From this post on whipped butters, I found two questions that went unanswered...
From p (July 2010): I've got a question for you... what is it that makes butters whippable? Is it just that they're soft but solid at room temp? Could I whip an oil & beeswax (no butter) balm? Just curious!!
Hi p! The answer to the first part is mostly yes. We can whip them because they're filled with lovely fatty acids that are solid at room temperature. Butters tend to have lots of nice fatty acids like stearic and lauric acid that are great thickeners. Not all butters are whippable at room temperature - shea, mango, and babassu are, but cocoa butter and kokum butter aren't. This because they have different melting points. But that's kind of obvious!
I did some experiments on whipping oils with various thickeners that might interest you...(although I see you posted there and I didn't respond to your question then! Sorry, p!)
As for the second part of the question, there's an interesting balm I found on Voyageur for non-petroleum baby jelly that uses oil and beeswax. 94% castor oil, 5% beeswax, and 1% Vitamin E. I've tried it - I liked it. You could try this with another oil, but it won't work as well as there's an interesting interaction between beeswax and castor oil! Beeswax is partially soluble in castor oil, so you get a thicker and more viscous product when you mix beeswax and castor oil together than you would mixing something like sunflower oil and beeswax. This is one of the reasons we see these two ingredients together in lipsticks - they prevent the colour from feathering into fine lines around your lips!
So the short answers are...
1. Butters have fatty acids that are solid at room temperature, which is why we can whip them.
2. And you could make a balm from beeswax and an oil, but it won't be the same as whipping a butter!