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I observed a fence composed of plastic-coated metal wires running vertically and horizontally at intervals of around 3 cm.

After it had rained, drops of water remained on the horizontal wires. I was surprised to see that the drops on each horizontal wire were situated just below the drop on the wire above. The drops seemed to form vertical columns.

The fence is similar to that shown here. [Image no longer available.]

What forces are responsible for this unusual regularity?

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  • $\begingroup$ Potentially good question. However, your link has broken. An image of the fence with the drops on it would have been useful. $\endgroup$
    – sammy gerbil
    Commented Sep 1, 2018 at 17:13

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This is partly a guess since you don't show a picture of the droplets, but here is a possible reason for the phenomenon:

A cylindrical film of a liquid is generally unstable due to an effect called the Plateau-Rayleigh instability. The slightest ripples in the surface of the liquid cylinder grow spontaneously and break up the cylinder into a series of droplets. A quick Google failed to find a great picture of this, but I found this image cribbed from here:

Drops

The maximum size of the drops (before they fall off the wire) will be a complicated function of the liquid density and surface tension and the contact angle the liquid makes with the wire, but for any given system like water on our fence the maximum size will be approximately constant.

Now I would guess that the instability is triggered where the vertical wires cross the horizontal wires, so the breakup starts at those points and proceeds inwards towards the centre of the horizontal sections. If the amount of water is the same on all the horizontal sections, and the film break-up starts in the same place on each section (at the vertical wires), and the maximum droplet size is the same in each section then you would expect each horizontal section to have roughly the same arrangement of droplets. By this I mean each horizontal section will have about the same number of droplets and they will be roughly equally spaced.

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  • $\begingroup$ 2 points are missing here, 1. what about droplets already on horizontal sections which do not get the cut off flow from vertical droplets taking exits ? 2. why do they move towards centre only ? why not further ? why not shorter ? $\endgroup$
    – Rijul Gupta
    Commented Jan 18, 2014 at 21:03
  • $\begingroup$ @rijulgupta: the amount of water on the wires is continually being increased by raindrops or drips from wires above, and continually being decreased by drops falling off the wire. At equilibrium we'd expect every bit of wire to have about the same amount of water on it. The RP instability and the other parameters will determine the lowest energy state for arranging the drops on the wires, and this will be the same for all the pieces of wire so you'd expect them to be about the same. I don't understand your question 2. The droplets aren't moving towards the centre. $\endgroup$
    – John Rennie
    Commented Jan 19, 2014 at 11:42
  • $\begingroup$ I meant that you haven't explained "othe breakup starts at those points and procedes inwards towards the centre of the horizontal sections". Why towards center ? $\endgroup$
    – Rijul Gupta
    Commented Jan 19, 2014 at 12:54
  • $\begingroup$ A cylindrical film of water is an unstable equilibrium i.e. it is stable but even a small perturbation will cause it to break up. The vertical wires are an obvious perturbation because the water surface has to curve at the point where the horizontal wire meets the vertical wire. The vertical wires represent a boundary condition. That's why when calculating the droplet distribution I would start at the vertical wires and work inwards. $\endgroup$
    – John Rennie
    Commented Jan 19, 2014 at 14:35
  • $\begingroup$ I'm not saying the water would actually form a perfect cylinder around the horizontal wire because obviously it would not. However this is the starting point to calculate the equilibrium configuration. $\endgroup$
    – John Rennie
    Commented Jan 19, 2014 at 14:35
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Any metal rod or column when held at 2 ends and no support at center will gives in to its own weight and sag, due to this the middle portion of the rod moves away(downwards) from the other constrained end parts; The phenomenon is known as Bending.

In the case of your fence, if you see each horizontal part it would be just held at the ends, this would make the part at the centre go a bit downwards, but it will not be visible untill you actually measure it using a protactor etc. However when water droplets lie on such slanted rods, they move towards the lowest part, as that is the middle portion, they go and stay there. This is what you are observing.

This is what I am talking about : enter image description here

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  • $\begingroup$ Thanks. I have added a link to an image similar to the fence I observed. I think the phenomenon you describe is unlikely in this picture. $\endgroup$
    – Avrohom Yitzchok
    Commented Jan 18, 2014 at 20:13
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    $\begingroup$ It does indeed, select any square of the mesh, you will find a straight rod joint at 2 ends, on this small rod the phenomenon I describe happens but it produces a negligible slope, droplets slide even at such a gentle slope and accumulate at centre. The image I have added is just to make sure you understand what I am talking about, it can and does happen at small scales such as yours too $\endgroup$
    – Rijul Gupta
    Commented Jan 18, 2014 at 20:20
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Perhaps at those spots they were clamped during the fabrication process: that may mean Rijul is partially right (can we test this by turning the fence upside-down ;)?).

My guess is that this clamping resulted in those spots being less hydrophobic or are slightly different shaped than the rest of the fence, hence causing the droplets to converge there.

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  • $\begingroup$ If it was the case, hydrophobic parts would push water particles in thr direction of line joining their centres, it won't push it tangentially, but since weight would overpower this force, the droplets will not move. Ofcourse in some cases the resulting force may be at some angle and force the droplets, but that won't account for regularity over entire mesh. Comments ? $\endgroup$
    – Rijul Gupta
    Commented Jan 18, 2014 at 20:36
  • $\begingroup$ Yeah I'm doubting the hydrophobic explanation myself. I imagine that these fences are made in the following way 1) A stack of metal wires 2) These are then held parallel and another parallel stack of wires but at a 90 degree angle is pushed together (I imagine with reasonable force) and they are welded together. That'd account for both the regularity and a curve in the wires. $\endgroup$
    – Kvothe
    Commented Jan 18, 2014 at 20:39

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