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## Electroacoustics tutorial 2.pdf

**Abstract**
Describes methods of measuring and analyzing the Particle Size Distribution (PSD)in a colloidal suspension or emulsion.

**Table of Contents**
2 Measuring the Particle Size Distribution.2
3 Plotting the Particle Size Distribution.3
Colloidal Dynamics Pty Ltd, Australian Technology Park, Eveleigh (Sydney) NSW 1430 Australia
Colloidal Dynamics Inc, 11 Knight Street, Building E18, Warwick, RI 02886 USA

**1 Introduction**
The particles in a colloidal suspension or emulsion are seldom all of the same sizeand they often have varying shapes. Describing the size and shape is therefore asignificant problem. Emulsion droplets can usually be assumed to be spherical (solong as the distances between the droplets is large enough).

For solid particles we often have to make do with general descriptions of shape likespheroidal, rod- or disk-shaped, even when the system contains individual particleswith other shapes.

The particle size may also vary over quite a wide range. It is not unusual for theparticles of a suspension produced in a grinding operation, for example, to vary by afactor of 100 from the smallest to the largest size. To describe such situations wenormally break the range up into a number of classes and try to find out how manyparticles are in each size range.

This range is called the particle size distribution (PSD), and it can be represented inthe form of a Table or a histogram (see Figure 1).

**Frequency histogram **
**Frequency **200

**Size (mean diameter (nm)**
FIGURE 1 A TYPICAL PSD IN THE FORM OF A HISTOGRAM

**2 Measuring the Particle Size Distribution**
A PSD such as shown in Figure 1 could be obtained by counting the particles ofdifferent sizes in a microscope (or electron microscope) image. This is, however, atedious and time consuming procedure and increasingly we seek methods ofestimating the PSD by indirect methods.

q In some cases we separate out the different sizes and then count (or otherwise
estimate) how many particles are in each size range.

Colloidal Dynamics Pty Ltd, Australian Technology Park, Eveleigh (Sydney) NSW 1430 Australia
Colloidal Dynamics Inc, 11 Knight Street, Building E18, Warwick, RI 02886 USA
q In the second procedure, we try to estimate the PSD without first separating out
The first method is the preferred one when we have plenty of time because it can, inprinciple, yield the most reliable results. There are, however, many situations inwhich it is much better to have a reasonable estimate of the PSD, especially if it canbe obtained quickly.

The most obvious such situation is in a flowing process stream where the particlesize might be a crucial factor in determining the success of a chemical engineeringprocess. Such situations are common in the ceramics industry, in the foodprocessing, cosmetics manufacture and pharmaceutical industries and even incomputer chip manufacture.

Scientists and engineers have applied great ingenuity to the development of suchparticle sizing methods in recent years and there are now a number of ways ofobtaining reliable estimates of PSDs in real time. It is important to recognize,however, that such methods will not normally all yield the same results when appliedto a particular system.

That does not mean necessarily that one is more accurate than the rest. Indeed, theonly time one can expect different methods to yield exactly the same result is whenall of the particles are spherical and of the same size. Different methods measuredifferent aspects of the distribution and sometimes, by combining results from two ormore methods, one can obtain information that is not otherwise available from theindividual methods.

**3 Plotting the Particle Size Distribution**
When the particle size distribution is very broad it is difficult to represent it accuratelyon the normal scale. It is often advantageous in that case to plot the frequencyagainst the logarithm of the size rather than the size itself. A comparison betweenthe two is shown in Figures 2 and 3.

**Particle Size Distribution**
**Re **0.018

**lat **0.016

**ive **0.014

**fre **0.012

**qu **0.01

**en **0.008

**cy **0.006

**Radius ( micron)**
FIGURE 2 A TYPICAL PSD PLOTTED WITH RESPECT TO THE RADIUS (MICRONS)
Notice how asymmetric the plot is in Figure 2 and how the conversion to the log plot(Figure 3) makes for a much more symmetric frequency distribution. The symmetricplot is in this case the normal error curve or the Gaussian distribution function and isthe basis of all standard statistical formulae.

Colloidal Dynamics Pty Ltd, Australian Technology Park, Eveleigh (Sydney) NSW 1430 Australia
Colloidal Dynamics Inc, 11 Knight Street, Building E18, Warwick, RI 02886 USA

**Particle Size Distribution**
**Relative frequency**
**log (radius (micron))**
FIGURE 3 THE SAME PSD AS IN FIG 2 PLOTTED WITH RESPECT TO LOG (RADIUS (IN MICRONS ))
Figure 3 shows that this particular size distribution is a

*log normal distribution*. Sinceit is so close to the normal distribution curve when plotted in this way, it can be veryeasily represented. In fact if one specifies the median size

* *(which in this casecorresponds to the maximum frequency) and the spread of the distribution, the entirecurve is fully specified.

This is the way that most particle size distributions are represented. Almost any realdistribution can be approximated in this way, unless it is one that has two or moremaxima. Such

*multi-modal distributions* are usually thought of as being the sum oftwo or more normal (or log-normal) distributions.

In some industrial situations it is important to be able to distinguish the presence of abimodal distribution (where, for example, the presence of a population of largerparticles might interfere with the main process). The particle size methods that firstseparate the different sizes and then measure them are intrinsically better able todetect the presence of a bimodal distribution.

It is, however, sometimes possible to detect such situations, in a rapid real time (on-line) measurement, but only if the peaks in the size distribution are sufficientlyseparated from one another.

Colloidal Dynamics Pty Ltd, Australian Technology Park, Eveleigh (Sydney) NSW 1430 Australia
Colloidal Dynamics Inc, 11 Knight Street, Building E18, Warwick, RI 02886 USA

Source: http://www.titanex.com.tw/doc/tecsupport/TN-ZP-Particle%20Size%20Distribution.pdf

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