The Equation of Motion of Particles in Fluids—An Historical Perspective

This is a review article that covers the history of the development of the equation of motion for solid particles in fluids, starting with the early work, before the Navier–Stokes equations were developed. Particular emphasis is placed on the development of the transient equation of motion, which features the history (or memory) term and the added mass (virtual mass) term. The salient features of the equation and the methods of their derivation are pointed out. Creeping, non-inertia flows as well as advective flows are surveyed, with particular emphasis on their effects on the functional form of the history term. Modifications to the hydrodynamic force due to possible interface slip are also examined. The review also deals with the inclusion of the weaker lateral (lift) forces and the inclusion of the effects of Brownian movement, which gives rise to thermophoresis—an important source of nanoparticle movement and surface deposition. The drag on irregularly shaped particles—another important feature of nanoparticles—is also examined. The review concludes with a short section on significant unknown issues and work that may be carried out in the near future for the theoretical and computational development of the subject.