Particle size distribution approximate approaches

Particle Size Distribution Determination. To consider the full PSD, a population balance or age distribution analysis on particles must be employed. Table II gives a summary of recent work concerning the determination of PSD s in emulsion systems, using both the "monodispersed" approximation and the population balance approach. More details can be found in the literature sources cited in the Table. 

With practice much may be learned from the shape of the sedimentation curves shown in Figure 17. Thus, a curve with a rapidly changing slope indicates a poly-dispersed sample, while a curve approaching a straight line indicates mono-dispersion. Two samples have approximately the same particle-size distribution when their slopes at corresponding times are the same. The curves are also valuable since they give a graphical comparison of the density. The relative densities of various materials sized in this manner are in accordance with the point of ordinate interception. 

Improvement in the quality of the adsorbent layer and methods of sample application, and the availability of scanning densitometers for in situ quantitative analysis were all important developments in the evolution of HPTLC. The new HPTLC plates are prepared from specially purified silica gel with average particle diameters of between 5 to 15 micrometers with a narrow particle size distribution. These plates give HETP values of about 12 micrometers and a maximum of about 5000 usable theoretical plates in any separation. By contrast, conventional TLC plates prepared from silica gel with average particle diameters of 20 micrometers and a rather broad particle size distribution gave HEPT values of about 30 micrometers and a maximum of approximately 600 usable theoretical plates. The new HPTLC plates can provide an increase in performance approaching an order of magnitude over conventional TLC plates. Thus, it is possible to carry out separations on HPTLC plates that were not posible by conventional TLC, and also... 

In summary, the diflBculties in determining aggregate form factors, particle form factors, phase shifts, and distribution functions combine to make the Rayleigh-Debye approach too complicated for practical application. On the other hand, the coalesced-sphere approach using the Jobst approximations to the Mie scattering eflBciencies allows rapid correlation of turbidity with particle size distributions. Consequently, a coalesced-sphere approach was adopted for experimentation in the E. coli-PEI system. 

Equation (6.3.8) provides the route to determining L t) from L (/) at least as discrete approximations. Thus, the complete growth rate L[/, t] is obtainable by this approach. The property of invariance enables the mapping of the measurement of particle size distribution at each instant into that at the initial time. The consistency with which the different calculations collapse into a single distribution provides a test of the efficacy of the process. The result shown in Fig. 6.3.4 does indicate that the method has considerable potential since the estimated initial distributions collapse to that assumed. 

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