Particle size determination of porous powders using the SediGraph

Sedimentation analysis based upon Stokes’ Law provides a convenient method for determining particle size distribution (PSD). A single solid (or nonporous) sphere settling in a fluid has a terminal settling velocity which is uniquely related to its diameter. The SediGraph determines particle size distributions using the sedimentation method. By measuring the gravity-induced settling velocities of different size particles in a liquid with known properties, the particle sizes are determined. The rate at which nonporous particles fall through a liquid is described by Stokes’ Law as

• Dst = [18ηV/(ρs – ρ1)g]1/2
• Dst = Stokes’ diameter
• η = fluid viscosity
• ρs = density of the solid
• ρ1 = density of the liquid
• V = settling velocity
• g = acceleration due to gravity

The measured particle size distribution is a function of the particle skeletal density. The skeletal density is defined as the mass of discrete pieces of solid material divided by the volumes of the pieces and closed (or blind) pores within the pieces. Such information is easily obtained with a helium pycnometer. However, for most pure materials the handbook value for density is quite sufficient.

A fully wetted porous particle settling in a liquid has an effective density different from the skeletal density. The effective density is a linear combination of the particle percent porosity times the density of the fluid plus (100% – % porosity) times the particle skeletal density. In the form of an equation, this statement becomes

• ρes = [P – ρf + (100 – P)ρs/100]
• ρes = effective sedimentation density for a particle with open pores
• P = percent open porosity of the particle
• ρf = density of sedimentation fluid
• ρs = skeletal density of the nonporous particle

A powdered Si/Al catalyst substrate serves as a good example. The skeletal density of this material is 2.60 g/cm3.

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