Friday, 10 June 2016

Orientation of Dispersible Aspirin

Part of my medication is to take dispersible aspirin daily. I take it with a small amount of water and it breaks down into a powder like consistency that can be swallowed easily.

A couple of days ago I noticed that the aspirin had landed on its edge. I’ve been taking it for about 15 months and had never noticed that before. Could I calculate how frequently I should have observed this state?

The pill appeared to be in the shape of a cylinder about 6mm in diameter and 1mm high. Assuming the shape is no more complicated than that, makes the calculations a lot easier.

Pill with approximate dimenbsions

If I consider the cylinder edge on, it becomes a simple rectangle whose centre of gravity is the point where the two diagonals meet. When falling through water this imaginary rectangle will nearly always turn around the corner which hits the flat bottom of the glass first such that the long side of the pill lies parallel with the glass bottom.

Centre of Gravity
Which way to fall?
The circumstances which dictate that the pill will land on the shorter edge of this imaginary rectangle are governed by the position of the centre of gravity of the cylinder in relation to the perpendicular line at the point where the corner of the cylinder meets the flat bottom surface of the glass. If the centre of gravity is on the side of the shorter edge then clearly the pill will turn towards the shorter dimension.

The calculation turns out to be ridiculously simple. For 1 corner the centre of gravity will tend to the shorter edge one in six times. For the other corner the same logic applies but for the other side of the semi-circle. So there is no increase in frequency that this will happen. (On the other hand one might argue the opposite flat edge will indeed double the frequency. But the consideration of the rectangle was only imaginary to simplify the calculations. There is only one continuous short dimension.)

Following that logic I should expect to see the pill fall on its shorter edge far more frequently I’ve noticed. How can I account for it?

It must be concerned with the dispersible nature of the pill. There is certainly a time lag before the pill is completely dispersed. I guess that complete dispersal takes about two minutes. But that’s not enough. I also need to consider the process or pathway the dispersal takes.
Corners gradually crumble.

A best guess is that the sharp edges of the pill will degrade first. The impact of this will to reduce the range over which the centre of gravity will tend towards the smaller dimension.This is likely to be very rapid.

I’m only surprised that I’ve seen it land on its edge at all.

Addendum (16 June 2016). I've just noticed that I nearly always put the pill in the glass before adding the water. This negates the whole of the the above, since it's almost impossible for the pill to stand on its edge in these circumstances. Even so I won't delete the blog.

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