Two bubbles attract or repel?

Question

I have this weird thought that bothers me, but unfortunately, I know little physics and I thought I can get help to mentally settle it.

Here we go:

Let's say you have infinite sand or at least a vast quantity of it. And no gravity. Just sand, tight in a vast container

You manage to inflate two big (relative to the sand grains) balloons inside the sand. Due to size, the balloons will push the sand to create tension, as the sand is tightly packed.

If you bring the balloons close to each other, will they repel due to this tension or attract? Does the shape matter?

Answer 1

It would be be better to think about two bubbles in a giant self-gravitating blob of water.

The bubbles would attract each other, but it takes some thinking to see what that means. The bubbles themselves do not attract or repel. Mass attracts mass, and the bubbles have no (or very little) mass. Never the less, the water around bubbles pushes the bubbles around, and the effect on the bubbles is the same as an attraction.

Each bit of water is attracted to all the other bits of water. If you add up all the attractive forces, it is the same as if the bit was attracted to the center of the blob.

Suppose there was a rock in the blob. It is denser than water, and therefore attracted to the center more than nearby water. The rock pushes water below it out of the way and sinks. Water that was below rises to where the rock was.

For a bubble it is the reverse. Water next to the bubble is attracted to the center. Water sinks and the bubble rises. Even though all gravity is attractive, the effect is as if the bubble "repels" the center.

Suppose there were two bubbles. Both will rise to the surface. This is not because the bubbles repel each other, but because they both "repel" the center.

But each bubble replaces a bit of water. The total force of gravity is slightly reduced by the existence of the bubble. Each bubble will be slightly less repelled by the center than it would be without the other bubble. If a bubble reduces repulsion, that is the same as increasing attraction. So you can see that adding another bubble increases attraction to the center.

In a similar way, two bubbles attract each other.

• Consider spots A and B inside the blob. Water in spot A is attracted by water in spot B.
• If you replace B by a bubble, water in spot A is less attracted to B than it would have been. The water at A is repelled by the bubble at B.
• If you also replace water at A by a bubble, the water near A is less attracted to B. It pushes less toward by than it would have. This is equivalent to the bubble at A being less repelled by the bubble at B.

Again, a reduction in repulsion of two bubbles is equivalent to an attraction between the bubbles.

Answer 2

Let's suppose a big container, but not so big that gravitational effects become relevant. When the baloons are inflated, the sand is forced to be more compact in the neighborhood. But unlike a fluid, the pressure is not evenly distributed to all container. It is like a pile foundation, that compact locally the soil, but not 100m away.

So, if 2 baloons are inflated close, the sand volume between them is more stressed than the average of the container. The consequence is that, if A and B are the points of the initial center of inflation of each one, these points will be a little more distant after the inflation is finished.