Cross-section polydispersity

Cross-section polydispersity entails, in most cases, the disappearance of the oscillations due to the Bessel functions. A monotonously decreasing curve is then observed. Note that in the case where 2 = 1, the intersection with the -axis, q is q = Unr, while the intersection between the two types of behavior given by Equations 4.31 and 4.33 occurs at q, whose value is q = lhzr. ... 

Guenet JM. Scattering by a network of prolate, cross-section-polydispersed cylinders applicable to fibrillar thermoreversible gels. J Phys II 1994 4 1077-1082. 

With a polydisperse aerosol having ni particles of cross-sectional area Aj, it is necessary to sum y for each particle size over all particle sizes, or... 

We shall now consider polymers made of chemically identical monomers in solution in one solvent. In this case, expression (7.2.37) for the cross-section can be simplified because, then, there exists only one contrast length, independently of the fact that the system may be either monodisperse or polydisperse. 

Consider now drop coalescence in a polydisperse emulsion in the process of sedimentation in a gravitational field in the presence of a uniform external electric field. Since the capture cross section of drops does not depend much on the direction of the electric field, the direction of Eq is taken to be arbitrary. 

The average absorption Cahs,X and scattering Csca,x cross-sections (in tn ) of a suspension of polydisperse microorganism cells can be related to its spectral absorption /C i and scattering <7, x coefficients according to (Pilon et al., 2011)... 

Fig. 7 compares the experimentally measured (A and C) absorption Cahs,x and (B and D) scattering Csca,x cross-sections between 400 and 700 nm of monodisperse latex spheres 2.02 and 4.5 pm diameter with Lorenz—Mie theory predictions using the complex index of refraction of latex reported by Ma et al. (2003). Flere also, the good agreement between theoretical and experimental results successfully validated the experimental setup and the data analysis. Similar vaHdation has been performed with the same polydisperse polystyrene latex microspheres and randomly oriented and infinitely long glass fibers considered for validating the scattering phase function measurements, as illustrated in Fig. 6 (Berberoglu and Pilon, 2007).

We consider the one-dimensional, frictionless flow of wet steam in a duct of constant cross-sectional area. The vapour is the continuous phase and, for simplicity, the droplet population is assumed to be monodispersed with droplets of radius r, density pf and mass m = 47Cr pf/3. (Methods of dealing with a polydispersed droplet cloud are discussed in [8]). If there are n droplets per unit mass of mixture,the wetness fraction is given by y=nm. 

Jong et al. [143]. Porous microfluidic devices were fabricated by phase separation micromolding. Oil-in-water emulsions with 190 pm size and polydispersity 2.5% were produced inside 150 pm diameter porous microchannels. Sugiura and co-workers [144—148] proposed a microfabricated silicon geometry containing at least 400 microchannels of small dimensions (typical cross-section 6x13 pm) (Figure 8.25). Not all the channels were initially active, but as the pressure of the... 

According to a standard theory for a globular micelle system with low polydispersity [11,14], the neutron scattering cross section per unit volume at Q = 0 (1(0)) is given by... 

The measured mean extinction cross section Cextaneas( meas) of a polydisperse particle system can be calculated from the quantity distribution qo x) and the theoretical extinction cross section Cext,theo( meas which depends on the measurement cross section ri eas and the particle size x. 

Fig. 12.9 Root mean square deviation of simulated transmission signals a(J) of polydisperse particle collectives as fimction of the theoretical relative extinction cross section CextreUheo- The mean particle size is xp m = 1000 pm, the root mean square deviation of the particle size

The increase of the corrected simulated relative extinction cross sections, with larger widths of the particle size distribution, tends to increase slightly with an increasing transmission. This effect appears for all theoretical relative extinction cross sections and principally can be explained by a dependence of polydispersity effect of other effects. Therefore, a correction of the polydispersity effect must be carried out as a function of the mean value of the transmission. 

---