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We study the role of phase change and thermal noise in particle transport inturbulent flows. We employ a toy model to extract the main physics: condensingdroplets are modelled as heavy particles which grow in size, the ambient flowis modelled as a two-dimensional Taylor-Green (TG) flow consisting of an arrayof vortices delineated by separatrices, and thermal noise are modelled asuncorrelated Gaussian white noise. In general, heavy inertial particles arecentrifuged out of regions of high vorticity and into regions of high strain.In cellular flows, we find, in agreement with earlier results, that dropletswith Stokes numbers smaller than a critical value, $St < St_{\rm{cr}}$, remaintrapped in the vortices in which they are initialised, while larger dropletsmove ballistically away from their initial positions by crossing separatrices.We independently vary the P\'eclet number $Pe$ characterising the amplitude ofthermal noise and the condensation rate $\Pi$ to study their effects on thecritical Stokes number for droplet trapping, as well as on the final states ofmotion of the droplets. We find that the imposition of thermal noise, or of afinite condensation rate, allows droplets of $St < St_{\rm{cr}}$ to leave theirinitial vortices. We find that the effects of thermal noise become negligiblefor growing droplets, and that growing droplets achieve ballistic motion whentheir Stokes numbers become $\mathcal{O}(1)$. We also find an intermediateregime prior to attaining the ballistic state, in which droplets movediffusively away from their initial vortices in the presence of thermal noise.

Transport of condensing droplets in Taylor-Green vortex flow in the presence of thermal noise