eli5: How big a crack does water need to leak through and does the material of the container impact the size required?


eli5: How big a crack does water need to leak through and does the material of the container impact the size required?

In: 13

I’ve looked at some papers, and it seems that usually the material of the container doesn’t directly affect the result, but the roughness of the crack “walls” does, as does the crack geometry.

The crack geometry includes lengh too (container wall thickness), and of course water pressure is also a factor.

So your answer is “it depends”. It depends on more than just the crack size, but crack length, width, roughness, and water pressure.

here’s one of the papers:

This becomes more of a rate consideration. To have flow, the space has to be big enough to allow the molecule through essentially unimpeded, AND the open space has to be connected the entire distance. Unconnected pore space is not very useful to flow.

Down at the molecular scale (sub-micron size range, down near the nanometer (1/1000 of a micron, or 10 angstroms), there will be interaction of the liquid’s molecules with adjacent neighbors of the container material, and this is a sort of friction (resistance to flow as the adjacent molecules attract or repel each other when close). With large open spaces, the resistance is only an issue at the edge of the open space, so flow is unimpeded toward the middle of a pipe or crack, but does drag along its edges (water moves slower at the borders of the space). Even rivers show the effects of drag at the edges and bottom (flow goes from free flow/max flow speed to no flow over a very short distance between pure liquid and the “wall” of the passageway).

When you get down to the size range of a few molecules thick, this resistance to flow (interaction with the walls) actually matters, can fill the entire tube or fracture, and to overcome it you need to provide a much larger force to impose the flow (increase differential pressure to overcome the resistance of near-molecule interactions).

The material of the “container” matters because each compound will have its own particular electromagnetic zone of influence (charge space). The materials can also affect the nature of the “pipes” (cracks/flow pathways), so clays, which stack like sheets upon each other, can have a lot of open space, more open space than a quartz silt would (as examples) but the narrowness of the interlayer space means all water is interacting with the clay surface, the entire route that it has to flow (and it is a longer route because it is back and forth, a switchback path rather than almost straight through). On top of the simple constriction and path length aspects, clay has a very strong charge distribution so grabs passing water molecules fairly strongly compared to quartz, which lacks that charge disparity in its structure. Clay is thus generally speaking way less “leaky” than a quartz silt of similar porosity and explains why clay is generally favored as natural seals for landfills or whatever storage we do not particularly want to see leaking.

Oh, I also forget to mention that different fluids have different viscosities (natural resistance to flow) so some liquids will not flow without a strong head (pressure differential) even if the space is pretty wide open: the liquid’s molecules interact with each other and are a form of self-produced friction.

A crack is only a leaky one if the pressure (force on the liquid inside the container) is high enough to overcome all of the various forms of resistance that the container will present. Typically, there is a minimum gap width that has to exist for the situation before flow can commence freely. Part of this is due to the resistance to flow in small passageways, and part of it is simply a matter of unit volume per time (slow flow through a small hole cannot let much volume through it; just no room for it). The rate can be offset somewhat by pressurization, by pushing on the liquid inside the container, but there are limits.

As a general idea (and it varies depending on materials), the zone of flow resistance is a few molecules thick from wall into fluid. nanometer-sized passages tend to be pretty resistant to leakage. And even if there is leakage, the volumes of lost material will be extremely tiny. Free flow is not going to happen and what does manage to pass will be doing it very slowly. Faster than by diffusion (migration of molecules, one at a time, through random movement) but not fast in the way we look at things.

Strictly speaking, diffusion occurs in pretty well anything. Diffusion is the (extremely slow) movement of molecules from regions of high concentration to regions of low concentration. The occasional molecule changes place, or wheedles its way in somehow, into the walls of the container. Eventually, some luck molecule makes it the entire way across the barrier. But it is really slow.

Point is, nothing is truly impermeable. Time frames matter (keeps the liquid inside long enough for our needs, is the basic idea we look for). Many ceramics (like for coffee cups) have a lot of open space inside, but the spaces do not connect well at all, so the cup is impermeable. Some clay-based containers are leakier than others, and you might see some sweating if they are imperfectly sealed, but even then, the amount of liquid being lost is tiny so the user doesn’t much care, usually.