Size-frequency distribution plotting

Using the data given in Problem 1 of the previous chapter plot the corresponding size-frequency distributions. 

T] = 0.00125 Pa s. Alternatively, for comparison purposes, a size frequency distribution may be plotted or tabulated against free-falling diameter. 

FIGURE 2.5 Optical microscopy photographs showing the effect of stirring speed on morphology and particle size of tristearin monostearate 2 1 (w/w) produced at (A) 500 rpm, (B) 750 rpm, and (C) 1000 rpm. Bar corresponds to 650, 650, and 347 pm in panels A, B, and C, respectively. (D) Frequency distribution plot of microspheres produced at 500 rpm (o), 750 rpm (x), and 1000 rpm (0). Data are the mean of three different microsphere batches. Lower panel impellers employed for microsphere production, from left to right a 3-blade rotor with a diameter of 55 mm (taken as reference impeller), a 4-blade helicoidal rotor with a diameter of 50 mm, a 2-blade rotor with a diameter of 50 mm, and finally a double-truncated cone rotor with a diameter of 50 mm. 

Particle-Size Equations It is common practice to plot size-distribution data in such a way that a straight line results, with all the advantages that follow from such a reduction. This can be done if the cui ve fits a standard law such as the normal probability law. According to the normal law, differences of equal amounts in excess or deficit from a mean value are equally likely. In order to maintain a symmetrical beU-shaped cui ve for the frequency distribution it is necessary to plot the population density (e.g., percentage per micron) against size. 

Bulk particulates of various sizes can be analysed to display their particle size distribution and a frequency histogram plotted, as shown in Figure 1.8. 

The output of a Nd YLF laser is focussed by a series of lenses to a spot size of 0.5 pm upon a sample which may be positioned by an x-y-z stepping motor stage and scanned by a computer-controlled high frequency x-y-z piezo stage. Ions are accelerated and transmitted through the central bore of the objective into a time-of-flight (TOF) mass spectrometer. The laser scans an area of 100 x 100 pm with a minimum step size of 0.25 pm. TOF mass spectra of each pixel are evaluated with respect to several ion signals and transformed into two-dimensional ion distribution plots. 

As AD is made smaller, a histogram becomes a frequency distribution curve (Fig. 4.1) that may be used to characterize droplet size distribution if samples are sufficiently large. In addition to the frequency plot, a cumulative distribution plot has also been used to represent droplet size distribution. In this graphical representation (Fig. 4.2), a percentage of the total number, total surface area, total volume, or total mass of droplets below a given size is plotted vs. droplet size. Therefore, it is essentially a plot of the integral of the frequency curve. 

The distribution of particle sizes can be seen more readily by plotting a size frequency curve, such as that shown in Figure 1.6, in which the slope Ax/Ad) of the cumulative... 

The results from the first study suggest rather clearly that conversation group sizes are limited at about four individuals (one speaker and three listeners) (Dunbar et al. 1995). Fig. 3 plots the cumulative frequency distributions for the number of individuals that a speaker can reach (i.e. conversation group size less one, since there is always only one speaker at any given moment per conversation Dunbar et al. 1995). All three datasets in the sample suggest that the number of listeners rapidly approaches an asymptotic value at around three. 

Example 1.2 A coarsely ground sample of com kernel is analyzed for size distribution, as given in Table El.3. Plot the density function curves for (1) normal or Gaussian distribution, (2) log-normal distribution, and (3) Rosin-Rammler distribution. Compare these distributions with the frequency distribution histogram based on the data and identify the distribution which best fits the data. 

From this distribution calculate the average diameter da9. Plot the size-frequency curve. 

When summation curves are made of the particle-size distribution obeying the exponential law, it is found that the curve follows an exponential relationship similar to that obtained when the frequency distribution is plotted. ... 

It was observed many years ago that particle size data which were skewed and did not fit a normal distribution would very often fit a normal distribution if frequency were plotted against the logarithm of particle size instead of particle size alone. This tended to spread out the smaller size ranges and compress the larger ones. If the new plot then looked like a normal distribution, the particles were said to be lognormally distributed and the distribution was called a lognormal distribution. By analogy with a normal distribution, the mean and standard deviation became... 

Unfortunately, most emulsions do not have a single droplet size. There are small, medium and large droplets present, and it is important to be able to characterise the emulsion for this. This is done by counting the number of particles that is smaller than a specific size, for many different sizes. The resulting data can then be plotted on a curve, the cumulative distribution curve. Alternatively, one can count all particles that have a size within an interval of sizes (e.g., 1-2 pm), and do this for all intervals. Plotting all the numbers obtained for all intervals, then results in a frequency distribution. The two distributions are closely related the derivative of the cumulative curve to the particle size, will give a (continuous) curve that is similar to the discrete frequency distribution obtained earlier, and the smaller the intervals are chosen, the closer the derivative will follow the frequency distribution (see Figure 15.4). 

Note the upper limit of group size is used in plotting cumulative frequency distribution curves. The group midpoints are used in plotting histograms and non-cumulative distribution curves. 

Particle Size Distribution Changes. The number frequency distribution of particles for the base and end latexes are plotted in Figure 3. No particles in the end latex formed by agglomeration had a diameter larger than 9600 A. Furthermore, particles of 1300-9600 A constituted only about 1.2% of the total number of particles. The small particle size (200-400 A) that had constituted more than 5% in the base latex disappeared completely. The peak of the distribution curve shifted from about 380 A to 700 A. 

Fig. 1 a) Strength data of a silicon nitride ceramic tested in four point bending (4PB) in a Weibull plot and b) the relative frequency distribution of flaw sizes. The data points were determined by fracture experiments. 

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