Dispersion criterion

The maximum allowable particle diameters for typical reactor diameters are included in Figure 7. Especially at low conversion levels, the last criterion is more severe at a given reactor length, whereas with increasing conversion the axial dispersion criterion should be satisfied. 

It follows from Eq. (3-12) that, in the presence of material dispersion, these profiles must have the following forms to satisfy the linear-dispersion criterion... 

Unfortunately none of the various proposed forms of the potential theory satisfy this criterion Equation XVII-78 clearly does not Eq. XVII-79 would, except that / includes the constant A, which contains the dispersion energy Uo, which, in turn, depends on the nature of the adsorbent. Equation XVII-82 fares no better if, according to its derivation, Uo reflects the surface polarity of the adsorbent (note Eq. VI-40). It would seem that after one or at most two layers of coverage, the adsorbate film is effectively insulated from the adsorbent. 

The criterion of maintaining equal power per unit volume has been commonly used for dupHcating dispersion qualities on the two scales of mixing. However, this criterion would be conservative if only dispersion homogeneity is desired. The scale-up criterion based on laminar shear mechanism (9) consists of constant > typical for suspension polymerization. The turbulence model gives constant tip speed %ND for scale-up. 

Optical Properties. Haze is the most common optical property problem that depends on colorants. Because dyes ate dissolved into the resin system, they contribute Htde or no practical haze to the system. Pigments can have significant haze, which is a combination of the pigment itself and the quahty of dispersion of the pigment. In an opaque appHcation haze is not a concern, but in transparent or translucent appHcations haze development becomes an important criterion in colorant evaluation. 

For many laboratoiy studies, a suitable reactor is a cell with independent agitation of each phase and an undisturbed interface of known area, like the item shown in Fig. 23-29d, Whether a rate process is controlled by a mass-transfer rate or a chemical reaction rate sometimes can be identified by simple parameters. When agitation is sufficient to produce a homogeneous dispersion and the rate varies with further increases of agitation, mass-transfer rates are likely to be significant. The effect of change in temperature is a major criterion-, a rise of 10°C (18°F) normally raises the rate of a chemical reaction by a factor of 2 to 3, but the mass-transfer rate by much less. There may be instances, however, where the combined effect on chemical equilibrium, diffusivity, viscosity, and surface tension also may give a comparable enhancement. 

Plug flow is approached at low values of the dispersion coefficient or hi values or Peclet number. A criterion developed by Mears (Chem. Eng. Sci., 26, 1361 [1971]) is that conversion will be within 5 percent of that predicted by phig flow when... 

To reiterate the definition of chromatographic resolution a separation is achieved in a chromatographic system by moving the peaks apart and by constraining the peak dispersion so that the individual peaks can be eluted discretely. Thus, even if the column succeeds in meeting this criterion, the separation can still be destroyed if the peaks are dispersed in parts of the apparatus other than the column. It follows that extra-column dispersion must be controlled and minimized to ensure that the full performance of the column is realized. 

After some early uncertainty in the literature about the nature of the pressure sensitive bond, Dahlquist [5,6] related modulus data to tack-temperature studies and observed that the compression modulus of the adhesive had to be less than about 3 X 10 dyne/cm (3 x lO Pa) before any adhesive tack was observed. This was explained as the highest modulus that still allowed the adhesive to be sufficiently compliant to wet out or come into molecular contact with the substrate and form dispersive bonds. As other investigators [7-9] accepted this requirement it was termed the Dahlquist Criterion . 

The criterion for the validity of Equation 8-141 is Npg 1.0. A rough rule-of-thumb is Npg > 10. If this condition is not satisfied, the correct equation depends on the boundary conditions at the inlet and outlet. A procedure for determining dispersion coefficient Dg [ is as follows ... 

In general, the multiphasic heterogenous nature of the impact grade styrene-based polymers is the root cause of their opaque-turbid nature. In determining the transparency of the blends, size and the size-distribution pattern of the dispersed phase along with the refractive index difference between the continuous and the dispersed phases are two very important criterion [133]. 

Conventionally fillers are divided into reinforcing, active, and inert ones. The reinforcing class includes mainly fibrous materials. Disperse fillers may also perform the reinforcing function, and then they are called active. For the criterion of activity of a filler it has been proposed to employ, for example, the extent of variation of the relative viscosity of the melt or solution caused by introduction of a filler [23] — the greater the variation the better the affinity between the polymer and the filler. 

As seen in Chapter 8, the stability criterion becomes quite demanding when At is large. The axial dispersion model may then be a useful alternative... 

The spontaneous direction of any process is toward greater dispersal of matter plus energy. If we are to apply this criterion in a quantitative way, we need ways to measure amounts of dispersal. Scientists analyze the constraints on a system to measure the dispersal of matter. The more the system is constrained, the less dispersed it is. Scientists do calculations on the flow of heat to measure changes in the dispersal of energy. 

For purposes of this survey an important distinction must be made between a commonly used criterion of instability and the sense in which the term is used here. A stable dispersion is not necessarily one which will not settle, because the only disturbance involved in settling is motion of translation of the parti-... 

In a practical sense, stability of a dispersion ofttimes is accompanied by a retarded separation of the phases. Unfortunately, a quantitative definition cannot be based on this rate of separation because of the overwhelming influence of density, viscosity, and thermal effects. In short, a kinetic criterion, such as sedimentation rate, is not as likely to portray stability as one based on thermodynamic considerations. In this latter category are sediment volumes, turbidity, consistency, and electrical behavior. 

Perhaps the best rheological stability criterion is the volume occupied by the sediment per unit volume of original dispersion. A flocculated dispersion settles rapidly to a high sediment volume, while a deflocculated one settles slowly to a low volume, as shown in Figure 8. Of course, the ultimate volume depends on the concentration of the dispersion and in order to give a criterion of more fundamental interest the concept of relative sediment volume RSV may... 

For higher efficiency in catalytic action and smaller quantitative needs, the catalysts often are used in a highly disperse state. An important practical criterion for such catalysts is the specific reaction rate [i.e., the reaction rate per unit mass of the catalyst... 

A basic assumption of OPA is that the purest spectra are mutually more dissimilar than the corresponding mixture spectra. Therefore, OPA uses a dissimilarity criterion to find the number of components and the corresponding purest spectra. Spectra are sequentially selected, taking into account their dissimilarity. The dissimilarity of spectrum i is defined as the determinant of a dispersion matrix Y,. In general, matrices Y, consist of one or more reference spectra, and the spectrum measured at the /th elution time. 

As another criterion of stability, a critical flocculation temperature(OFT) was measured. The measurement of CFT was carried out as follows the bare latex suspension was mixed with the polymer solution of various concentrations at 1+8 °C by the same procedure as in the adsorption experiments. Then, the mixture in a Pyrex tube(8 ml, U.0 wt %) was warmed slowly in a water bath and the critical temperature at which the dispersion becomes suddenly cloudy was measured with the naked eye. 

We present an improved model for the flocculation of a dispersion of hard spheres in the presence of non-adsorbing polymer. The pair potential is derived from a recent theory for interacting polymer near a flat surface, and is a function of the depletion thickness. This thickness is of the order of the radius of gyration in dilute polymer solutions but decreases when the coils in solution begin to overlap. Flocculation occurs when the osmotic attraction energy, which is a consequence of the depletion, outweighs the loss in configurational entropy of the dispersed particles. Our analysis differs from that of De Hek and Vrij with respect to the dependence of the depletion thickness on the polymer concentration (i.e., we do not consider the polymer coils to be hard spheres) and to the stability criterion used (binodal, not spinodal phase separation conditions). 

In a backwards-in-distance solution for advective transport in the absence of dispersion or diffusion, the Courant criterion limits the time step. In one dimension, the grid Courant number is the number of nodal blocks the fluid traverses over a time step. By the Courant criterion, the Courant number Co must not exceed one, or... 

Considering dispersion and advection simultaneously, the stability criterion for the forward-in-time, backward-in-distance procedure becomes,... 

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