Particle size and shape, as well as particle size distribution (PSD) are key determinants of bulk solids behavior [1–4]. A particle can be defined as a single unit of material having discrete physical boundaries that define its size. Particle science is typically limited to particulate systems within a size range from 10–3 to 104 μm.
The measurement and selection of appropriate average particle size is a difficult task because of inherent particle characteristics. Particle shapes are often irregular, so describing a particle’s size is not straightforward. This one-page reference provides information on methods for describing and measuring particle size.
Particle geometry effects
The bulk behavior of particulate material is greatly dependent on its geometric properties at those scales. In industrial processes, particle size and shape affect phenomena such as the following [2]:
• Catalyst-material reactivity
• Bioactivity and dissolution of pharmaceutical agents
• Setting time of cement
• Agglomeration
• Sedimentation rate
• Flow through porous media
• Flowability of powder
• Packing density of materials
• Permeability of packed beds
• Rate of settling by particles in a fluid
• Gas-solid separation efficiency in a cyclone
• Solids mixing and segregation of solid ingredients
• Handling of solids-containing fluids
Describing particle size
Specifying the sizes of irregularly shaped particles is commonly conceived by representing the size using a simple linear dimensional descriptor, such as diameter. However, because solid particles are irregular and non-uniform, determining the diameter of a non-spherical particle depends on how it is measured. There are several approaches available to representing the size of a particle, categorized into three areas described below.
Equivalent spherical diameter. Equivalent-spherical-diameter methods determine diameters by measuring a size-dependent property of the particle and relating it to a single linear dimension [2]. The equivalent sphere diameter takes advantage of the ideal shape of a sphere represented by the single dimension. The equivalent spherical diameter is the diameter of a sphere that shows the same controlling characteristics as the particle under investigation. The controlling characteristics could be volume, surface area, surface-area-to-volume ratio, settling velocity or other characteristics. Several commonly used equivalent-sphere diameters are shown in Figure 1.
FIGURE 1. With the equivalent spherical diameter approach, particle sizes are represented by an equivalent sphere with the same controlling characteristics (volume, surface area, others) as the particle
Stoke’s diameter is the diameter of a sphere (dst) having the same density and settling velocity as the particle under investigation in laminar flow conditions.
Statistical diameter. The commonly used statistical diameters are Feret’s diameter and Martin’s diameter. Feret’s diameter is defined as the distance between two parallel tangents, while Martin’s diameter is defined as a length of the chord that bisects the particle outline (Figure 2).
FIGURE 2. Statistical diameters of a particle can be defined in different ways. Commonly used ones are Feret’s (B) and Martin’s (C)
Equivalent circle diameter. Equivalent circle diameters, such as the projected area diameter (area of circle with the same area as the projected area of the particle under investigation), can also be used (Figure 2A). These measures are outdated due to their statistical nature and poor reproducibility because there are many possibilities to estimate distance between tangents and bisector.
Measuring particle size
There is no single standard method to measure particle size. Each method has pros and cons. Some of the standard methods that are used to measure particle size and size ranges are shown in Table 1 [3].
References
1. Trottier, R. Dhodapkar, S. and Wood, S., Particle Sizing Across the CPI, Chem. Eng., April 2010, pp. 59–65.
2. Patel, C.M., Particle Size Characterization and Analysis, Chem. Eng., July 2019, pp. 54–60.
3. Lawrence, J., Powder and Bulk Solids Handling: Particle Size and Distribution Analysis, Chem. Eng., November 2017, pp. 55–59.
4. Johanson, K., Selecting the Proper Mill for Your Product, Chem. Eng., November 2013, pp. 47–54.