Particle volume concentration distribution

Observed particle volume concentration distributions in the water column of Lake Zurich. Samples obtained on August 8,1984 at the depths indicated. 

Figure 14.6. Observed particle volume concentration distributions in the water column of Lake Zurich. Samples obtained on August 8, 1984 at the depths indicated, (ppm = III liter". ) (From Weilenmann et al., 1989.)...

Figure 5. Simulated particle volume concentration distributions in the epilimnion of Lake Zurich, assuming a net particle production flux of 8.2 cm3 m-2 day 1 and an areal hydraulic loading for the lake of 10 4cms J. For no coagulation and sedimentation, a(i,y)s,Cxp = 0 and pp = pw for sedimentation only, a(i, j)s,exp = 0 and pp = 1.05 g cm 3 for coagulation and sedimentation, >. y)s, p = 0-1 and Pp — 1-05 gcm-3. Other assumptions stated in the text. Simulations performed by M. Wiesner of Rice University, Houston, TX.

Model simulations of particle volume concentrations in the summer as functions of the particle production flux in the epilimnion of Lake Zurich, adapted from Weilenmann, O Melia and Stumm (1989). Predictions are made for the epilimnion (A) and the hypolimnion (B). Simulations are made for input particle size distributions ranging from 0.3 to 30 pm described by a power law with an exponent of p. For p = 3, the particle size distribution of inputs peaks at the largest size, i.e., 30 pm. For p = 4, an equal mass or volume input of particles is in every logaritmic size interval. Two particle or aggregate densities (pp) are considered, and a colloidal stability factor (a) of 0.1 us used. The broken line in (A) denotes predicted particle concentrations in the epilimnion when particles are removed from the lake only in the river outflow. Shaded areas show input fluxes based on the collections of total suspendet solids in sediment traps and the composition of the collected solids. 

Insitec EPCS is covered in detail in section 10.7. They are laser-based instruments for in-line particle measurements that provide information on particle volume concentration and size distribution. Unlike other... 

Insitec now forms part of Malvern Instruments but is still based in California for process and laboratory R D. The EPCS are laser-based instruments for in-line particle measurements that provide information on particle volume concentration and size distribution. EPCS instruments are part of the larger group of electro-optical instruments (MALLS) whose principle of operation is based on light scattering from a group (or ensemble) of particles. Unlike other instruments operating on this principle, the EPCS can perform direct measurements of particle laden flow stream provided the concentration is within operating limits. 

The particle volume distributions in this lake have a single size peak that increases somewhat with depth. Particle volume concentrations decrease substantially with depth from the epilimnion (the upper 5 m) through the thermoc-line and then into the hypolimnion. The total particle volume concentration in the epilimnion (as indicated by the area under the curves for depths of 1 or 5 m) is about 10 cm3 m 3 (ppm) the distributions in the bottom waters indicate total volume concentrations of about 1 cm3 m-3 in the hypolimnion. 

The particle volume concentration in the distribution of the annulus section... 

Typically one is concerned with the effect of changes in the recipe or temperature upon the particle size distribution. Figure I shows the particle volume (weight) distributions resulting from changes in the initiator concentration, all other variables held constant. The curves show the expected changes in the distributions for up to a ten-fold change in the initial initiator concentration. It is obvious from the curves alone that both the mean and the standard deviation decrease as the initiator concentration increases, This behavior is as expected since the total volume of particles must be the same for all distributions (same total... 

Fig. 10 The influence of particle volume concentration on particle size distributions determined by ultrasonic spectrometry.

Equations to calculate size distributions from sedimentation data are based on the assumption that the particles fall freely in the suspension. In order to ensure that particle-particle interactton does not prevent free fall, an upper-volume concentration hmit of around 0.2 percent is recommended. 

Equations (12.40) to (12.45) describe the velocities u, v, w, the temperature distribution T, the concentration distribution c (mass of gas per unit ma.ss of mixture, particles per volume, droplet number density, etc.) and pressure distribution p. These variables can also be used for the calculation of air volume flow, convective air movement, and contaminant transport. 

Gauthier et al. [38] studied radial migration of spherical particles with a concentration of 5% by volume in the mixture for the following values of parameters a = 0.019 cm R = 0.4 cm V = 0.127 cm3/s, n = 0.64. At the start of the time period, a particle deficit was observed at the channel walls, three minutes later the particles were uniformly distributed in the channel, ten minutes later 75 % of particles... 

Inspection of Fig. 15.3 reveals that while for jo 0.1 nAcm , the effectiveness factor is expected to be close to 1, for a faster reaction with Jo 1 p,A cm , it will drop to about 0.2. This is the case of internal diffusion limitation, well known in heterogeneous catalysis, when the reagent concentration at the outer surface of the catalyst grains is equal to its volume concentration, but drops sharply inside the pores of the catalyst. In this context, it should be pointed out that when the pore size is decreased below about 50 nm, the predominant mechanism of mass transport is Knudsen diffusion [Malek and Coppens, 2003], with the diffusion coefficient being less than the Pick diffusion coefficient and dependent on the porosity and pore stmcture. Moreover, the discrete distribution of the catalytic particles in the CL may also affect the measured current owing to overlap of diffusion zones around closely positioned particles [Antoine et ah, 1998]. 

It is seen that the distribution is bimodal, with the coarse mode dominating the aerosol volume concentrations. The 1979 average volume concentration of aerosol less than 10 ym diameter was 32.4 ymVcm. From its large standard deviation, it is clear that the coarse particle mode exhibited considerable variation throughout the year. Records show that high coarse mode volume concentrations accompanied moderate-to-high wind speeds. The coarse material was very likely wind-blown dust of crustal composition. 

Figure 2. Normalized aerosol volume distribution, China Lake, CA (1979 average)—average of 254 measurements. The error bars are standard deviations. The distribution is normalized with respect to total aerosol volume concentration of particles less than 10 lOn in diameter.

At last, note logical inconsistency of the method presented. Non-uniform concentration distribution, corresponding to the Poisson fluctuation spectrum (2.1.42), is introduced through initial condition imposed on Z(r,t) - see (2.1.71), (2.1.72). However, equation (2.1.42) disagrees with the starting kinetic equation (2.1.40) the solution of the latter in the absence of reaction, Fi = 0, is Ci(r, t — oo) = nj(0). Consequently, we can find dispersion of a number of particles within an arbitrary volume ... 

Fig. 1 (a) Typical clean Northern European median number size distribution (measured at SMEAR II station in Hyytiala, Finland). The approximate modal locations and size ranges of different integral properties of the aerosol number size distribution used are shown (b) variance of number concentration as a function of particle diameter (c) variance of (computed) volume concentration in the same station (adapted from Asmi (2012), [11])... 

In precipitation, particle formation is extremely fast due to high supersaturations which in turn lead to fast nucleation. At least in the beginning, size distributions are narrow with particle sizes around one 1 nm. Nanomilling in stirred media mills is characterized by relatively slow particle formation kinetics, particle sizes ranging from several microns down to 10 nm and high sohds volume concentrations of up to 40%. Large particles may scavenge the fine fractions. The evolution of the particle size distribution can be described for both cases by population balance equations (Eq. (7)),... 

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