  We present Atacama Large Millimetre Array (ALMA) 2mm continuum observations
of a complete and unbiased sample of 99 870micron-selected sub-millimeter
galaxies (SMGs) in the Extended Chandra Deep Field South (ALESS). Our
observations of each SMG reach average sensitivities of 53 microJy/beam. We
measure the flux densities for 70 sources, for which we obtain a typical
870micron-to-2mm flux ratio of 14 +/- 5. We do not find a redshift dependence
of this flux ratio, which would be expected if the dust emission properties of
our SMGs were the same at all redshifts. By combining our ALMA measurements
with existing Herschel/SPIRE observations, we construct a (biased) subset of 27
galaxies for which the cool dust emission is sufficiently well sampled to
obtain precise constraints on their dust properties using simple isothermal
models. Thanks to our new 2mm observations, the dust emissivity index is
well-constrained and robust against different dust opacity assumptions. The
median dust emissivity index of our SMGs is $\beta\simeq1.9\pm0.4$, consistent
with the emissivity index of dust in the Milky Way and other local and
high-redshift galaxies, as well as classical dust grain model predictions. We
also find a negative correlation between the dust temperature and $\beta$,
similar to low-redshift observational and theoretical studies. Our results
indicate that $\beta\simeq2$ in high-redshift dusty star-forming galaxies,
implying little evolution in dust grain properties between our SMGs and local
dusty galaxy samples, and suggesting these high-mass and high-metallicity
galaxies have dust reservoirs driven by grain growth in their ISM.
