  Dissipative processes acting in rotating neutron stars are essential in
preventing the growth of the r-mode instability. We estimate the damping time
of r-modes of an hypothetical compact quark star made up by color flavor locked
quark matter at a temperature $T \lesssim 0.01$ MeV. The dissipation that we
consider is due to the the mutual friction force between the normal and the
superfluid component arising from the elastic scattering of phonons with
quantized vortices. This process is the dominant one for temperatures $T
\lesssim 0.01$ MeV where the mean free path of phonons due to their
self-interactions is larger than the radius of the star and they can be
described as an ideal bosonic gas. We find that r-modes oscillations are
efficiently damped by this mechanism for pulsars rotating at frequencies of the
order of 1 Hz at most. Our analysis rules out the possibility that cold pulsars
rotating at higher frequencies are entirely made up by color flavor locked
quark matter.
