Allen B. answered • 02/03/23
Physics Degree + Lifelong Hobbyist + 10+ Years Tutoring Experience
By "space" I assume you mean free-fall or microgravity, the environment on space stations and in-flight spaceships. (You do experience significant gravity on other worlds and while a spaceship's engines are thrusting. You can also spin a ship or station to get artificial gravity, though that's not been tried yet.)
It's true that liquids are not pulled "down" in microgravity. This makes for a sometimes uncomfortable experience in the first few days in space, as fluids from your legs are free to redistribute up into your head and torso. Your body adjusts, but it takes time. Fortunately, your body doesn't depend on surface tension to hold that liquid; the tension of your skin and the membranes of cells and organs is enough to hold either the normal pressures felt on Earth or the altered pressures from the shifted fluids in microgravity.
Likewise, your body doesn't depend on gravity to make your digestion work! Peristalsis is the rhythmic squeezing of autonomic smooth muscles lining the gut from the upper esophagus all the way to the other end. There are also valves at key places in the gut (for instance, each end of the stomach). These provide more than enough pressure to keep food and waste moving in the right direction -- although the process can feel strange in those first few days in space! Space sickness is very much a real thing, and many astronauts have struggled with it until the body acclimates.
You can test out peristalsis yourself. Find a safe way for your head to be below your stomach -- leaning off a low bed or a chair, for instance. You'll find swallowing takes a bit more effort as you're fighting gravity... but unless you have a medical condition, it should work just fine. If it works with gravity the wrong way, it'll certainly work with no gravity at all.
(Crossposted from Quora)
