The Stokes-Einstein relation for the self-diffusion coefficient of a spherical particle suspended in an incompressible fluid is an asymptotic result in the limit of large Schmidt number, that is, when momentum diffuses much faster than the particle. When the Schmidt number is moderate, which happens in most particle methods for hydrodynamics, deviations from the Stokes-Einstein prediction are e...

The low Mach number limit for classical solutions of the full Navier-Stokes equations is here studied. The combined effects of large temperature variations and thermal conduction are taken into account. In particular, we consider general initial data. The equations lead to a singular problem whose linearized is not uniformly well-posed. Yet, it is proved that the solutions exist and are uniform...

In this work, the stencil adaptive method is applied to investigate the effects of a magnetic field on mixed convection of Al2O3-water nanofluid in a square lid-driven cavity. The incompressible Navier-Stokes equations are solved by an adaptive mesh method which has superior numerical advantages compared to the traditional method on the uniform fine grid. The main objective of this study is to ...

Exact expressions are derived for the pair and three-body hydrodynamic interactions between a sphere and a number of small particles immersed in a viscous incompressible fluid. The analysis is based on the Stokes equations of low Reynolds number hydrodynamics. The results follow by a combination of the solutions for flow about a sphere with no-slip boundary condition derived by Stokes and Kirch...