This is a quick look inside a cheap plastic peristaltic pump bought from China via ebay. Peristaltic pumps work by rotating rollers so that they pinch a loop of silicone tubing against an outer surface and force pockets of liquid through it. The primary advantages of these pumps is that they are simple, the liquid is pumped in situ in the tube and they are capable of pumping very precise quantities of liquid. They're widely used as dosing pumps for adding chlorine to pools or water supplies, adding detergents into industrial washing machines or dispensing ingredients into drinks.
Up to now they've tended to be very expensive, but ebay has quite a few listings for these pumps at around 10 UK pounds (about $15 US) which is actually very affordable.
This video shows the inside mechanism of these pumps, which in this case is very simple since all the tensioning seems to originate from the springiness of the silicone tube itself. I've not actually run this pump in earnest yet, so I'm now sure how it's going to handle the test of time, but I've got some silicone tube on order for testing purposes. I'd guess the biggest weakness may be the thin plastic spindles on the roller support plate, but then again, they are only there to guide the rollers and not physically drive them.
According to one of the ebay listings they are designed to accommodate 4.7mm outer diameter 2.5mm inner diameter tubing. This is probably an imperial to metric conversion from 3/16ths of an inch. I noticed that there is room for a deeper tube in them so I'm going to try standard 6mm aquarium airline tubing since it's easily available. I reckon as long as the wall thickness is about 1mm it will fit and pump correctly in the unit. (Or it may just turn into a pile of crunchy plastic.)
Quick update... I've tried the standard airline tube in and although it works it doesn't get pinched tight enough by the rollers to form a proper airtight seal, and thus has reduced lifting and pumping capability. However, the thinner silicone tube supplied with the pump is a good tight fit inside the standard silicone airline tube and gives good results.