The Navier–Stokes–Vlasov–Fokker–Planck System as a Scaling Limit of Particles in a Fluid

Convergence of a system of particles, interacting with a fluid, to Navier–Stokes–Vlasov–Fokker–Planck system is studied. The interaction between particles and fluid is described by Stokes drag force. The empirical measure of particles is proved to converge to the Vlasov–Fokker–Planck component of the system and the velocity of the fluid coupled with the particles converges in the uniform topology to the the Navier–Stokes component. A new uniqueness result for the PDE system is added.

Slowly Vibrating Axially Symmetric Bodies-Transverse Flow

Stokes drag on axially symmetric bodies vibrating slowly along the axis of symmetry placed under a uniform transverse flow of the Newtonian fluid is calculated. The axially symmetric bodies of revolution are considered with the condition of continuously turning tangent. The results of drag on sphere, spheroid, deformed sphere, egg-shaped body, cycloidal body, Cassini oval, and hypocycloidal body are found to be new. The numerical values of frictional drag on a slowly vibrating needle shaped body and flat circular disk are calculated as particular cases of deformed sphere.

Stokes' law, viscometry, and the Stokes falling sphere clock

Clocks run through the history of physics. Galileo conceived of using the pendulum as a timing device on watching a hanging lamp swing in Pisa cathedral; Huygens invented the pendulum clock; and Einstein thought about clock synchronization in his Gedankenexperiment that led to relativity. Stokes derived his law in the course of investigations to determine the effect of a fluid medium on the swing of a pendulum. I sketch the work that has come out of this, Stokes drag, one of his most famous results. And to celebrate the 200th anniversary of George Gabriel Stokes’ birth I propose using the time of fall of a sphere through a fluid for a sculptural clock—a public kinetic artwork that will tell the time. This article is part of the theme issue ‘Stokes at 200 (part 2)’.

The fluid mechanics of poohsticks

The year 2019 marked the bicentenary of George Gabriel Stokes, who in 1851 described the drag—Stokes drag—on a body moving immersed in a fluid, and 2020 is the centenary of Christopher Robin Milne, for whom the game of poohsticks was invented; his father A. A. Milne’s The House at Pooh Corner , in which it was first described in print, appeared in 1928. So this is an apt moment to review the state of the art of the fluid mechanics of a solid body in a complex fluid flow, and one floating at the interface between two fluids in motion. Poohsticks pertains to the latter category, when the two fluids are water and air. This article is part of the theme issue ‘Stokes at 200 (part 2)’.