Pouring problems in physics: minimum opening? A.k.a. the "oatmeal problem"

Question

Is there any established physics which studies the minimal opening of containers so that its contents can flow out without jamming?

I am wondering on what characteristics of the contents this will vary, as well as on the shape of the opening. Of course the problem might become more complex when the contents are flexible or a mixture.

Perhaps this is studied in hydrodynamics, although the contents may not always be liquid? So is there any study as hydrodynamics, but which is actually related to solids (or even better: perhaps both liquids as well as solids and/or even other states)?

Very pragmatically, this is coming from what might be called an "oatmeal problem", namely: how big a hole should I cut in the corner of my oatmeal bag, not needing to cut it again when I notice the first cut wasn't sufficient to let my breakfast flow in; i.e. when the oats have stopped flowing out after the initial drop (note that pressing the bag might work somewhat but usually this will make the oats come out only very slowly).

Answer 1

The flow of solid granules tends to be addressed in Chemistry or Chemical Engineering rather than Physics journals, and is usually concerned with measurement technology rather than building useful predictive models. eg Measuring the flowing properties of powders and grains which appears in the Journal of Powder Technology.

A general introduction to the topic is provided in Flow abilities of powders and granular materials evidenced from dynamical tap density measurement which might be obtained free on Research Gate. (Granular materials might be the best search key for the topic.)

Flow through "small" openings is often clogged by the formation of a "bridge". What is "small" depends on the ratio of diameters of opening and particles. In the linked paper the obstruction can be unblocked by vibration - the obvious expedient of shaking the container - provided the ratio is not too small. For many shapes and sizes of granules (eg glass beads, sand particles, mica flakes) "bridging" causes difficulty for ratios less than about 5.

Outflow and clogging of shape-anisotropic grains in hoppers with small apertures found a qualitative change in outflow behaviour for aspect ratios above 6, and a further change at about 10 when long vertical holes begin to penetrate the entire granular bed.

The topic is often studied by computer simulation of ideal models. The practical difficulty of the topic is that there are so many factors which affect the flow and clogging of solid particles : size and shape and their distribution, hardness/elasticity of granules, moisture content, chemical properties, static electricity, trapped air (in powders).

Answer 2

Oatmeal is a granular substance and the flow characteristics of such are very complicated. The problem is the formation of arches at the opening and these are not easily dealt with using fluid flow techniques. As common experience informs, the breaking of these arches sometimes involves shaking the container. This sets up complex nonlinear compression pulses that have been studied a great deal in recent years. Sometimes the mathematics of soliton propagation can shed light on what is actually happening. If you google with selected keywords (granular, nonlinear, soliton, arching, etc.) you will uncover a rich literature.