We present Atacama Large Millimeter/submillimeter Array (ALMA) Cycle 0 Band 7 observations of an extremely metal-poor dwarf starburst galaxy in the Local Universe, SBS0335-052 (12+log(O/H)~7.2). With these observations, dust is detected at 870micron (ALMA Band 7), but 87% of the flux in this band is due to free-free emission from the starburst. We have compiled a spectral energy distribution (SED) of SBS0335-052 that spans almost 6 orders of magnitude in wavelength and fit it with a spherical dust shell heated by a single-age stellar population; the best-fit model gives a dust mass of (3.8+/-0.6)x10^4 Msun. We have also constructed a SED including Herschel archival data for IZw18, another low-metallicity dwarf starburst (12+log(O/H)=7.17), and fit it with a similar model to obtain a dust mass of (3.4+/-1.0)x10^2 Msun. Compared with their atomic gas mass, the dust mass of SBS0335-052 far exceeds the prediction of a linear trend of dust-to-gas mass ratio with metallicity, while IZw18 falls far below. We use gas scaling relations to assess a putative missing gas component in both galaxies and find that the missing, possibly molecular, gas in SBS0335-052 is a factor of 6 times higher than the value inferred from the observed HI column density; in IZw18 the missing component is 4 times smaller. Ultimately, despite their similarly low metallicity, the differences in gas and dust column densities in SBS0335-052 and IZw18 suggest that metal abundance does not uniquely define star-formation processes. At some level, self-shielding and the survival of molecules may depend just as much on gas and dust column density as on metallicity. The effects of low metallicity may at least be partially compensated for by large column densities in the interstellar medium.
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