Set in the near future, the interior of the spaceship is coated with thin layers of Teflon approximately 10mm average thickness on top of titanium alloy which in case you are wondering it is weakly magnetic. I need the crews to be able to walk around the catladders and platforms instead of floating everywhere in a very spacious area, no nets, safety harness/ropes, FTL, wrap, artificial gravity and ET allowed. Is there any durable and affordable footwear to allow the crews to walk around the spaceship effortlessly instead of free fall?
Velcro is easy to use insofar as you an put the 'fluffy' side of the velcro on almost any surface, and then just adhere the 'hook' side of the velcro to the underside of your shoes. Let's say you're on a ladder. Your hands can still grip the rungs covered in the fluffy part, but your shoes adhere to it, making purchase easier.
Ideally, you'd also wear velcro gloves, so you could launch from one side of the ship to the other and control your arrival at the next bulkhead with your hands and swing your feet into position.
The other advantage to this kind of footwear is that you don't even need to make it especially; you could just tape the velcro onto the bottom of some standard sneakers, and even replace it if it starts to wear.
Although it doesn't take advantage of the magnetic properties, this is actually the most practical because the holding forces of velcro make it quite useful for this kind of environment while still giving people the ability to break the hold to move about. You should also be able to use it as a good hold point for cargo and specific personal items like tablets and other devices you'd normally leave on a desk beside you in full gravity, meaning that the solution is versatile beyond astronaut mobility; it's more or less a gravity replacement for your personal items and in some cases cargo as well, if you use it correctly.
You don't actually need any footwear to move in micro gravity.
Hands are the perfect tools to grab onto ladder rungs and with a little training, our toes can hold onto them fine enough. In micro gravity humans don't have to walk upright, they can pull themselves along handholds and ladders in all directions.
The ISS is a fine example of how a single hand hold (or foot hold) can anchor an astronaut just fine and leave both hands free to work with.
As long as there are no sharp edges, you don't need any footwear at all. For reasons of sanitation thin socks and gloves are more than enough. To make grabbing rungs with your feet easier, the socks should be coated in a non-slip substance and at least the big toe should be seperated (like a mitten for feet). Seperating each toe would probably be more practical for the astronaut, though.
Imagine a latex glove for feet: it adapts to the form of the foot, is non-slippy and keps the walls of your space ship clean.
I am not sure that holding the feet somewhere would be of any help for moving in microgravity.
Our body is used to either walk or swim. Walking for a biped is basically a continue series of controlled falls: the body leans forward, using gravity and feet traction to move and then the other foot to start te cycle again.
Taking out gravity from this process would make it more difficult to walk and control movement. With no gravity to act on the body, the torso would have a hard time following the movement of the legs. One would have to basically lay parallel to the floor and move like climbing a ladder.
Floating in microgravity would be a preferred way to move, thanks to its resemblance with swimming.
Gel window cling polymer slime.
These things are popular and fun. They are made of hard tacky polymer goo. They will adhere indefinitely to a window. If you are making toys, you can adjust the tackiness to make something like the tumbling men - also polymer slime but gooeyer such that they stick then gradually peel away.
The polymer sticks to itself better than to smooth surfaces like glass (or certainly teflon). Polymer slime shoes would give you some traction but not so much the shoe comes off of you.
That 10mm layer of teflon has similar thickness and properties to Marley, a vinyl floor covering used in nearly all serious ballet studios and performance spaces. Also good for other forms of dance in bare feet or soft shoes (or hard shoes with soft coverings aka pointe shoes).
Ballet slippers are designed to be durable, comfortable, and to protect the foot from friction (lack of gravity doesn't means there isn't friction as a foot twists while pushing off from a surface) and other concerns.
More importantly, they are designed not to fall apart in ways that leave little pieces lying around (or floating around, as the case may be). Little bits of stuff are dangerous for dancing.
The standard ballet slipper is made of soft leather or canvas (canvas wears out faster but might be okay in low-gravity; leather can last for years) with a cloth lining. There are elastic straps over the top so the shoe is always perfectly secure. The bottom of the shoe has leather soles, either one long one or two smaller ones at ball and heel.
If you need magnets, they can go into split sole (the kind with two pieces of leather on the bottom) shoes. Use flat, thin, flexible magnets under or within the covering for the ball of the foot.
If you need velcro or another sticky substance, it can also go on the leather soles of the slippers.
Ballet slippers are light, compress for storage, are not that expensive (unless you are outfitting a serious dancer), and are widely available commercially in a variety of styles and a huge range of sizes. Colors are mostly pink and black with some tan/brown and white available, but I'm sure could be any color with a large special order.
Named one of the top five science breakthroughs of 2012 by CNN Money, Geckskin™ is so powerful that an index-card sized piece can hold 700 pounds on a smooth surface, such as glass, yet can be easily released, and leaves no residue.
Geckskin™ offers tantalizing possibilities for synthetic devices that can easily attach and detach everyday objects such as televisions or computers to walls, as well as medical, industrial, clothing, and home applications.
Unlike traditional pressure-sensitive adhesives, which rely on viscoelasticity for adhering to surfaces, Geckskin™ relies on a concept known as draping adhesion. Draping adhesion is created with materials that can drape to create conformal contact with a surface while still maintaining high, elastic stiffness in directions where forces will be applied. This design enables adhesive loads to be more evenly distributed across the pad surface, while also allowing for a rapid and low-energy transition between attachment and detachment.
Geckskin™ is composed of stiff fabrics—such as carbon fiber or Kevlar—with soft elastomers, such as polyurethane or polydimethylsiloxane (PDMS). It uses commodity materials, not nanotechnology. The key innovation of Geckskin™ was the integration of a soft elastomer (the pad) with a stiff fabric (the skin), allowing the pad to drape over a surface to maximize contact. Further, as in natural gecko feet, the skin is woven into a synthetic tendon, yielding a design that plays a key role in maintaining stiffness and rotational freedom. The end result is an adhesive device that is powerful, easily removed, and leaves no residue.
The first thing that you think when reading this is suction-cups of some sort. They are equally if not worse than velcro. This is not what I mean.
Imagine having some sort of shoes or gloves that have a duct-system built into them. Like a vacuum cleaner. This way a singular fan or air-pump can be used to create different levels of suction depending on area of usage. Or one might even have individual suction systems for each shoe/glove or piece of attire that needs "Gas-based artificial gravity".
This can be configured to increase or decrease suction when one lifts a foot or similar via sensors.
This solution is feasible although hard to accomplish realistically. Usage in vacuum or low air-density will be severely hampered since it depends on the density of the gas to function as intended.
This system could also theoretically be used in low-zero gravity as a form of transportation if one reverses the airflow to blow instead of suck.
In microgravity you don't need a strong magnet and shaped field sheet magnets exist, so just a flat sheet of shaped field magnet (aka polymagnets) comparable in shape and thickness to the soles of thin shoes. Sandwich it between a a bonded cloth layer for durability. Something like a pair of tall dojo shoes in design will let you walk around comfortably all day with a little practice. You can even shaped the magnetic pattern to keep the force comfortably distributed.