Sedimentation of a single soluble particle at low Reynolds and high P\'eclet numbers

We investigate experimentally the dissolution of an almost spherical butyramide particle during its sedimentation, in the low Reynolds high P\'eclet regime. The particle sediments in a quiescent aqueous solution, and its shape and position are measured simultaneously by a camera attached to a translation stage. The particle is tracked in real time, and the translation stage moves accordingly to keep the particle in the field of the camera. The measurements from the particle image show that the radius shrinking rate is constant with time, and independent of the initial radius of the particle. We explain this with a simple model, based on the sedimentation law in the Stokes' regime and the mass transfer rate at low Reynolds and high P\'eclet numbers. The theoretical and experimental results are consistent within $20\%$. We introduce two correction factors to take into account the non-sphericity of the particle and the inclusions of air bubbles inside the particle, and reach quantitative agreement. With these corrections, the indirect measurement of the radius shrinking rate deduced from the position measurement is also in agreement with the model. We discuss other correction factors, and explain why there are negligible in the present experiment. We also compute the effective Sherwood number as a function of an effective P\'eclet number.