Particle Image Velocimetry (PIV) is a non-intrusive measurement technique for studying the velocity of particles in some type of flow. This is most commonly either a gas flow in a wind tunnel, or a liquid flow of some viscous fluid. The medium is then seeded with some sort of tracer particles and then illuminated periodically by some high power light source, which is often a laser. The idea is to obtain successive digital images from charged coupled device (CCD) cameras. These images can then be analyzed by a computer, which determines the velocities of the tracer particles, which can be used to understand the velocity of the given medium. The advantage of this technique is that it does not require the placement of any type of probe in the medium, which could affect the overall flow. This lack of interference is what gives it its non-intrusive quality. Also, where a probe can only measure the velocity at a single point, PIV can return information about the flow of the entire field.
In this experiment, under the supervision of Dr. Goldstein, we are interested in understanding the fluid mechanic properties of an injected jet of a specific concentration salt solution into a gradient salt solution tank. As the jet descends into the tank a corkscrew effect is observed, caused by the change in difference of density between the jet and the surrounding fluid. Of particular interest there appears to be some areas of circulation near where the jet enters the tank. Also, we know that the jet is pulling in fresh water from the top of the tank because of a no-slip boundary, and we know that it must come back up to the top at some point, but we’re not sure what path it takes in returning. For the most part the basic fluid mechanic properties of this system are not understood. By observing the overall flow of the fluid we hope to find out just what is going on.
This phenomenon has been observed in laboratory experiments. In particular, Wu and Libchaber report when studying the movement of micron-sized beads in a bacteria bath that the movement of the bacteria, Escherichia coli, is not due to Brownian motion but to “transient formations of coherent structures, swirls and jets, in the bacteria bath.” Thus, since this motion has been observed in a biological process it becomes applicable to a wide range of fields, particularly those interested in chemotaxis.
For the beginning of this experiment I first concentrated on creating a simple particle tracker. I created an animation consisting of a single black sphere traveling across a white background. The path of the sphere could vary, but to keep things simple I had it follow a sinusoidal path from one side of the image to the other. To determine the location of the sphere in any given image I used a method known as cross-correlation. This method involves taking a picture of the sphere, referred to as the kernel, and basically sliding it around in the image until a match is found. For each pixel in the image the intensity of each pixel in the kernel is multiplied by the intensity of the surrounding image pixels. In this way values are calculated for all of the pixels in the image and the cross-correlation matrix is formed. So, if the kernel has dimensions a and b, then the value of the cross-correlation matrix for a given pixel in the image (x,y) is: