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

Two-fluids plane or axisymmetric Poiseuille flow at optimum: A (quasi)analytical study