The force balance equation would seem to indicate that a finer screen (with a higher bubble point) would be preferable. However, fine screen has higher flow losses and a much smaller effective thickness which as we shall see is very important for transient performance.
The basic force balance above does not begin to capture the intricacies of gallery arm use because unsteady effects are ignored. These transient effects often dictate loads on the screen bubble point many times larger than the steady state loads.
The unsteady governing equations are:
Continuity (equivalent thickness vs. time):
Conservation of Momentum (acceleration and pressure):
Equation of State (pressure vs. equivalent thickness)
The severity of the transient depends upon the arm size (which dictates the liquid velocity change) and the screen compliance (equivalent thickness at bubble point). The smaller the arm, the larger the transient. The less liquid the screen can supply per unit area, the more severe the transient.
The reason transients are so severe with gallery arms is that the liquid within the arm must be accelerated to ensure gas free delivery. These changes in flow velocity in the arms must occur quickly - before gas penetrates the relatively thin screen thickness. Without accounting for the transient loads, one is virtually guaranteed a small puff of gas at every transient event. This gas may accumulate in a trap or downstream filter and be ingested in one fell swoop by the thrusters.
For more information on the design, use, and physics of galleries please see
AIAA 97-2811 Propellant Management Device Conceptual Design and Analysis: Galleries