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In a series of papers, we present a comprehensive analytic study of theglobal motion of growing dust grains in protoplanetary discs, addressing boththe radial drift and the vertical settling of the particles. Here we study howthe radial drift of dust particles is affected by grain growth. In a firststep, toy models in which grain growth can either be constant, accelerate ordecelerate are introduced. The equations of motion are analytically integrableand therefore the grains dynamics is easy to understand.  The radial motion of growing grains is governed by the relative efficiency ofthe growth and migration processes which is expressed by the dimensionlessparameter Lambda, as well as the exponents for the gas surface density andtemperature profiles, denoted p and q respectively. When Lambda is of orderunity, growth and migration are strongly coupled, providing the most efficientradial drift. For the toy models considered, grains pile up when -p+q+1/2<0.Importantly, we show the existence of a second process which can help discs toretain their solid materials. For accelerating growth, grains end up theirmigration at a finite radius, thus avoiding being accreted onto the centralstar.

Growing dust grains in protoplanetary discs - I. Radial drift with toy growth models