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Gravity Fingers Mathematically Explained

Since I have my math exam tomorrow, it seems only natural I should write about something math related. 

When water soaks down into the ground, it does not do so evenly, but rather forms spikes known as gravity fingers (see image below). Though it is a well known phenomenon in fluid mechanics, no one has been able to explain, mathematically, why it happens. In a recently published paper however, mathematicians at MIT give a both simple and elegant explanation. They got the idea when one of the researchers observed that gravity fingers looked very much like water flowing down a window (when you look at the picture it looks really obvious, it was definitely the first think I though of), which is a well understood phenomenon. Then it was just a matter of taking the equations describing that and apply it to water movement in soil. 

The short explanation to this phenomenon is that in order for water to flow down a window or in soil, the surface tension of the water has to be overcome. This will cause the water to flow in a finger-like pattern because as water builds up in the fingers, the weight overcomes the surface tension. My understanding of the phenomenon is that small indentations in the bottom flow line are bound to form no matter what because the soil/window is not perfectly uniform (and can never be), and when this happens the flow rate at the indentations increase because of the extra weight, leading to gravity fingers. 

Gravity fingers

December 14, 2008 Posted by | Math | , , , , , , , , , , , , | Leave a comment