For the calculation of the effective added mass and the kinetic energy density
of a mixture of liquid and massless identical gas bubbles the mixture is thought
to be embedded in an unbounded volume of pure liquid. In fact the solitary
bubble is now replaced by a cloud of bubbles. Again a frame of reference will
be chosen that moves with the liquid velocity at infinity. In this frame the
potential describing the velocity field due to the motion of the bubbles is X.
Now we will look for expressions for the impulse and the added mass of the
cloud of bubbles as a whole.