Sauter mean diameter

The Sauter mean diameter is a characteristic size of a particle size distribution. It is defined as follows: one would the volume of the particles of a bed of equal size forming spheres whose entire surface is equal to the total surface of the particles, these balls have the Sauter mean diameter as a diameter.

Importance

The Sauter mean diameter is mainly used for the description of particle size distributions of solids ( eg sand) and crushed liquids (eg sprays or drops in emulsions). The according to DIN ISO 9276-2 correct term for the Sauter mean diameter is:

Widely used in the literature can be found, among others, but also the following designations ( d equivalent to x, with and without a comma, often without macron due to software limitations):

The Sauter mean diameter is formulated mathematically as:

Wherein the specific surface

The ratio of total surface area and total volume of the particles. The specific surface area can be described similarly to the equivalent diameter of form factors.

A further application is the description of porous solids. In this case, more emphasis is placed on the porosity in the mathematical formulation:

Wherein the porosity and the volume-based inner surface referred to.

The porous solids, for example, consist of tightly packed together adhering to the points of contact or sintered particles between which spatially linked through pores are free.

Is the free volume (pore volume) in relation to the total volume (total particle volume pore volume ) and the entire inner surface in relation to the total volume.

Consists of porous solids from a pack of equal spheres of radius in the volume, then:

Follows for the Sauter mean diameter of it:

So just the sphere diameter.

The Sauter mean diameter is an important parameter in the statistical description of liquid or gas flows through porous solids. Thus, between the locally over several pore diameter averaged flow velocity and the locally averaged pressure gradient is a linear relationship:

Wherein the permeability of the porous solid and the viscosity of the liquid or gas respectively. For geometrically similar structure, including the same porosity, the permeability is proportional to the square of the Sauter diameter: