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ISO Terms for Sand Sedimentation Balances

Currently, the ISO working group (WG2) of technical committee TC24 has prepared a working draft — "Determination of particle size distribution by gravitational liquid sedimentation methods - Part 4: Balance method". The convener of WG2 has invited me to participate as an expert in this field.

My special task is to define standards in the range of the transitional sedimentation regime, i.e., in the region between the Stokes' law and Newton's law. For quartz density particles sedimenting in water and similar liquids, the range is valid for sand-sized particles, and the sedimentation must be stratified (from one level into clean liquid, line-start methods).

The sedimentation of a single particle is the most accurate method for determining the size of a particle if we are aware of all influencing factors:

1. Size definition must be independent of non-spherical (irregular) particle shape.
The volume-equivalent sphere diameter dn of an irregular particle, the nominal volume diameter (Hakon WADELL, 1934), is independent of particle shape. It equals:
dn = (6.V/π)1/3 where V is particle volume.
2. Sedimentation methods employ the equivalent of a sphere settling in the same liquid and under the same acceleration due to gravity using formulas for settling velocity valid in the given flow regime, such as:
a) by George Gabriel STOKES (1845): spheres sedimenting in laminar flow (small Reynolds’ number, usually 10-7<Re <0.1);
b) by A. A. KASKAS (1964): spheres sedimenting in laminar, transitional and impact (Newton) flows (10-7<Re <104);
c) by Jiri BREZINA (1977, 1979): shape factor (SF) defined irregular particles (sedimentation equivalent to a rotational ellipsoid) sedimenting in all regimes (10-7<Re<104).

However, in the sedimentation of more particles, the particles will mutually affect the sedimentation of each other. These additional particles in suspension will increase both the suspension density and viscosity, in proportion to their instantaneous local concentration and particle surface area.

Generally, a sample of particulate solid material should undergo the type of sedimentation, in which the following factors are exactly known:

1. The nature of the acceleration, which moves the particles, such as gravitational or centrifugal acceleration.
2. The instantaneous local particle concentration.
3. The particle surface area – which is important when dealing with fine and/or markedly non-spherical particles.

In sedimentation balances, acceleration is due to gravity and therefore easy to determine. The instantaneous local particle concentration is the main problem.

Sedimentation balances designed for fine particles such as those by SARTORIUS, GALLENKAMP, METTLER, CAHN and other companies, operate within the laminar (Stokes’) regime (10-7<Re <0.1 or 0.3). In this case, the settling particles do not have sufficient force to overcome the viscous force of the liquid and to separate from each other.

To maximize the mutual distance among the particles, Sven ODÉN (1915) suggested homogenizing the suspension in the sedimentation column. This homogeneous suspension avoids a hydrodynamic instability: every level of the column has the suspension density, which, starting at a zero vertical gradient, becomes increasingly positive as sedimentation proceeds. In other words, the suspension density does not decrease but increases downwards during settling.

However, the sedimentation length of particles is known only for those particles that started at the top. To mathematically subtract the particles with an unknown sedimentation length, the first derivative of the sediment weight accumulating on the balance pan (sedimentation function/curve) must be recorded.

The sedimentation of a homogeneous suspension includes the following disadvantages (error sources):

1. The majority of the particles has an unknown sedimentation length.
2. The particles with a known sedimentation length are those that started at the top of the column. They are descending most rapidly and therefore they all must pass slower particles, that are hindering them.
3. The suspension density and viscosity are increasing downwards with the particle concentration, which is also increasing downwards during sedimentation.

The balance pan collects the sediment and creates a suspension shadow of particle-free (clear) liquid below the pan. The lower density of this liquid introduces a hydrodynamic instability. With the growing concentration of particles suspended above the pan, the clean liquid induces a buoyant force pushing the pan upwards and increases with the progress of sedimentation. The shadow below a balance pan in a homogeneous suspension decreases the sediment load.

Kurt LESCHONSKI (1962, Staub, vol. 22, p. 475) has developed a device, which compensates the buoyancy (German patent). Use of his compensation method is inevitable even for balance pans that have a protective cylinder at the pan's edge (such as that shown schematically in Figures 1 and 2 of the Proposal).

Of course, the clear liquid that is overlain by the homogeneous suspension above the pan will flow upwards (as bubbles) around the pan. This will then cause streaming errors within the overlying suspension. However, using the Leschonski's compensation tube  - an equal volume of the overlaying heavier suspension can flow down to replace the volume of the clear liquid.

Sedimentation balances for sand-sized particles, such as the Sand Sedimentation Analyzer™ (MacroGranometer™) by Granometry (Jiri BREZINA, 1969 through 1979), may attain the highest precision level: they operate within the transitional hydrodynamic regime (0.1<Re<3.104), in which the particles have enough force to overcome the viscous force of the liquid, separate from each other and ultimately settle with less dependency on each other. This is the reason why the sand-sized particles are not required to sediment in a homogeneous suspension: the sample can be introduced for sedimentation at the uppermost level of a clear liquid (line-start method - term introduced by Brian H. KAYES, 1969). Then the concentration of particles will rapidly decrease as they settle. Suspension streaming can then be restricted up to the uppermost 5 cm of the sedimentation column. This type of suspension and sedimentation is referred to as stratified because each layer contains particles that have the same sedimentation velocity.

Synonyms:
Settling Tube             - used in America, Europe, most countries of Asia
Sedimentation Tower - used in Australia and New Zealand, rarely in GB.

A sedimentation balance for sand-sized particles consists of the following parts:
http://www.grano.de/analyzer.htm

Stratified sedimentation/suspension is described:
http://www.grano.de/article1.htm#stratsusp

Advantage of Stratified Over Homogeneous Sedimentation

Particles settling in groups must be allowed to sediment at mutual distances such that their settling velocities become close to those of single particles. Sedimentation of coarse (sand-sized) grains in water generates forces which liberate the grains from each other: these forces surpass viscosity of the water because the Reynolds' number of the particle is greater than 0.1. Therefore, the coarse grains need not be homogenized for sedimentation, but can be introduced at the top of a particle-free clear fluid. Particles become distributed vertically according to their settling velocity, which is identical for particles at each level: as a result, the so called stratified suspension develops (H. J. Skidmore, 1948, ref. 98; John S. McNown and Pin-Nam Lin, 1952, ref. 90), and stratified sedimentation takes place.

Stratified sedimentation enjoys fundamental accuracy advantages over homogeneous sedimentation. First, the sedimentation length of all particles is known in a stratified suspension. In homogeneous suspension, the sedimentation length is known only for the topmost particles at the beginning of sedimentation; other particles interfere with them and their weight must be eliminated mathematically by taking a derivative. Secondly, the particle concentration (and thus the amount of particle interference) rapidly decreases in the expanding volume of stratified suspension, but it increases toward the bottom of the homogeneous suspension.

A sedimentation balance for sand-sized (0.05 – 4 mm quartz density) particles that uses stratified sedimentation consists of the following parts (see figures here: http://www.grano.de/analyzer.htm ):

1. A settling tube composed of glass modules (ISO 3587/1976, 4704/1977), flanges and gaskets as defined in EN 12 585), vertical tube with an inner diameter of 20 cm; a horizontal tube (inner diameter of 30 cm) of a cross piece needed to accommodate an underwater electronic balance. The settling tube provides a sedimentation distance of 180 cm (measured from the Venetian blind lamellae to the top of the balance pan). The glass walls provide both the needed vibratory and thermal stability.
2. A Venetian blind for release of the sample and dispersion of particles in the upper 5 cm of the settling tube. After the lamellae open, they vibrate at about ±5° around their vertical position, and at a frequency of 10-20 Hz. 25 lamellae (each 20 cm long, 0.7 cm wide, 0.03 cm thick) are covered by 0.7 cm of water. After the sample is dispersed onto the closed lamellae, the water surface must be covered by a rigid plate allowing no air bubbles to form: this avoids vibrations, which could be formed by waves on a free, uncovered water surface. In addition, the closed water surface prevents evaporation of the water which cin turn could cool the top of the water and thereby cause streaming.
3. An underwater electronic balance, with a balance pan of 26 cm in diameter. The balance sensitivity: ±0.01 % of the sample mass of 0.1 – 5 gram. The balance response should be fast (at 30 millisecond for 99 % of the total weight) to record the fastest particles (at 30 cm/sec). Therefore, the underwater weight of the sample must depress the pan by a minimum (maximum 0.1 millimeters by the 10 gram of a mass of quartz). If a spring balance is used, the spring must be very rigid. This permits unhindered sedimentation in the 20 cm wide sedimentation column (this is the width that requires the 26 cm maximum diameter pan).
4. Shock absorbers for holding the settling tube and insulating it from environmental vibrations (frequencies >20 Hz should be eliminated).
5. The Balance electronics must provide a high quality digital signal with the highest possible signal-to-noise ratio (S/N greater than 90 decibel).

Room temperature

The temperature of the immediate surroundings should not change during the course of the analysis (maximum 20 minutes). Neither should the air temperature vary by more than ±0.5 °C (Celsius temperature is more suitable than Kelvin, because it is identical for differences) during the analysis. To avoid water streaming in the settling tube, a positive vertical temperature gradient of at least +1° C/meter is required. A local vertical gradient of as much as 1° C/cm in the upper 5 cm of the sedimentation column will counteract streaming when the sample is introduced.

However, special care must be taken to avoid any infrared radiation onto the settling tube, i.e. IR radiation from any warmer object in the vicinity of the tube, especially onto its lower part.