To kick things off: I saw this picture the other day of a foot after soaking in a wet boot for 3 days. Picture turned B/W to spare you most of the gore, but by the amount of white, wrinkly mess you can tell it's not pretty:

Assuming we'll need a portable implementation, how does one dry shoes from inside without taking them off?

On the surface, there appear to be a couple of methods to choose from to remove moisture:

None of the above is immediately suitable, and some may even be entirely insufficient for the task.

and is stored in the fabric, inner shoe or insole, and perhaps to a lesser degree in calluses - all of which need to be dried as well.

With rain and water ingress subject to other mitigation measures or treated as intermittent with the ability to recover from, one thus needs to be able to extract a steady flow of water as excessive humidity or micro-capillary condensation. How much?

[1] states,

"Two key observations emerged. First, sweat secretion from the experimental foot averaged 30 ml · h, peaking in the last 5 min at 50 ml · h. Second, approximately 70% of the measured sweat flow emanated from the upper skin surfaces, with only 30% coming from the plantar surface."

As fancy as it may be, membrane dehumidifiers can be immediately excluded, as they only manage to remove 0.1 ml/dm²/h. They also do not appear to be amenable to pleating and may disintegrate after the first few 100 km of walking.

Desiccant packs are not great either - silica gel can store up to 37% water (wt/wt), while zeolite desiccant materials are around 5-35% wt/wt.

Super-absorbent materials can bind up to 500 times their weight in de-ionized water, and up to 50 times their weight when it comes to saline solutions. Sweat is salty, which could however be handled by using a short-lived membrane and diffusion. The search for "hygroscopic superabsorbent materials" yields some results [2] that are closer to 1:1 ratio and not intended to work with moisture alone, instead calling for de-ionised water immersion.

In [3], "super hygroscopic polymer films (SHPFs) composed of renewable biomasses and hygroscopic salt, exhibiting high water uptake of 0.64-0.96 g g at 15-30% RH" are explored and compared. It is further stated that, "The key steps of atmospheric water harvesting (AWH) involve moisture capture and water release, followed by a simple filtration or purification process (Fig. 1a). The earlier approaches, such as fog capturing and dew condensation, require the presence of high relative humidity (RH) (>90% RH), which is not a viable solution considering more than one-third of the global terrestrial area has an average annual humidity less than 40% (Fig. 1b)."

Spiderweb diagrams for classes of desiccants are given in Fig.1, with the presented SHPFs on the right having the most favorable properties:

This material looks indeed rather nice if one were to cycle air through it, and probably make it hot-swappable in small canisters for regeneration at a later time.

What are the prospects of simply pumping air through an inner shoe and thereby removing moisture? The specific heat of moist outside air [4] is close to 1 kJ/kg/K for ambient temperatures, with a density of around 1.2 g/L. When drawn in from a 0°C environment and heated to 30°C, this requires 36 Ws to heat. at 10-100 ml / s, this is a delightfully low power level suitable for Li-Ion battery operation.