Salt-finger Experiments
Dan Kelley (Dalhousie University)
Addendum to presentation at AST-2000 meeting
Halifax, NS, Oct 2000.

Introduction

A laboratory model of salt-finger may be set up with any two substances that diffuse at different rates. In the ocean, the ``substances'' are heat and salt. Unfortunately, heat is difficult to control in the laboratory, and spurious convective motion tends to occur, confusing the fluid flows under study.

For example, experiments set up in a beaker suffer from the fact that the beaker itself transmits heat, leading to so-called ``side-wall'' flows. Imagine a setup with a layer of cold water sitting below a layer of hot water ... heat transmitted along the walls of the beaker will heat up the cold water near the edges of the container, causing convection as fluid near the walls warms and grows less dense. This effect can be reduced, in relative terms, by using a very thin-walled beaker or beaker that is so large that the side-wall flows are a minor part of the overall flow. But we're still left with the problem of heat-flow through the beaker, e.g. from a warm fluid to a cool room. This too will set up convection patterns inside the beaker, and for this reason it is common to insulate beakers with thick styrofoam. Uh oh, now we can't see the flow! Fine, you say, we'll have to cut a hole in the styrofoam for a viewing port. But won't that let heat escape or enter the domain? Sheesh!! You get the picture.

So, for practical purposes, e.g. for a classroom demonstration purposes, it's better to use ``substances'' other than heat and salt.

The sections below discuss two methods. The first is probably easiest.

Method 1: heat/dye fingers

The following instructions are courtesy of Barry Ruddick, who credits the advice of George Veronis.

Float a layer of hot water over a deeper layer of cold water. The hot layer shoulld be about 5 cm thick. The hot water should have a FEW grains of sodium flourescein dye dissolved into it. This has a trivial effect on the density, so it's easy to float the layer on top of the cold by using, say a scrap of cardboard.

Then you just leave it sit. The surface heat loss decreases the temperature difference, and when the density ratio R_rho becomes less than 100, fingers can form. This works so well because the first fingers to form at large density ratio are also very large. Also, the long time (10-50 minutes) for fingers to form allows time for viscous dissipation of all the initial disturbances that induced by filling, and this yields fingers that are quite regular.

You start the class off by filling the tank, then go on with the lecture. Five minutes before the end o the class, turn off the lights, and use a flashlight to show the fingers.

This works best in a tank with square side-walls. To construct it, use 1/4-inch plate glass in the correct size pieces, with the edges smoothed with emery cloth to prevent cuts. Then clean all edges with alcohol, and then glue them together with clear silicone seal. Duct tape provides a convenient clamp while this ``glue'' sets.

Method 2: sugar/salt fingers

Every kitchen has the materials needed to set up a salt-finger experiment. Sugar and salt diffuse at different rates. Sugar diffuses more slowly than salt diffuses, so sugar in our experiment plays the role of salt in the ocean. Just to confuse things, salt in the experiment takes the role of heat in the ocean, since salt diffuses faster than sugar.

You'll need a beaker with transparent sides, two mixing containers, some sugar and salt. You'll also need some food coloring, dye, or ink ... something dark enough to see when diluted but that can be cleaned up and. If you're doing this in a kitchen, don't use a poison dye or your roommates and family will sue me. You'll also need a piece of paper to which you've glued a string that is twice as long as your beaker is high.

In one container, mix the ``top'' fluid, with 1 part salt and 2 parts sugar for 48 parts fresh water. Add a few drops of food coloring, or ink

In the second container, mix the ``bottom'' fluid, with 2.5 parts salt and 1 part sugar for 48 parts water.

Half-fill the clear-sided beaker with the ``bottom'' fluid. Then cover the surface with the paper, and dangle the string over the top of the beaker. You might want to tape the string on the outside of the beaker, or at least keep a finger on it. Then, carefully pour the ``top'' fluid on top of the paper. The paper acts as a momentum buffer, to prevent the ``top'' fluid from mixing into the ``bottom'' fluid. You'll be able to pour faster as time goes along.

Then, carefully pull out the paper with the string. This is a step that is easy to mess up, but if you read these directions fully before starting, I bet you'll have cut the paper to a shape, and attached the string in such a way, that you can pull the paper out without mixing the whole beaker up!

If you've succeeded in leaving a sharp interface between the two layers, sit back and wait. After about a half hour, you should notice salt-fingers forming at the interface, forming a very fine comb feature.

For more on this sort of lay-person's experiment in salt-fingers, see Strong, C. L., 1971, THE AMATEUR SCIENTIST: Experiments with salt fountains and related instabilities in water, Scientific American 124-127.