Bubble pentagonal dodecahedral

FIG. 1 A foam column, pentagonal dodecahedral bubble, and the cross-section of a PB channel. 

The values of p and p follow from the fact that there are 12 films and 30 channels in a pentagonal dodecahedral bubble. Because each film is shared by two bubbles and each Plateau border channel is shared by three bubbles, we have p = 6 and rip = 10. The liquid volume fraction is given by the sum of liquid per unit volume in the Plateau border channels and the liquid per unit volume in the films as ... 

For a pentagonal dodecahedral bubble, the number of Plateau border channels per bubble intersected by a horizontal plane is p/5. The number of bubbles intersected by a horizontal plane can be obtained as shown below using a technique common in dealing with the flow of fluids in porous media [22,23]. 

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