Results

    We see from the results of the trials with the gelatin that a dike does not need to begin to propagate right under a load for that dike to propagate to the load.  The affect of the load reaches out to a point where the dikes curve towards the load and then when it hits that point the load no longer affects the dike and it will propagrate straight up.  Figure 2 shows the paths of the air dikes and why they curved towards the edge of the load instead of continuing on their path to the middle of the load.  The arrows represent the direction of the maximum compressive stress, we see that path of the air dikes follows the arrows right up to the surface.  The dikes travel in the direction of the maximum normal stress and since the compressive stress creates the normal stress the maximums are in the same direction.  The maximum compressive stress is located at the edge of the surface load which is why that maximum normal stress is achieved at the edges of the load.





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)

    There is another reason why the air dikes take these paths and that is because the load is right on the gelatin and it is harder for the dike to break the surface under the load.  But we know for a fact that is not the whole answer because of the air dike that propagated right up the middle.  This dike went right to the middle of the load and broke through the surface there, it did not bend out to the edge of the load. 
    This whole process depends on the driving force of the air dike through the gelatin.
  We find that there is an equation for the driving force of the dike when there is no surface load:

f = ΔpgV

    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.


     This is why mountains that are volcanic erupt multiple times.  The compressive stress on the Earth from the mountain causes dikes from further off distances propagate to them.  Mountains that have erupted before will probably erupt again, by either pulling magma dikes from other magma chambers or different parts from the same magma chamber.


    picture 6: Mt. Rainier behind Seattle (Steger, 2005)


    A reason for studying volcanoes and learning much as possible about them could end up saving lives.  Many people live in what could be the path of distruction for many of these volcanoes.  Mt. Rainier a large mountain with a very large load is an active volcano that looms in the distance over Seattle, Wa.  Since volcanoes pull magma from many distant sources volcanoes could erupt more frequently than we know, and for Seattle this could be bad news.


picture 7: Magma logo (Thelen, 1995)


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