Why doesn't the paint touch the corners?
February 14, 2011 5:21 AM   Subscribe

This recent post on MetaFilter on pour painting and this comment about how the paint, when poured slowly on to the top face of a cube, does not run down the corners of the cube, got me thinking about why it didn't ... but after a day thinking about viscous liquids I'm still completely stuck for a scientific explanation. Can anyone enlighten me?
posted by KirkpatrickMac to Science & Nature (7 answers total) 5 users marked this as a favorite
If you pour paint onto the centre of the top face of a cube, the middles of the edges are quite bit closer than the corners (basic geometry).

So the paint reaches the middles of the edges first. Paint pours over the edges. Cohesion causes the paint to 'prefer' to stay with other paint, rather than flowing away in random directions. Also, as paint flows over the edges, the depth of the paint is locally reduced, creating a slight gradient. These two things combined mean that the paint will flow towards the edges and not the corners.

Of course, if you pour the paint faster, it will also reach the corners; but the flow will still be greatest at the centres of the edges.
posted by le morte de bea arthur at 5:36 AM on February 14, 2011 [4 favorites]

If you used a different liquid whose adhesion to the cube overcame its cohesion, the liquid would spread out very rapidly to cover the surface.
posted by le morte de bea arthur at 5:37 AM on February 14, 2011 [1 favorite]

Gravity is pulling the paint down once it pours over the edge of the top. It is harder for the paint to roll over new territory than it is to roll over already painted areas. (The cohesion adhesion concept put another way.)

Awful car analogy: suppose you have a parking lot with a 20 foot wide, 100 foot long strip of ice. It is on an incline. Cars drive up to the higher of the short edges, hit the ice and slam on the brakes. They will veer in all directions, and stop pretty quickly once the hit dry pavement. As you put more and more cars onto the ice, they will gravitate toward the bottom. Even though all the cars start at mostly the same point and at mostly the same speed, they will line the edges of the ice and not spill over very much at all. Even if they are hit by other cars along the line.
posted by gjc at 6:37 AM on February 14, 2011

Viscosity isn't the answer to this one. It is of secondary importance, but it's not what drives the motion of the paint.

The comments above are correct in general, but they don't really get to the heart of the problem. What you are asking about is called surface wetting or wettability.

Consider the edge of a drop of liquid sitting on a flat surface. Draw an angle between the flat surface and the tanget line to the drop at the surface. This is called the contact angle. The contact angle is driven by the surface tensions of the three phases: the fluid-air interface, the fluid-surface interface, the surface-air interface.

When the fluid-surface interface has a very low energy---the liquid and the surface are very thermodynamically compatible---the fluid will cover the surface completely, and the contact angle will be very small. Think of water spreading on ice. It wets the surface in a very thin coat, drops of water don't last on an ice surface. This is a high wettability situation.

When the fluid surface interface is high energy---the fluid and the surface don't like each other---then the fluid tighens up into a ball, minimizing its surface area. Think of oil on a non-stick pan or mercury on glass. This is low wettability.

When the fluid is moving on the surface, you get secondary viscosity and elestic effects, but the fluid-surface interfacial energy (the general term for surface tension) is the effect in the driver's seat. Note that this is strongest when the fluid is fairly thin, no more than a few millimeters. Larger than that and the gravity-viscosity fluid flow takes over. If you poured too much paint over the top, gravity would overwhelm the interfacial energy and paint would flow over the corners. In the videos, the artists are being careful not to do that. So, the paints do the interesting things shown in the videos.

Consider the paint flowing over a surface. A paint drop has a moderate contact angle that it likes to have. Paints are in the middle of the two cases above. They don't wet the surfrace like water on ice, but nor does paint make little beads like mercury. In the middle of the cube, a flat area, it can be close to that moderate contact angle, and the surface, inferfacial energy is minimized. At the edges, however, the surface angle suddenly rises by an extra 90 degrees. At the corners, the surface angle rises even more. This is energetically unfarvourable, so the paint can't wet the corner or the edges. The paint flowing down the cube ths angles in, directed by the curvature of the meniscus of paint at the coner on the top. Thus, the front of flowing paint angles inward toward the middle.

There are geometric effects going on here which explain why more paint flows down the middle than the edges. If that were the only factor, the paint would flow down the cube faces in vertical lines. It's the thermodynamics of surface energy minimization that casue the paint edges to be off the vertical.

Themodynamics beats gravity! Take that Newton!
posted by bonehead at 9:41 AM on February 14, 2011 [5 favorites]

Draw a circle in a square with overlapping center points. Expand the circle until it touches the edges of the square. Where does it touch first?
posted by jeffamaphone at 11:12 AM on February 14, 2011

Draw a circle in a square with overlapping center points. Expand the circle until it touches the edges of the square. Where does it touch first?

Asker was asking about the vertical edges of the sides, not the edges of the top.
posted by gjc at 2:54 PM on February 14, 2011

Asker was asking about the vertical edges of the sides, not the edges of the top.


posted by jeffamaphone at 10:41 AM on February 15, 2011

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