Solid, yielding mantle - Mantle Convection for Geologists - page 35

also demonstrated that the viscosity is lower in the upper few hundred kilometres
of the mantle and larger at greater depths.
At the beginning of this section I posed the question of how large the mantle
viscosity is. These results show that it is very much larger even than a billion times
the viscosity of honey - something like a thousand billion billion times. The earlier
guess was wrong by 12 orders of magnitude! Even though the estimate made here
is very rough, it has given the right order of magnitude, though it differs by a factor
of 8 from Haskell's value. Thus our rough estimate is very valuable, because it
has replaced serious ignorance with some useful knowledge. It is important, of
course, to bear in mind that the estimate is not expected to be very accurate, but
it is reasonable to believe (even without comparisons from other studies) that it is
accurate to better than one order of magnitude. There is another virtue of the very
simple approach used here, which is that it allows the physics to remain clearly in
view, without being obscured by mathematics.

4.3 Dependence of viscosity on temperature
You probably know that cool honey is more viscous that warm honey. Honey that
has been kept in a refrigerator is much more viscous than honey at room temperature
on a hot day. Even a temperature change from 20 ◦ Cto30 ◦ C might change the
viscosity by an order of magnitude or so. It turns out that rocks at the high pressures
and high temperatures of the mantle behave similarly. An increase of temperature
from 1300 ◦ C to 1400 ◦ C can reduce the viscosity by about a factor of 5.
The reason for this strong sensitivity to temperature is that rock deformation
occurs by the movement of defects within the crystalline structures of the rock's
minerals. Atoms are constantly in motion, jiggling around their mean position in
the crystal, and the amount of jiggling increases with temperature. The movement
of defects depends on atoms occasionally jiggling into a neighbouring position,
and the probability of such a jump increases rapidly as the amplitude of the atom's
jiggling increases. This is a well-studied process, called thermal activation, and
thermally activated processes have a typical form of dependence on temperature.
This form, calibrated by experiments, can be used to deduce the following depen-
dence of viscosity on temperature T [39]:

μ r exp E ∗
R

1
T −

,

1
T r

μ = (4.9)

where μ r is the viscosity at a reference temperature T r , R is the universal gas
constant and E ∗ is called the activation energy.