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We model the ALMA and VLA millimeter radial profiles of the disk around HLTau to constrain the properties of the dust grains. We adopt the diskevolutionary models of Lynden-Bell \& Pringle and calculate their temperatureand density structure and emission. These disks are heated by the internalviscosity and irradiated by the central star and a warm envelope. We consider adust size distribution $n(a) da \propto a^{-3.5} da $, and vary the maximumgrain size in the atmosphere and the midplane, $a_{\rm max}=100\ \mu$m, 1 mm,and 1cm. We also include dust settling and vary the dust-to-gas mass ratio from1 to 9 times the ISM value. We find that the models that can fit the observedlevel of emission along the profiles at all wavelengths have an atmosphere witha maximum grain size $a_{\rm max} = 100 \ \mu$m, and a midplane with $a_{\rmmax}=1$ cm. The disk substructure, with a deficit of emission in the gaps, canbe due to dust properties in these regions that are different from those in therings. We test an opacity effect (different $a_{\rm max}$) and a dust massdeficit (smaller dust-to-gas mass ratio) in the gaps. We find that the emissionprofiles are better reproduced by models with a dust deficit in the gaps,although a combined effect is also possible. These models have a globaldust-to-gas mass ratio twice the ISM value, needed to reach the level ofemission of the 7.8 mm VLA profile.

Exploring the Grain Properties in the Disk of HL Tau with an Evolutionary Model