We address the flows of dense suspensions of particles within the framework of two-velocity continuum. Thermodynamics of such a continuum is developed by the method suggested in the papers of Landau and Khalatnikov. As an application, we consider the convective settling problem. We capture the Boycott effect and prove that the enhanced sedimentation occurs in a tilted vessel due to vortices. We do not call on additional interphase forces like the Stokes drag, the virtual mass force, the Archimedes force, the Basset-Boussinesq force and etc. Instead, we apply a generalized Ficks law for the particle mass concentration flux vector.