# Lava Bubble Layers

1. Jan 31, 2004

I've got the answer to this problem, but I didn't find it clear enough as an explanation on how to backsolve it. I was wondering if you guys could help me with it.

Thanks!

Here it goes...

Answer: "1.5 cm/s downward (the bubbles rise but layers descend)."

Problem: "Some solidified lava contains a pattern of horizontal bubble layers separated vertically with few intermediate bubbles. (Researchers must slice open solidified lava to see these bubbles.) Apparently, as the lava was cooling, bubbles rising from the botton of the lava separated into these layers and then were locked into place when the lava solidified. Similar layering of bubbles has been studied in certain creamy stouts poured fresh from tap into a clear glass. The rising bubbles quickly become sorted into layers. The bubbles trapped within a layer rise at speed v1; the free bubbles between the layers rise at a greater speed v2. Bubbles breaking free from the top of one layer rise to join the botton of the next layer. Assume that the rate at which a layer loses weight at its top is (dy/dt)=v2 and the rate at which it gains height at its botton is (dy/dt)=v2. Also assume that v2=2.0*v1=1.0 cm/s. What are the speed and direction of the motion of the layer's center of mass?"

2. Jan 31, 2004