The Arch
Grains at an orifice can lock into a self-supporting arch, and the flow stops. The silo is still full. Nothing has broken, nothing has been withdrawn, and no quantity of material above the hole makes any difference to whether it happens.
A ratio, not a quantity
Whether an arch forms depends on the orifice measured in grains — D/d —
and on essentially nothing else. Above about 4.5 grain widths it stops
happening; below, it is the normal outcome.
The first version of this measurement said everything clogs, at every width, including widths that in a laboratory never jam — six runs out of six, at every orifice tested. The instrument was wrong, not the silo. It called any stop a clog, and a bin that has finished draining has also stopped: it runs down to a last layer of grains on the floor, with nothing left over the hole, having done nothing unusual. An arch is discharge stopping while there is still material over the hole. Both conditions are now required, and the clogging runs additionally keep the bin full so the question cannot arise at all.
What this is in the other medium
A withdrawal path has the same shape as an orifice, and the same failure. It is worth being exact about which parts of the analogy carry.
- What carries. A queue that clears smoothly at one rate of arrivals can stop dead at another, without any parameter changing and without anything being broken. The transition is sharp, it is a property of a ratio, and it is invisible in any figure describing how much is stored.
- What carries. Enlarging the store does not help. In the silo it is provably irrelevant; in a protocol it is the first thing anybody points at.
- What does not carry. Grains are not adversarial and do not all decide to leave at once because they read something. A run is a correlation an arch does not have, and it makes the real case worse rather than better.
- What does not carry. An arch can be broken by hitting the silo. There is no equivalent, and a protocol that has one has a privileged operator, which is a different problem with its own page in a different category of site.
Repose — and the part that is moving is smaller than the bin
Long before anything stops, most of a discharging bin is in repose. A narrow flow channel runs from the surface to the orifice; the material outside it stands still, and the boundary migrates inward as the level drops. The silo on the front page draws that channel by colouring what is moving, and it is a small part of the picture.
The silo beside this one is the same solver as the front page, with one difference that changes everything it can show: it is not refilled. A grain is drawn in the accent once it has moved a full diameter since the gate opened, so the channel writes itself into the bed and the material outside it stays dark. When the bin runs out it is filled again and the cycle restarts.
The front page cannot show this, and not because of a colour choice. A bin refilled as fast as it empties has no stagnant material — everything put in at the top has to come out of the bottom. A dead zone is a property of a bin that is draining, so the binary picture is only ever drawn on one.