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Last Updated on Tuesday, 01 October 2013 02:23

Settling velocity 

Variable 1: Logarithmic Settling Velocity, PSI; Laboratory, Standard and Local

Synonyms of ‘settling’: sedimentation, fall;

Synonyms of ‘velocity’: rate.

Settling velocity is the most natural dispersity variable measured by sedimentation. In the Macro­Granometer™, the depositing sample is weighed at sedimentation time instants, which correspond to a series of 0.02-intervals of settling rate logarithm, PSI (English transcription of the Greek letter j, or capital Y) according to G. V. MIDDLETON, 1967:

PSI = -log₂v = -logarithm to the base 2 of settling velocity in centimeter/second.

The Macrogranometer’s™ PSI range:

PSI is a very useful dispersity unit for two main reasons:

1. Most of the well known negative PHI distribution skewness of some water deposited medium sands does not occur in PSI distribution of the same material as shown by Jiri BREZINA (1963) by transformations of the log grain size into the log settling rate (he used his BETA settling rate). The negative skewing effect is shown on pages 6 - 10 (Figs. 1 - 4 and Fig. 7).
2. Settling rate is free of assumption about a constant shape and/or density, and can be converted very efficiently into another dispersity variable.

Superiority of the settling rate over grain size as dispersity unit

1. In sedimentological studies, sedimentation, not a sieving is a process which controlled the sediment origin. Therefore, a grain settling rate, not its size, reflects the hydrodynamic origin and location of the sample grains. Sieving is a very poor technique because of many non-sedimentologic influences, such as woven sieve holes, different sieving time for fine and coarse grains, sieve shaking direction, discontinuous measuring due to limited sieve intervals. 
2. Settling rate is a variable, which can be measured by the highest accuracy. No optical or other method allows the grain size to be measured that accurately. In fact, the settling rate can be used for calculating the grain size with unprecedented accuracy. My MacroGranometer, limited by a weighing constant of 0.026 seconds on the sedimentation length of 180 cm, allows thus the size resolution of 0.01 mm with coarse grains (4 mm = -2 PHI) and 7.42*10-7 mm with fine grains (0.05 mm = 4.32 PHI). 
3. Non-spherical grain shape makes the sedimentational grain size finer, similarly as it increases the grain specific surface. But, a non-spherical shape makes the sieve grain size greater, which is inconsistent with grain specific surface decreasing with grain size. Grain properties, which are affected by the grain specific surface, such as permeability are therefore incorrectly estimated when sieving grain size is used instead of sedimentationl grain size.

However, because the measuring terms - gravity acceleration and temperature - may vary, the PSI values referring to the measured data are valid for the laboratory terms only, and - strictly speaking - are not compatible with PSI data measured at a different temperature and/or under a different gravity acceleration. In order to recognize this effect, we call the measured PSI laboratory PSI, and introduce a standard PSI valid for internationally acceptable standard terms (the conversion is accomplished by our SedVar™ program):

distilled water, temperature 24.00°C, gravity acceleration 980.665 gal.

The main advantage of the standard PSI is that it is internationally comparable. Of course, the con­version involves a slight inaccuracy due to current estimation and non-constancy with grain size of both particle shape and density; however, the possible error is usually smaller than 0.01 PSI.

Nevertheless, a more important error of any PSI may be introduced by impurity of the distilled water used for sedimentation. All conversions assume that the distilled water is free of dissolved admixtures; in particular, dissolved gas decreases strongly kinematic viscosity and density of water, which are calculated from the measured temperature for absolutely pure water.

The term “distilled water” is recently used even for water purified by methods other than heat distillation, which requires boiling and vapor condensation. These other methods based on filtration, ionic exchange and/or (electro)osmosis may meet highest purity requirements common in analytical chemistry, but they do not remove dissolved gas (air). Water purified this way should be called demineralized or deionized but not distilled. The dissolved gas can be removed (deaerated) by boiling (supported by vacuum) and vibration (ultrasonic treatment). Also, special care must be given to the way in which the deaerated water is transported and filled into the sedimentation column: disturbance and mixing with air must be avoided.

Standard and local PSI are compound (bivariate) variables because each is defined only if two of the three quantities (PHI, Rs, SF') are constant, and the remaining one becomes a PSI joint variable. This is why three versions of the standard PSI (=for three material types) are recognized, identified by File Name Extension, and can be calculated (see also the three Reynolds number versions, page 13):