On Earth (under the influence of gravity) a horizontal tube in which water is flowing may form a layer of air at the top of the tube (since less denser than water). But on the ISS (which experiences micro-gravity) it does not happen. In fact air may form a cone shape in the tube preventing the flow of water (as shown in the image) how does the ISS overcomes this situation?
Do they use a motor to pump water?
There are two answers to the question of fluid flow in micro-G: heat pipes with capillary flow and pumps.
Heat pipes are installed in several places on both American and Russian segments to take extra heat off pieces of avionics with largest loads. Heat-pipes are by definition two-phase, liquid and vapor (ammonia-based).
The ISS has water loops in the life support system (including condensate collection), and cooling loops in the thermal control system.
Internal loops
External loops
Life support system has electric and manual pumps. Plumbing work may include manually pumping through air blockages but the loops aren't critical.
Cooling loops are critical, and are single-phase (liquid throughout). All the pumps are electrical.
US: there are two internal water loops (low- and moderate temperature).
Russia: two redundant switch-on-fail Triol loops
Each US water loop has a Pump Package Assembly with a centrifugal pump, an accumulator, a gas trap, filters, a flowmeter and T (temperature) and P (pressure) sensors.
In the Russian segment, each loop has four pumps and one accumulator.
So, to answer your question: it is the gas trap that prevents air from accumulating in the loop, and the accumulator that makes up for smaller leaks.
In the external ammonia-filled loops (there are two of them), there is again an accumulator which contains a fixed charge of nitrogen to maintain ammonia in the liquid state.
For each of Russian external loops, there is one accumulator.
And now you know how important plumbing is...
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