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### On some integrable cases of particle motion in a fluid

#### Abstract

Analytical solutions are obtained for certain types of spherical particle motion in a fluid. This is achieved by transforming Lagrangian particle dynamics equation using reasonable approximation for the particle drag coefficient. Two major cases are considered: constant size particles and mass-variable, evaporating liquid droplets. Fluid flow configurations that allow analytical integration of equations are identified.

Solutions are illustrated using cylindrically symmetrical pipe flow profiles. Obtained solutions will be quite helpful in many areas, for example, in particle dispersion, sedimentation and fire suppression applications.

Solutions are illustrated using cylindrically symmetrical pipe flow profiles. Obtained solutions will be quite helpful in many areas, for example, in particle dispersion, sedimentation and fire suppression applications.