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Context: Recent observations with the Atacama Large Millimeter Array (ALMA)have shown that the large dust aggregates observed at millimeter wavelengthssettle to the midplane into a remarkably thin layer. Aims: We intend to findout if the geometric thinness of these layers is evidence against the verticalshear instability (VSI) operating in these disks. Methods: We performedhydrodynamic simulations of a protoplanetary disk with a locally isothermalequation of state, and let the VSI fully develop. We sprinkled dust particlesand followed their motion as they got stirred up by the VSI. We determined forwhich grain size the layer becomes geometrically thin enough to be consistentwith ALMA observations. We then verified if, with these grain sizes, it isstill possible to generate a moderately optically thick layer at millimeterwavelengths, as observations appear to indicate. Results: We found that evenvery large dust aggregates with Stokes numbers close to unity get stirred up torelatively large heights above the midplane by the VSI, which is in conflictwith the observed geometric thinness. For grains so large that the Stokesnumber exceeds unity, the layer can be made to remain thin, but we show that itis hard to make dust layers optically thick at ALMA wavelengths (e.g.,tau(1.3mm)>=1) with such large dust aggregates. Conclusions: We conclude thatprotoplanetary disks with geometrically thin midplane dust layers cannot be VSIunstable, at least not down to the disk midplane. Explanations for theinhibition of the VSI include a reduced dust-to-gas ratio of the small dustgrains that are responsible for the radiative cooling of the disk. A reductionof small grains by a factor of between 10 and 100 is sufficient to quench theVSI. Such a reduction is plausible in dust growth models, and still consistentwith observations at optical and infrared wavelengths.

Razor-thin dust layers in protoplanetary disks: Limits on the vertical shear instability