Green Theorems and Qualitative Properties of the Optical Flow

How can one compute qualitative properties of the optical flow, such as expansion or rotation, in a way which is robust and invariant to the position of the focus of expansion or the center of rotation? We suggest a particularly simple algorithm, well-suited to VLSI implementations, that exploits well-known relations between the integral and differential properties of vector fields and their linear behaviour near singularities.

Bubble Behavior in a Taylor Vortex

We present an experimental study on the behavior of bubbles captured in a Taylor vortex. The gap between a rotating inner cylinder and a stationary outer cylinder is filled with a Newtonian mineral oil. Beyond a critical rotation speed (ω[subscript c]), Taylor vortices appear in this system. Small air bubbles are introduced into the gap through a needle connected to a syringe pump. These are then captured in the cores of the vortices (core bubble) and in the outflow regions along the inner cylinder (wall bubble). The flow field is measured with a two-dimensional particle imaging velocimetry (PIV) system. The motion of the bubbles is monitored by using a high speed video camera. It has been found that, if the core bubbles are all of the same size, a bubble ring forms at the center of the vortex such that bubbles are azimuthally uniformly distributed. There is a saturation number (N[subscript s]) of bubbles in the ring, such that the addition of one more bubble leads eventually to a coalescence and a subsequent complicated evolution. Ns increases with increasing rotation speed and decreasing bubble size. For bubbles of non-uniform size, small bubbles and large bubbles in nearly the same orbit can be observed to cross due to their different circulating speeds. The wall bubbles, however, do not become uniformly distributed, but instead form short bubble-chains which might eventually evolve into large bubbles. The motion of droplets and particles in a Taylor vortex was also investigated. As with bubbles, droplets and particles align into a ring structure at low rotation speeds, but the saturation number is much smaller. Moreover, at high rotation speeds, droplets and particles exhibit a characteristic periodic oscillation in the axial, radial and tangential directions due to their inertia. In addition, experiments with non-spherical particles show that they behave rather similarly. This study provides a better understanding of particulate behavior in vortex flow structures.