Coexisting thermodynamic phases of lipid molecules at the air-water in
terface often exhibit microscopically observable domains with a variet
y of sizes and shapes. The size and shape equilibration of these domai
ns generally involve fluid flow in the monolayer as well as in the aqu
eous subphase. The present work treats the problem of the rate of size
equilibration of a circular solid domain surrounded by a liquid compo
sed of the same substance. The pressure at large distances from the do
main is maintained constant, so that there is monolayer flow toward or
away from the central domain. The central domain accordingly increase
s or decreases in size until a state of stable or metastable equilibri
um is reached. Calculated rates of domain size change are discussed in
terms of different experimental conditions, including applied electri
c fields.