Method: Observing sand flow in an adapted Hele-Shaw cell

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Flowing sand can be conveniently observed in a narrow chute with transparent walls, constructed as described below.

Such an apparatus is often referred to as a 'Hele-Shaw cell' (Makse, 1997, 1998). The Hele-Shaw cell was invented circa 1898 by Henry Selby Hele-Shaw to study fluid flow, and consisted of horizontal plates separated by perhaps only 1 mm (to approximate two-dimensional flow).

The original Hele-Shaw cell design is adapted for studying granular materials by standing it vertical, differentiating it from the original by using adjectives such as 'vertical' (orientation of the plates), 'granular' (grains instead of fluid), and 'quasi-two-dimensional' (because there is a perhaps-significant third dimension in these relatively widely spaced plates).

So described below is a vertical, quasi-two-dimensional, granular Hele-Shaw cell used to observe the flow and behaviour of granular materials. I'm interested in using it to observe the flow of natural dune sand.

Preparation

Fig 1. Paw Hole sand in 'Hele-Shaw cell'

To reduce the amount of sand required, I built a sloping cell, as pictured to the right. Clear 3mm-thick Plexiglas is used for the front of the cell, and the back is 2mm-thick white Plexiglas. The bottom is a strip of 3mm-thick Plexiglas 1.9 cm high (thus the cell is 1.9 cm wide). A U-shaped length of masking tape is positioned sticky side up over the bottom spacer such that the bottom of the cell had exposed sticky tape (soon covered with sand grains); this avoids sand sliding down a bare, slippery Plexiglas surface. The upper (left, in figure 1) end is left open so that sand can flow in at all heights from a paper hopper. The lower (right) end can be blocked with the same width of material that forms the bottom of the cell, or left partially open (so that sand can flow out of the cell after reaching a certain height). Spacers of the same width as the bottom are used at the top of either end of the cell to maintain spacing.

To discharge static electricity (which can cause sand grains to cling to the Plexiglas, especially in dry air), the inside Plexiglas surfaces are covered with anti-static plastic lens cleaner (regular plastic-eyeglass cleaner); rather than wiping it off, it was spread evenly in a thin coating and left to dry. Clamps alone hold the pieces together, as shown in figure 1. The cell was clamped to a 2x3 of wood and mounted approximately at the angle of repose (the angle at which the sand rests after avalanching).

All the plexiglas pieces were obtained at a local plastics shop (from their off-cuts bin, as it turns out). The width of the cell was strongly influenced by the presence in the off-cut bin of a long narrow piece 1.9 cm wide.

The flow rate is governed by the size of the hole at the bottom of the paper funnel feeding the paper hopper at the top of the cell. Sand could be dropped directly into the cell from the funnel but using a hopper helps absorb some of the kinetic energy of particles falling from the funnel (which otherwise might bounce down the slope).

Sand is retrieved by unclamping the cell from the table (fig 1) and dumping it sideways onto a wide sheet(s) of paper. Be sure the paper is clean to avoid picking up dust and lint.

Some Considerations

Fig 2 (video): Wall effect (W = ~40d). Use video control to move back-and-forth.

Wall effect

Grains near the wall of the cell have less freedom of movement because of the wall. This effect is strong within 5 to 10 grain diameters (GDR MiDi, 2004). The video in figure 2 shows sand of grains with a diameter (d) of about 0.5 mm flowing in a chute 19 mm wide; there is an obvious wall effect. We can expect flow to be strongly affected in cells narrower than 10 to 20 grain diameters. Widening a cell frees an increasing portion of the flow from a wall effect, but there is increasing potential for the view through the wall to become unrepresentative of what is going on in the center of the flow, and increased scope for flow features in the third dimension.

Uniform feed

Sand usually consists of grains of a range of sizes. If we want the input to the cell to have a uniform grain distribution, how do we achieve that? The process of mixing can cause granular materials to segregate; stirring sand in a bowl may cause finer grains to descend ('brazil nut' effect). Once in the hopper, there might be flow mechanisms within the hopper cone that result in sorting. It may not be easy to create a uniform feed.

(I mix sand from the cell by repeatedly stirring it and over-turning it by lifting the paper upon which it was dumped, aiming to keep finer grains from settling. I use a large conical hopper to feed sand into a smaller hopper at the top end of the cell, which may introduce some sorting.)

Prior flow

If grains are not identical, flow can be affected by what preceded it. For example, steady flow through an open-ended cell (spilling over a lower barrier) can build up a layer of finer grains, gradually changing the angle of repose of the entire slope.

References

Groupement De Recherche Milieux Divisés, 2004. On Dense Granular Flows. European Physical Journal E 14, 341-365.

Makse, H.A., Havlin, S., King, P.R., Stanley, H.E., 1997. Spontaneous stratification in granular mixtures. Nature 386, 379381.

Makse, H.A., Ball, R.C., Stanley, H.E.,Warr, S., 1998. Dynamics of granular stratification. Physical Review E 58, 33573368.