# Thread: mean particle diameter

1. ## mean particle diameter

Dears,

In designing many material handling equipment such as airslide, we need a parameter which called mean particle diameter, so

What is the practical definition of mean particle diameter?
when we have only particle size distribution such as K20, K40, K50, K70, K80, K90 and K100, how we can find mean particle diameter?

Is it true to say that particle size for K50 refer to "mean particle diameter"?

In the glossary of terms of Mr. Lyne Bates, I have found these two definitions that I am nor sure if they are equivalent to mean particle diameter or not?

diameter, mean: Several mean diameters can be presented of particle size distribution data. To understand them, consider an experimental study (for example, by microscopy) where the population of particles is counted within several finite size classes. It is found that there are i particles within any size interval (i), which has an arithmetic mean diameter of d i . The full size distribution is obtained by accumulating data over several size intervals, becoming more accurate if the intervals are small, so that di becomes a better estimate of the real average particle size within the interval.

mean particle size: Dimension of a hypothetical particle such that, if the total mass of the particulate system was wholly composed of such identical particles, they would all have that dimension.  Reply With Quote

2. Dear Mohandes.

Have a look at:

https://www.horiba.com/fileadmin/upl..._Guidebook.pdf

A mean particle size is normally the mass weighted average of a particle size distribution.

have a nice day  Reply With Quote

3. ## practical estimation

Dear Teus,

Many thanks for your attention.

However, most of the time, we have only particle size distribution such as K10, K30, K50 , K70, K80, K100.(for example if K50=2mm, it means 50% of material is below 2mm)
I would like to know in designing for example airslide, practically you use which of the above parameters? you suggest K50 or because of unsymmetry K70?
I need a rule of thumb.

You know that in most projects all we have about the material is only particle size distribution in a table format.  Reply With Quote

4. Dear Mohandes,

From:
size distribution such as K10, K30, K50 , K70, K80, K100.(for example if K50=2mm, it means 50% of material is below 2mm)
You can derive a sieve analysis, whereby each sieve retains a fraction f(i) % of d(i)of the sample.

The mean particle diameter is then calculated as:

d(mean)=∑[f(i) % * d(i)] / (100%)

From this d(mean), and the product properties (Material density), a suspension velocity is derived.

For an air slide, the upward air velocity above the fabric must be higher than this suspension velocity.
Then the particles are separated in the air stream and lose their internal friction.

The required air pressure is the combination of all pressure drops plus the static height of the material times the fluidized density.

The material must be classified to the Geldart diagram A (aeratable)

For most materials, air slide designs are known and moreover a simple test can easily be arranged
by an air slide manufacturer.

Have a nice day  Reply With Quote

5. ## 'Mean'particle size

The difference in terms in the Glossary is that one description relates to the mean size of one particle according to the way that it is measured and the other term refers to the mean size of a mass of particles. For practical purposes, the dimension of interest depends on its relevance to the application.  Reply With Quote

6. I would suggest that with relation to the design of air slides, the 'particle size' measurement of interest should relate to the drag coefficient that determines its elutriation velocity.  Reply With Quote

7. Originally Posted by Lyn Bates The difference in terms in the Glossary is that one description relates to the mean size of one particle according to the way that it is measured and the other term refers to the mean size of a mass of particles. For practical purposes, the dimension of interest depends on its relevance to the application.
So you mean we don't have a specific definition for the "mean particle diameter" in bulk material handling application?  Reply With Quote

8. ## Mean Particle Diameter Originally Posted by mohandes So you mean we don't have a specific definition for the "mean particle diameter" in bulk material handling application?
The answer to your question is that there is not a unique definition for ‘Mean Particle Diameter’. There are many such values and interest in them varies according to how it will affect the behaviour of the particle(s) in given practical conditions.

I would approach this question on fundamental grounds. The expression ‘Mean diameter’ is imprecise as there are many ways to describe a ‘Mean’: - arithmetic, geometric, in terms of standard deviation, equivalent sphere, Sauter mean particle size and so on. As will be seen in the Glossary, there are also various ways to consider the ‘Diameter’ of a particle. In practice, therefore, interest in such a descriptive dimension is relative to a specific factor of significance.

This first means that it should be made clear whether the description applies to a single particle or is taken to represent the ‘average’ value of a collection of particles.

The second step is to consider the relevance of this ‘mean’ value to the particular process condition under consideration. i.e. what is the dimensional feature of prime interest?. Assessing the results of sieving, segregation or fluidisation may each involve different behaviour to that in a pneumatic conveying system. This situation emphasises the need for understanding the basic principles involved before applying some published factor or formula to a practical application as guidance seems to be lacking on the selection of a particular way of defining the ‘Mean particle Diameter’, or perhaps the more common ‘Mean particle Size’, relevant to a given use of the bulk material.  Reply With Quote

9. Dear Mohandes,

Mean particle size is indeed related to the specific purpose where it is used for.

A pneumatic conveying calculation of a product, consisting of a variety of particle sizes, which interact in collisions and thereby exchanging kinetic energy until the overall material velocity is equal.

The assumption here is that the various particle size fractions are accelerated and have acquired the corresponding kinetic energies and that afterwards, through collisions, the kinetic energy is spread over the particle size fractions, resulting in an equal v_particles=v_product

This results in:

size_(particle-kinetic_mean )=√(1/(∑_1 to n (Fraction_n/(size_particle_n)^2 )))

For a mean particle size, related to the suspension velocity:

size_(particle_suspension_mean )=∑_1 to n (Fraction_n*√(size_particle_n ))^2

Here, the total energy to keep the collection of particles in suspension is equal to the energy to keep a collection of a uniform particle size of size_(particle_suspension_mean ) in suspension.

A particle size based on particle surface is relevant for chemical reactions.
In the cement industry is the Blain Number used.

particle size δ=(20303/Blaine)^2 in micron

Have a nice day  Reply With Quote

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