ratio of channel void volume V° to the retention volume V. Thus R is experimentally accessible because V is the measured volume required to displace a given particle size" through the channel. However, the equation also shows that R is related to X, which is related to d through the previous equation. Thus a linkage is formed between particle diameter d and experimental retention volume V. It has been estimated that particle diameters accurate to 1-3% can be obtained by using this approach (2). 

In bubble columns, the estimation of parameters is more difficult than in the case of either gas-solid or solid-liquid fluidized beds. Major uncertainties in the case of bubble columns are due to the essential differences between solid particles and gas bubbles. The solid particles are rigid, and hence the solid-hquid (or gas-solid) interface is nondeformable, whereas the bubbles cannot be considered as rigid and the gas-liquid interface is deformable. Further, the effect of surface active agents is much more pronounced in the case of gas-liquid interfaces. This leads to uncertainties in the prediction of all the major parameters such as terminal bubble rise velocity, the relation between bubble diameter and terminal bubble rise velocity, and the relation between hindered rise velocity and terminal rise velocity. The estimation procedure for these parameters is reviewed next. 

At high velocities, due to the onset of turbulence, the drag on the sphere increases above that predicted by Stokes equation and particles settle more slowly than the law predicts. However, settling velocities can be related to particle diameters by applying Newton s equation which is available as an empirical relationship between C, and Re. The upper size limit for Stokes equation is limited, due to the onset of turbulence, to Reynolds number smaller than 0.25. 

The relation between particle size distribution and NMR spectrum has been modeled in the NMR layer model 156). Here I describe a simple version a more elaborate one has been proposed by Makowka et al. 157). We start by constructing size histograms from TEM micrographs. To do this, it is customary to consider the images on the inicrograph as circles with diameter d equal to that of effectively spherical metal particles that cause the image. Furthermore, this diameter is converted to the total number N y of atoms in the particle by (for the FCC structure, four atoms per unit cell)... 

Lei Nij be the number of collisions occurring per unit lime per unit volume between the two classes of particles of volumes u,- and Uj. All particles are assumed to be spherical, which means that i and j are uniquely related to particle diameters. When two particles collide, according to this simplified model, they coalesce instantaneously to form a third whose volume is equal to the sum of the original two. In terms of the concentrations of particles and with volumes u,- and Vj, the collision frequency is... 

The V term is directly related to particle diameter and the electrical field strength of ench electrode, and inversely proportional to the fluid viscosity, This term is difficult to calculate for performance predictions, but it is typically between 0.1 and 0.7 ft/s (0,03 and 0.21 m/s) for solid-in-gas systems,... 

For solid particles, both transparent and absorbing ones, in water, only positive photophoiesis has been observed. " " The relation between particle velocity Mph (in M-ni/s) and lasCT beam intensity Jo (in 10 W m ) was measured in Ref. using an Ar" -ion laser (Aq = 514.5 nm) power of 0.1-0.8 W focused into a beam with wq 40 p,m. The result was Mph 1.1 Jb for latex particles of 9.87 p,m diameter with m(589 nm) = 1.191, and Uphih 4.87o for carbon black particles of 12 p,m diameter with m(489 nm) = 1.27 — i X 0.52. The observed variation of velocity with particle size and optical constants corresponded qualitatively to Eq. 4. The authors of Ref. measured the size dependence of photophoretic velocity for polystyrene microparticles (n no = 1.59) in water in the range 2a = 0.78-2.84 pm, using a... 

In the reported study, Cu particles were used with diameters between 20pm and 250pm to investigate the relation between particle size and these oscillations. 

In Figure 13 the relation between the intrinsic coercivity and the particle diameter dis given. The figure is based on a described model (35). The maximum is found around the critical particle diameter. In general the particle diameter and size is not very well defined. For the multidomain particles (d > ) the is smaller than the intrinsic anisotropy field of the particle. Nucleation effects cause a decrease in as the increases. This behavior is... 

Now, we show the relation between the ratio of 8 to Tq, 8/ro and the volume fraction of carbon black (p in Table 18.1, when the diameter of the hard particle (including carbon black, the GH layer and a little more contribution from the cross-links at the surface of particle) is tq and the distance between the hard particles is 8. In the carbon black-filled rubber (ip g 0.23-0.25), the fact that the stress of the filled system is 10-15 times larger than that of the unfilled rubber as shown in Figure 18.1 indicates that more than 90% of the stress of the system is supported by the supernetwork and the remainder of the stress results from the matrix rubber. In the present calculation, however, we can ignore the contribution from the matrix mbber. 

The relation between bed voidage e and fluid velocity uc for particulate fluidisation of uniform particles which are small compared with the diameter of the containing vessel is given by ... 

The study of shape and crystal structure of small metallic particles is of prime importance in modern catalysis science. The relation between reactivity and structure is still not well known. The main problem in studying small metallic particles is that conventional techniques fail in the manometer diameter range. However it is possible to overcome these difficulties by the application of non-conventional methods. It is the purpose of this paper to review some of these methods and to present some results on the characterization of gold and platinum particles. 

Interrelation between different equivalent diameters is derived from the relations between the real values of the volume of solid Vs and surface area A of a particle with equivalent diameters Di and D-, where i and j are the methods of measurement or types of equivalent sizes. In a general case,... 

If flow conditions within the bed are streamline, the relation between fluid velocity uc, pressure drop (—A P) and voidage e is given, for a fixed bed of spherical particles of diameter d, by the Carman-Kozeny equation (4.12a) which takes the form ... 

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