Particle analysis: Obtaining representative subsamples

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The goal

Some particle analysers can work with only small samples, and thus it is sometimes desired to obtain a subsample of sand that has the same particle-size distribution as a larger source sample. For example, if a laser diffraction particle analyser requires sample size of five grams of sand, how can those five grams be obtained from a larger sample, such that the five gram subsample has the same particle-size distribution?

The obstacles

Despite usually appearing to be homogeneous, dry sand is quite prone to being or becoming inhomogeneous when jostled. Grains in a bag of sand are almost certainly not evenly distributed by size; smaller grains will tend toward the bottom, due to percolation (they fall downward between the gaps of larger grains). Stirring or shaking 'to mix it well' can actually make things worse, depending on the sizes present, as movements provide more opportunity for the smaller grains to fall downward.

This is a well-known, well-studied problem. Subsampling techniques are reported to vary substantially in their expected sampling error:

MethodEstimated maximum
sample error
Spinning riffling0.4%(best method)
Chute splitting3.4%
Table sampling7.0%
Scoop sampling17.1%(a common method)
Cone and quartering22.7%

Table 1. Reliability of selected subsampling methods [Chemical Engineers' Handbook, 7th edition]

Solutions

With spinning riffling, the best of the subsampling methods above, the entire sample is slowly deposited into a series of containers, each of which collects a fraction of the sample (figure 1 and 2). Rotation, either of the collectors or of the depositor, spreads the deposit evenly over the containers. Further divisions can be obtained by repeating the process with one (or more, combined) of the resulting fractions, until the desired subsample quantity is obtained.

The objective is to deposit a stream of grains such that any concentration of grains of a particular character is spread over several (ideally, all) collection bins. Thus it is best to have a high number of revolutions while the grains are flowing. A rule of thumb is that at least 20, better 100, rotations ought to occur during the time it takes to deposit the sample.

Commercial spinning rifflers are available, eg., US$2000 on eBay. First, however, we thought we'd give it try as a 'do it yourself' project. This web page describes what we did.

Splitting/spinning Riffling

Paper cone riffle splitter

Fig 1. Paper cone riffler. Funnel is moved. After Gerlach (2002).

Gerlach (2002) describes a simple paper cone riffle splitter (figure 1a) constructed from a piece of paper with a few 'Orgami' folds. A square of paper is cut into an octagon (by getting a second identical square, centering it over the original, then rotating it 45 degrees; cut off the exposed parts of the underlying original). The octagon has four pairs of opposing points; fold the octagon in half such that the fold goes through one pair of opposing points; unfold and do it again for the other three pairs, always folding in the same direction (this creates the ridges illustrated by dashed lines in figure 1b). Then create the 'valley' folds in the opposite direction by folding the octagon in half, bringing opposite edges together, for each pair of edges. The result should be a cone-shaped 'mountain' with eight 'valleys' each separated by a ridge, as in figure 1b.

Containers are placed at the mouth of each trough of the paper cone, as in figure 1a. A funnel (which could also be constructed from paper) with a small opening is loaded with sand and then moved in a uniform circular motion around the apex of the splitter, such that sand falling onto the slopes and into the eight troughs falls into the collection containers. The funnel should complete at least 20 circuits while draining.

Alternatively, the collectors and cone could be mounted upon a turn-table, so that the funnel could be held steady, along the lines of the spinning riffler discussed next.

Spinning riffler

Fig 1b. Spinning riffler. The collectors rotate, funnel is fixed.

Spinning riffling involves dropping the sample onto pie-shaped containers arranged in a circle (figure 1b). The containers need not be the same width.

DIY spinning riffler

Below is a video of a do-it-yourself spinning riffler operating, with collection bins made of aluminum foil over cardboard, rotated using an old phonograph turntable at 33 rpm. The collection bins are one-eight, one-quarter, one-eight, and one-quarter sections.

Fig 2. Video of an operating spinning riffler, with funnel.

Here are some construction considerations:

The pie-wedge-shaped bins in figure 2 were constructed of uncorrogated cardboard surfaced with aluminum foil held by a thin layer of epoxy, as described below. One corner of each bin was left open so that material could be poured out.

Fig 3. Cardboard backing for bins

To prevent grains from falling between bins, the foil on one edge of each bin was folded downward so that it would overlap with the edge of the neighbouring bin, as shown in figure 4 below.

Fig 4. Aluminum foil overlap to cover the gap between bins

With an old phonograph turntable providing 33 revolutions per minute, to reach the desired number of revolutions (20 to 100) requires the sand to be depositing onto the spinning riffler for at least a minute, and better, two minutes. To a limit, this can be accomplished by making the opening of the funnel smaller. However, eventually the opening becomes so small that grains jam and some other method is required to deliver the sand to the spinning riffler. For aeolian dune sand with a median diameter of about 300 microns, this became a problem when the total sample size was less than about 10 grams -- leading to the additions described in the next section.

Conveyor belt and vibrating hopper for spinning riffler

This 'spinning riffler' project went into 'overtime' when it turned out that some of the samples were too small to feed for at least a minute or two through the funnel of the simple spinner described in the previous solution. We tried two other methods of providing a steady feed to the spinning riffler: a conveyor belt (which was inadeqaute on its own), and an additional vibrating hopper (which was successful). In the combination, sand spread over a slow-moving conveyor belt is delivered sand to a vibrating hopper that deposits it onto the spinning riffler (figure 5).

Fig 5. Conveyor belt delivering sand to a vibrating hopper trough.

A conveyor belt alone is too bursty; sand tends to stick until the angle of yield is exceeded, then fall from the end of the conveyor in a burst until reaching the lesser angle of repose. Burstiness is not desirable, of course, as it works against the goal of the spinning riffler. To smooth out the bursts, a vibrating hopper was added. Figure 6 shows a video clip of it operating. There are three independent pieces of equipment: conveyor, vibrating hopper, and spinning riffler. Sand falls from one to the next, reminiscent of 'Rube Goldburg' machines.

Fig 6. Video of an operating spinning riffler, with vibrating hopper and conveyor belt.

The conveyor belt plus hopper worked well. Being able to spread the full sample along the belt enhances the operation of the riffler. However, it may work equally as well to have just a long vibrating hopper, with the sample spread along the length of the hopper and then delivered gradually, via vibration, to the riffler (if all grain sizes would be transported at an equal rate; perhaps a risky assumption).

Figure 7 shows the design of a vibrating hopper constructed from a length of thin aluminum, coated with aluminum foil, suspended from three points by elastic bands from a wooden paint stirring stick. It's mounted on a camera tripod for easy control of the angle and position. Vibration is provided by a 1.5 VDC motor with an offset (eccentric) weight on its shaft. Some trial-and-error was required to get a vibration mode that was not too vigorous.

Fig 7. Vibrating trough, suspended at three points by elastic bands. 1.5 VDC motor with eccentric weight.

Here are some considerations:

As mentioned, the conveyor belt and vibrating trough are probably only worth considering if the sample size and texture wouldn't be well-handled by just a funnel.

Related pages

Sampling dune sand. Getting a good sample to start with.

References

Gerlach, Robert W. et al, 2002. Gy's sampling theory in environmental studies. 1. Assessing soil splitting protocols. Journal of Chemometrics 16: 321-328.