Numerical simulation of sedimentation in the presence of 2D compressible convection and reconstruction of the particle-radius distribution function

Numerical simulation of the sedimentation of a polydisperse suspension in a convectively unstable medium is presented. For the simulation of 2D compre ssible convection, the full system of hydrodynamic equations is solved by t he explicit MacCormack scheme. Velocities and positions of suspension parti cles are calculated simultaneously with the solution of the equations. Init ially, the particles are randomly distributed in the computational region. The total weight of sedimented matter is recorded during the numerical expe riment. The results are compared with the sedimentation of the same suspens ion without convection. To reconstruct the particle-radius distribution fun ction from the sedimentation curve, a new method is used. This method is ba sed on the solution of the sedimentation integral equation by the Tikhonov regularization method and was recently developed by the author. To illustra te this technique, sedimentation of cement powder in air is simulated. The suspension contains 50 000 particles. The particle radii are assumed to be log-normally distributed. Heat-driven convection is completely determined b y the top and bottom boundary temperatures of the computational region and lateral boundary conditions. It is shown that convective motions of a mediu m with sedimented particles lead to the following effect: the fine disperse fraction of the suspension remains suspended much longer than without conv ection. Some particles will not sediment at all. The maximum radius of the particles of this fraction depends on the convection parameters (e.g. on co nvection cell size and convection velocities). These parameters, in their t urn, depend only on the temperature difference of the top and bottom bounda ries. The results of these calculations can be applied in geology and meteo rology for studying dust sedimentation in air as well as in technology. Hea t-driven convection can be used for separation of suspensions with the cut- off particle radius depending on temperature difference only.