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We introduce a new Lagrangian smooth-particle method to model the growth anddrift of pebbles in protoplanetary disks. The Lagrangian nature of the modelmakes it especially suited to follow characteristics of individual (groups of)particles, such as their composition. In this work we focus on the watercontent of solid particles. Planetesimal formation via streaming instability istaken into account, partly based on previous results on streaming instabilityoutside the water snowline that were presented in Schoonenberg & Ormel (2017).We validate our model by reproducing earlier results from the literature andapply our model to steady-state viscous gas disks (with constant gas accretionrate) around stars with different masses. We also present various other modelswhere we explore the effects of pebble accretion, the fragmentation velocitythreshold, the global metallicity of the disk, and a time-dependent gasaccretion rate. We find that planetesimals preferentially form in a localannulus outside the water snowline, at early times in the lifetime of the disk($\lesssim$$10^{5} \: \rm{yr}$), when the pebble mass fluxes are high enough totrigger the streaming instability. During this first phase in the planetformation process, the snowline location hardly changes due to slow viscousevolution, and we conclude that assuming a constant gas accretion rate isjustified in this first stage. The efficiency of converting the solidsreservoir of the disk to planetesimals depends on the location of the watersnowline. Cooler disks with a closer-in water snowline are more efficient atproducing planetesimals than hotter disks where the water snowline is locatedfurther away from the star. Therefore, low-mass stars tend to formplanetesimals more efficiently, but any correlation may be overshadowed by thespread in disk properties.

A Lagrangian Model for Dust Evolution in Protoplanetary Disks: Formation of Wet and Dry Planetesimals at Different Stellar Masses