Why does thermal insulation still rely so heavily on thickness? Is there a fundamental physical limit?

Quite an interesting discussion on materials sub-reddit today regarding the thickness of insulation and whether it relies upon material properties. Can we make insulating materials thinner? Exactly what physics is in play here? 

 Making insulation thick is inexpensive and does not add much weight either. Most of it is just air. And since air has very low thermal conductivity (.026 W/mK) it makes for an effective insulation. Aerogels work on the same principle: it's just a material frame for trapping lots of air ,of course with nano-scale pores suppressing conduction even further due to the knudsen effect.  But they are more difficult to manufacture , as compared to say thermal blankets which can be prepared by simple weaving. 

Regarding physical limits — yes there is one. If we look at Fourier's law of thermal conductivity, it scales inversely with length. So a thinner insulation transfers more power than a thicker one of the same material. 

And actually this property is utilised in regenerators in some types of engines and cryocoolers (eg stirling) where tightly spaced porous materials confine air in small gaps As length decreases it's power transfer per unit area rises and can approach metallic levels. The same air can have a power transfer rate of 26W/m^2K when it's confined at 1mm gap. 

Temperature plays a very important role too. For high temperatures exceeding 1000K, black body radiation becomes a significant loss factor and to confine it we need metals that reflect the radiation back. 

With any insulation the challenge is 3 fold. We want to cut off not just conduction (which is given by Fourier's law) but also convection and radiation. Adding bulk cuts off conduction and convection both. Radiation is managed by metallic strips or some other materials like graphite. 

But there are ways to make insulation thinner. The simplest is vacuum insulation. You just remove as much air from the gap as possible and there are too few molecules left to conduct. So the question is does your application allow you to maintain a good vacuum? If so then it's a cheap and less bulky option than other insulation technology. If not then traditional methods work ,they are not too expensive or heavy but they can be bulky. 

https://www.reddit.com/r/materials/comments/1w9m27e/comment/p8bfk2w