figure 2: This shows the path of the air dikes through the gelatin tank. The arrows are the direction of maximum comperssive stress in the gelatin. (Watanabe, 2002) |
Where f is the
driving force of the dike, Δp is the difference
in densities
between the air or magma inside the dike and the gelatin, g is the
acceleration
due to gravity, and V is the volume. Acting against the driving
force of the dike is the viscous and fracture resistances, this number
can change depending on what kind of gelatin you use or the ratio of
gelatin to liquid you use in making the gelatin. The equation for
resistance is:
f
=
η(v/t)wh
In this equation f is the resistance force, η is the
normal stress of the dike, v is the velocity the dike is propagating
at, t is the temperature of the gelatin, w is the width, and h is the
height. (Watanabe 2002)
Another thing we see in the results of the gelatin
dike trials is that the dikes would start out quickly but as the dike
went closer to the gelatin surface the dike would slow down. This
effect is directly related to the stress projected into the gelatin
from the load on the surface. If the load on the surface is large
enough it could actually stop the dike from propagating to the surface
and it could be stuck in the gelatin. One aspect that helps the
dike propagate vertically is the buoyancy of the dike, which means the
air inside the dike. In a real world situation this would be the
buoyancy
of the magma in the dike. The load affects the velocity because
not only does it apply compressive stress but it also adds negative
buoyancy that counteracts the buoyancy from the air dike. Since
the
negative buoyancy counteracts the buoyancy of the dike to find the
velocity of the dike at different heights through the gelatin you can
use the equation:
v
=(driving force)/c = (buoyancy - negtive buoyancy)c
Where v is the velocity of the dike, and the c is a coefficient that is
found from a result of the velocity of the dike without a load on the
gelatin. The negative buoyancy in the equation comes from a
direct effect of the load on the surface. The surface load does
not only apply a compressive stress from the top it also applies a
confining stress from the sides. The confining stress presses on
the sides of the air dike making it harder to part the gelatin, and
this confining stress becomes greater as you go up through the
gelatin. This is why the air dike slows down as it propagates up
through the gelatin.


| HOME |
INTRODUCTION |
BACKGROUND |
DATA |
RESULTS |
REFERENCES |