The prediction of the interfacial area formed when one liquid is injected into a second immiscible liquid through a single orifice or nozzle is necessary for calculations of heat and mass transfer rates in such processes. This paper considers the low flow velocity region prior to jet formation where uniform size drops are formed directly at the nozzle tip and break off in a regular pattern. Hayworth and Treybal ( 5 ) and Null and Johnson (8) both present photographs which illustrate the drop formation process.Harkins and Brown ( 4 ) derived an expression for calculating the drop volume at negligibly small flow rates by equating the buoyancy and interfacial tension forces and correctin the volume for the fraction of liquid which Although Rao et al. indicate that their analysis significantly reduces the error for many systems ( l o ) , it has some weaknesses, the most evident of which is its inability to predict a drop volume smaller than that given by the Harkins and Brown analysis. Drops of smaller than static condition size were observed in this study.This paper presents an improved correlation for drop volume based on the two-stage drop formation process and extensive experimental data. EXPERIMENTAL STUDYAlthough several sets of drop volume data exist in the literature ( 5 , 8, IO), it was felt that additional experiments were necessary to obtain a better understanding of the mechanism of drop formation and to provide a more stringent test of any proposed correlation by extending the range of variables studied. Experiments were designed to obtain drop diameter as a function of injection velocity and nozzle diameter for systems with a wide range of physical properties. In all systems the dispersed phase was of lower density than the continuous phase.The experimental apparatus is shown schematically in Figure 1. The test section consisted of a continuous phase tank, into whose bottom the desired nozzle was fastened. The tank.

If water is heated or cooled while flowing through a vertical pipe with a laminar motion, the velocity profile will differ from the parabolic shape for isothermal flow due to density variations in the fluid. If a constant heat flux is used at the wall and if the changes in temperature affect only the density appearing in the gravity term of the equations of motion, a condition is attained far downstream in the heat-transfer section such that there is no further change in the velocity profile. The shape of this fully developed velocity profile depends on the ratio of the heat flux to the flow rate. The stability of flow in an electrically heated pipe 762 diameters long was studied by detecting temperature fluctuations in the effluent. By use of a carefully designed entry and a long isothermal section prior to the heat exchange section, inlet disturbances were eliminated and transition to an unsteady flow resulted from a natural instability of the distorted profiles. It was found that the stability depends primarily on the shape of the velocity profile and only secondarily on the value of the Reynolds number, if at all. For upflow heating the flow first becomes unstable when the velocity profiles develop points of inflexion. Transition to an unsteady flow involves the gradual growth of small disturbances and therefore it is quite possible to have unstable flows without observing transition because the pipe is not long enough for the disturbances to attain a measurable amplitude. For downflow heating the flow instability is associated with separation at the wall. Transition to an unsteady flow is sudden and therefore transition occurs shortly after an unstable flow occurs. It is suggested that a change from a steady symmetrical to a steady unsymmetrical flow occurs in downflow when the profile develops points of inflexion.

A theoretical analysis is presented for predicting the size of drops formed from a laminar cylindrical jet when one Newtonian liquid is injected through a nozzle into a second immiscible Newtonian liquid. The analysis couples stability theory with the requirement that the disturbances travel at the same velocity as the jet interface. Comparison of the theory with experimental data for thirteen mutually saturated liquid-liquid systems covering a wide range of physical properties shows a mean error of 11.7% in prediction of the specific surface.It is generally agreed that the size of drops formed from laminar cylindrical jets is controlled by the amplification of disturbances which result from surface tension instability. Tyler (15) was the first investigator to apply Rayleigh's instability theory to the prediction of the drop size. He reasoned that if waves of length, A, are formed on a cylindrical jet, the volume of the resulting drop should be equal to the volume of a cylinder having the radius, a, of the jet and length A. The drop volume VF is then given by where the wave length of a wave is related to the dimensionless wave number ka by the equation

The injection of one liquid into another is important in many industrial operations. At low injection velocities drops are formed directly at the nozzle and their size is controlled by the forces acting on the forming drop (3). At higher injection velocities a jet of liquid issues from the nozzle and then breaks into droplets in a regular pattern. This breakup of a cylinder of liquid has interested many scientists.In 1873 Plateau (6) showed that a cylinder of liquid subject to surface forces is unstable if its length exceeds its circumference, because it can be divided into two spheres of equal volume with an accompanying decrease in surface area. This analysis indicated that surface forces are the cause of jet breakup and that the waves visible on the jet surface should have a wavelength equal to the circumference of the jet.

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