Packing fraction of particles with lognormal size distribution

2014 ◽  
Vol 89 (5) ◽  
Author(s):  
H. J. H. Brouwers
Clay Minerals ◽  
2000 ◽  
Vol 35 (2) ◽  
pp. 423-432 ◽  
Author(s):  
P. Uhlík ◽  
V. Šucha ◽  
D. D. Eberl ◽  
L'. Puškelová ◽  
M. Čaplovičová

AbstractThe Bertaut-Warren-Averbach (BWA) technique and high-resolution transmission electron microscopy (HRTEM) were used to characterize the products of dry-ground pyrophyllite. Mean crystallite thickness and crystallite thickness distributions were measured for each sample using the BWA technique. Mean crystallite thickness decreases during the treatment with respect to grinding time and energy applied per unit mass. The BWA data were checked by HRTEM measurements and good fits were obtained for samples having small mean particle thicknesses. Samples with thicker particles could not be measured properly by HRTEM because the number of particles counted from images is statistically insufficient. The shape of the crystallite and the particle-size distribution were used to determine the mechanism of pyrophyllite particle degradation. Particles initially having a lognormal size distribution are first delaminated randomly, then some are delaminated preferentially, thereby producing polymodal thickness distributions. Finally all particles undergo delamination yielding a lognormal thickness distribution.


2005 ◽  
Vol 62 (9) ◽  
pp. 3034-3050 ◽  
Author(s):  
R. Wood

Abstract This is the second of two observational papers examining drizzle in stratiform boundary layer clouds. Part I details the vertical and horizontal structure of cloud and drizzle parameters, including some bulk microphysical variables. In this paper, the focus is on the in situ size-resolved microphysical measurements, particularly of drizzle drops (r > 20 μm). Layer-averaged size distributions of drizzle drops within cloud are shown to be well represented using either a truncated exponential or a truncated lognormal size distribution. The size-resolved microphysical measurements are used to estimate autoconversion and accretion rates by integration of the stochastic collection equation (SCE). These rates are compared with a number of commonly used bulk parameterizations of warm rain formation. While parameterized accretion rates agree well with those derived from the SCE initialized with observed spectra, the autoconversion rates seriously disagree in some cases. These disagreements need to be addressed in order to bolster confidence in large-scale numerical model predictions of the aerosol second indirect effect. Cloud droplet coalescence removal rates and mass and number fall rate relationships used in the bulk microphysical schemes are also compared, revealing some potentially important discrepancies. The relative roles of autoconversion and accretion are estimated by examination of composite profiles from the 12 flights. Autoconversion, although necessary for the production of drizzle drops, is much less important than accretion throughout the lower 80% of the cloud layer in terms of the production of drizzle liquid water. The SCE calculations indicate that the autoconversion rate depends strongly upon the cloud droplet concentration Nd such that a doubling of Nd would lead to a reduction in autoconversion rate of between 2 and 4. Radar reflectivity–precipitation rate (Z–R) relationships suitable for radar use are derived and are shown to be significantly biased in some cases by the undersampling of large (r > 200 μm) drops with the 2D-C probe. A correction based upon the extrapolation to larger sizes using the exponential size distribution changes the Z–R relationship, leading to the conclusion that consideration should be given to sampling issues when examining higher moments of the drop size distribution in drizzling stratiform boundary layer clouds.


2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Jian Yang ◽  
Jianan Lu ◽  
Shanmeng Zhang ◽  
Dong Guan

To study the sensitivity of the surface acoustic wave (SAW) sensor towards particulate matter (PM), an analytic model has been built based on single particle perturbation theory of full size range and the lognormal size distribution of the PM. The sensitivity of the frequency shift to 1 nanogram of PM has been calculated. The model shows that the frequency shift is a result of the competition between the negative perturbation by mass loading and the positive perturbation by elastic coupling, determined by particle size distribution parameters, material, and SAW frequency. To verify the model, the relationship of the frequency shift of a 315 MHz SAW to the concentration of aerosols generated by two kinds of powders of different sizes was measured. The experiment is in agreement with the model: the sensor has shown negative sensitivity towards aerosols generated by the finer particles of 1 μm, 3 μm polytetrafluoroethylene (PTFE), and A1 Arizona dust and positive sensitivity towards aerosols generated by the coarser particles of 10 μm PTFE and A4 Arizona dust; and the negative sensitivity is about 1 order higher than the positive.


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