Numerical simulations are presented showing the effects of operating and geometrical parameters on the transition of laminar to Taylor vortex¯ow for induced rotational-axial¯ow in the gap of a pair of rotating cylinders. These simulations indicate that annular rotational ow becomes more stable in the presence of a small degree of axial¯ow and as gap width increases. The effect of rotational speed on the breakdown of laminar¯ow is more complex and for given radius ratio and axial¯ow rate depends on both the speed ratio and the direction of the rotation of the cylinders, counter-rotating¯ow generally producing a more stable¯ow than co-rotating. Limited experimental data are provided on the residence time distribution for¯ow of Newtonian liquids through the gap of two rotating cylinders. The data include results from experiments in which¯ow transition occurred from laminar to Taylor vortex¯ow. The ®ndings from these experiments are successfully analyzed and assessed using the simulations studies. List of symbolsDimensionless differential operator D m 2 s À1 Axial dispersion coef®cient L m Distance between two measuring points M ± Dimensionless angular velocity, À Xr X 0 Á N rps Rotational speed of cylinder P Pa Pressure P ± Parameter de®ned by Eq. (17) Pe ± Peclet number, À WL D Á Re ± Axial Reynolds number, À WR 2 ÀR 1 m Á R 2 Y R 1 m Radii of outer and inner cylinders R m m Mean radius, À R 1 R 2 2 Á r m Radial coordinate s ± Growth rate of disturbances T c ± Critical Taylor number given by Eq. (15) Ta ± Taylor number, À À 4AX 0 R 2 ÀR 1 4 m 2 Á Ta c ± Critical Taylor number t s Time Ur m s À1 Radial velocity component Vr m s À1 Tangential velocity component W m s À1 Axial¯ow velocity Wr m s À1 Axial velocity component x ± Transformed dimensionless radial coordinate z m Axial coordinateGreek symbols a ± Radius ratio,Wave number l kg m À1 s À1 Viscosity of the working liquid m kg m À1 s À1 Kinematic viscosity of the working liquid r ± Dimensionless growth rate Dr 2 h ± Dimensionless variance difference X 2 , X 1 rad À1

Power input data are presented for a twin flat disk up-and-down moving (vibromixer) impeller operating in a small vessel with a range of Newtonian liquids. Vibromixer power number and Reynolds number are defined and are used to establish the Newtonian power curve for this type of mixer. Drop size distributions are presented for xylene-in-water dispersions under turbulent flow conditions in the vibromixer and are shown to vary with the maximum velocity of the disk (2d.f). The Sauter mean drop diameter of the distribution is related to the vibromixer Weber number, (We = p(2df12D/u), by an equation of the type d,,/D = C with the coefficient C = 0.37. Des donnCes de puissance sont prBsentCes pour une turbine a dkplacement ascendant et descendant 21 disques plats jumelCs (vibromklangeur) dans un petit reservoir pour une gamme de liquides newtoniens. Le nombre de puissance et le nombre de Reynolds du vibromdangeur sont dkfinis et servent a Ctablir la courbe de puissance newtonienne pour ce type de mklangeur. Les distributions de tailles des gouttes sont prksentCes pour des dispersions de xylkne dans I'eau dans des conditions d'kcoulement turbulent dans le vibromelangeur, et on montre qu'elles varient avec la vitesse maximale du disque (2JCAfl. Le diambtre de goutte moyen de Sauter de la distribution est relic au nombre de Weber du vibromdangeur, (We = p(2nAfi2D/u), par une Bquation du type d32/D = C avec le coefficient C = 0,37.