Paper Number
AP1 

Session
Award Presentations

Title
Drift redux

Presentation Date and Time
October 12, 2017 (Thursday) 8:00

Track / Room
Award Presentations / Crystal C

Authors (Click on name to view author profile)

1. Khair, Aditya S. (Carnegie Mellon University, Chemical Engineering)

Author and Affiliation Lines (in printed abstract book)
Aditya S. Khair
Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA

Speaker / Presenter 
Khair, Aditya S.

Text of Abstract
One of the first problems that a student of fluid mechanics encounters is inviscid flow past a stationary sphere. Here, fluid elements simply follow streamlines. The situation is more interesting if, instead, the sphere moves steadily in a fluid that is quiescent at large distances; fluid elements undergo complex looping trajectories and can be permanently displaced. This displacement is known as “drift.” The “drift volume” is the volume of fluid between the initial and final positions of an unbounded, marked (as in with dye) set of fluid elements that is initially far ahead of the body and perpendicular to its path of travel. Physically, the drift volume is a measure of the amount of fluid entrained by the body. In 1953, Sir Charles Darwin (grandson of the naturalist) calculated that the drift volume induced by a sphere in inviscid flow equals one half of its own volume. Recent interest in quantifying drift in viscous fluids is motivated by applications to pool boiling; stratified flows; protein transport in membranes; and mixing by swimming organisms. In this talk, a framework to compute the drift volume in viscous flows will be presented, which interprets the drift volume as the time-integrated flux of fluid between streamlines via a conservation-of-mass argument. This enables computation of the drift volume without the need to resolve the trajectories of fluid elements. It will be demonstrated that viscosity has a dramatic influence on drift. For instance, if a body is towed by an external force (e.g. a sedimenting particle) the drift volume can be orders of magnitude larger than the volume of the body and diverges with the travel time of the body. Remarkably, this conclusion holds at all (finite) Reynolds numbers. Finally, the drift volume induced by a self-propelled swimmer is shown to be fundamentally different from that due to a towed body. The implications of this finding on the ability of intermediate Reynolds number (milli-meter sized) swimmers to transport fluid via drift will be discussed.