  The solution of the two-fluids plane or axisymetric Poiseuille flow is
derived analytically. Then, the conditions for the maximum flow rate of the
most viscous fluid are analyzed in terms of fluids volume fractions. The
axisymmetric case is totally analytical, whereas the plane one is not. In the
axisymmetric case, it is shown that an optimum can be found only if the most
viscous fluid (the liquid) is inside and the less viscous one (the gas) is
outside. In the plane case, the maximum flow rate of the "liquid" can reach 4
times that of the classical Poiseuille flow in the limit of vanishing viscosity
of the "gas".
