Lava lamps and oil wheels
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A lava lamp contains two things with similar density(/specific gravity), typically with one solid(ish) at room temperature.
Once heated up, blobs of that solid will have a higher density than the other liquid, and rise until they cool down and become higher density again, and fall.
While the mechanics are fairly simple to understand, it's hard to find two specific substances with the right properties: very similar density, something that coalesces nicely, and is dyeable, melts at the right temperature (often the light source is also the heat source), etc.
It seems that in many cases it's primarily wax and (distilled) water.
You can add glycerol to make the water thicker, to get a goopier effect.
The water may also contain (isopropyl) alcohol. Isopropyl and water mix at any concentration, making it an easy way to fine-tune the density for a somewhat wider range of wax.
You may also find that things like mineral oil work instead of wax, that an oil-and-wax combination is more to your tastes.
Shaking and such may create a mess of small bubbles that may not coalesce, though it may resolve itself after you cool the thing down, once or a few times.
A little bit of hydrophobicity helps here. Many paint solvents will work. Apparently dishwasher soap may too.(verify)
Basically, water-based coloring for water, oil-based dyes for the oil/wax.
To some degree you can count on the dye's properties to not mix with the other liquid. ...but you might need to experiment with oil dyes to find one that mixes properly with your oil.
For water, food coloring works, perhaps printer ink.
For oil and wax, candle dye may a good option. I'd say experiment with the liquid and more solid variants
Lava lamps tend to have incandescent bulbs as both a light and heat source.
Commercial lava lamps may have heat spreaders (metal ring-like things) on the bottom to try to heat the bottom somewhat equally and avoid permanently .
The amount of heat you'll need depends on the container size, and is one of the things you'll probably want to tweak to get a nice and balanced effect.
More heat tends to mean bigger clumps, and going up higher.
If the blobs stay at the top, use a smaller bulb, use a dimmer, or perhaps a small cooling fan on top.
You may like a dimmer, both to control behaviour and to allow different bulb power.
- US patent 3,570,156
Think seventies-ish psychedelic light show projections.
There are various completely different ways to do light shows, Oil wheels in some sort of projectors are one of them.
Oil wheels can contain various things, but are similar to lava lamps in that it's two liquids that don't want to mix.
It's different from lava lamps in that the temperature is lower, the wheel itself is thinner, you don't want it to coalesce too easily, so people generally settle on something like colored oil (rather than wax) and colored water. Glycerol instead of water also works(verify)
The oil can be mineral oil (e.g. baby oil), paraffin oil (think lamp oil), or similar, and can be colored with e.g. liquid candle dye.
You probably want less of the denser stuff.
The wheels themselves can be plexiglass or similar glued together (typically with some sort of spacers - you don't need/want much space, and it helps if the distance is consistent). Three layers mean you can have two independent color sets interact.