Page 92 - Fundamentals of Physical Volcanology

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THE ROLE OF VOLATILES 69

or

P V = P V (5.6)
1 1 2 2
where P is the pressure in the gas and V is the vol-
ume occupied by the gas, and the subscripts 1 and
2 refer to conditions before and after some change
takes place. This means that if the gas pressure
Bubble decreases, the volume of the gas increases, i.e., the
gas expands. So as magma rises and the pressure
exerted on it by the surrounding rocks decreases,
any gas bubbles within the magma also experience
this decrease in pressure and expand in volume
accordingly.
For example, if a bubble forms at a depth of
∼200 m beneath the surface and grows by decom-
pression until it reaches the surface then the initial
pressure on the bubble, P , is
Fig. 5.4 Migration of the molecules of a volatile into a 1
gas bubble from the surrounding liquid increases the
concentration gradient in the nearby liquid (shaded area), P = ρ gh (5.7)
1
driving more molecules towards the growing bubble.
where ρ is the density of the surrounding rocks,
When a bubble is very small the addition of even g is the acceleration due to gravity and h is the
−3
a relatively small amount of gas causes a relatively depth beneath the surface. So for ρ = 2800 kg m ,
large increase in the size of the bubble. As the gas g = 9.81 m s −2 and h = 200 m, the initial pressure
molecules in the magma closest to the bubble are P is 5.5 MPa. The pressure at the surface, P , is
1 2
the first to be added to the bubble, this sets up a 1 bar, i.e., 0.1 MPa. Therefore:
concentration gradient around the bubble in which
the number of gas molecules close to it is small com- V = (5.5/0.1) V (5.8)
2 1
pared with the number further away. This con-

centration gradient drives more molecules into the where V is the final volume of the gas bubble and
2
area of low concentration and thus drives more V is the initial volume. The volume of a bubble is
1
molecules towards the growing bubble, so further proportional to its radius cubed, and so the increase
growth can occur (Fig. 5.4). This growth by dif- in the radius of the bubble in this example is found
fusion is important when the bubble is small but from
becomes less important as the bubble grows bigger
because the percentage increase in bubble volume r = 55 1/3 r = 3.8 r (5.9)
2 1 1
for the addition of a given number of molecules
becomes less as the bubble grows, and also because Figure 5.5 shows the relative importance of
as the bubble grows there are less gas molecules left diffusion and decompression in bubble growth.
in the surrounding magma and so the concentra- Bubbles form at a depth of ∼220 m beneath the
tion gradient decreases. surface and grow by both diffusion and decom-
pression until they reach the surface. The bubble
radius increases by a factor of ∼1000 between the
5.5.2 Growth by decompression
nucleation depth (220 m) and the surface (Fig. 5.5).
Boyle’s Law (one of the Gas Laws) states that: Decompression over a distance of ∼200 m can
increase the bubble radius by only a factor of about
PV = constant (5.5) four; thus the growth of bubbles in this case is