Assignment: Pitch drop experiment
Pitch (or “Bitumen”) is a material with a very high viscosity. It seems solid, when you walk
on it, but on very long time scales it flows like a liquid. To demonstrate its flow, a spectacular
experiment has been set up in the 1930’s, which is still running (Fig. 1): The Bitumen was
filled into a funnel, from which it is-due to its high viscosity-dripping at a very small rate. On
the average, one drop falls every eight years.
(a) Determine the viscosity of the pitch by assuming the volume of the drop to be 1cm3.
Assume that the only resistance to flow occurs in the stem of the funnel (lower part), which
has a diameter of 1cm and a length l=3cm. Hint: Model this stem as a pipe, and assume that
the pressure that drives the bitumen through the stem is given by the hydrostatic pressure
(p=ρgh) from the weight of the bitumen on top (ρBitumen = 1.1 g/cm3, h = 7.5cm). Use the
Hagen-Poiseuille law for pipe flow.
(b) Another possibility to determine the viscosity of the pitch is to let a ball sink through the
material. Consider a steel ball (ρSteel = 7800 kg/m3) with a diameter of 10 cm and determine the
time that it needs to sink through 20 cm of the pitch. Could we observe this in our lifetime?
(c) Consider a homogeneous liquid with the same viscosity as that of pitch. The diffusion of
molecules in such a liquid is also very slow. A molecular relaxation time can be defined as the
time, in which a molecule in the material diffuses a distance equal to its own radius. Assume
that diffusion happens in the same way as in a “normal” liquid. Determine the relaxation time
of the material at room temperature assuming the molecule to be spherical and having a
diameter d = 5⋅10-10 m. How does this relaxation time compare to that of normal liquids of
around 10 picoseconds (10⋅10-12s)?
Fig. 1: The “Pitch drop experiment“
The funnel is filled with pitch (bitumen), which flows at a very slow rate due to its high
viscosity.