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.

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.

D. Eng. 'thesis,' Polytechnical Inst., Bucharest, 3. Fuchs, V. N., Koll. Zeit., 52, 262 (1930). 4. Scriven, L. E., and Sternling C. V., Nature, 187, 186 Manuscript receloed December 26, 1967; revision received Aprdl 15, Romania ( 1968). h = film thickness, mm. Q = flow-rate, cc./sec. T R = film radius, mm. (1960). 0 = radial velocity, mm./sec. ~1 2 , U13, a23 = interfacial tensions (see Figure 7 ) = distance along the film radius 1b68; The stability theory is used to predict jet length from jet inception to disruption for injection of one Newtonian liquid into a second immiscible Newtonian liquid. Knowledge of the length is essential for predicting the size of drops formed from jets. At low velocities jet length is controlled by the amplification of symmetrical waves which travel at the interfacial velocity of the jet. At higher velocities an abrupt lengthening of the jet may occur as a result of drop merging, 4nd the jet length is then controlled by the growth rate of sinuous waves which are strongly velocity dependent. Jet disruption results from a geometrical limitation on the maximum amplitude of the sinuous waves. Predictions show good quantitative agreement with experimental data for thirteen mutually saturated systems over a wide range of variables and qualitative agreement with limited experimental data on the effects of initial disturbance level and mass transfer. -= K' ( N w e 5 + 3 N w e / N R e ) DN (2b) The data of both Haenlein ( 8 ) and Merrington and Richardson for viscous liquids show good agreement with Equation ( 2 b ) , with values of In ( a N / . & ) corresponding to those found from Equation ( 2 a ) for low viscosity jets.Several experimental investigations (12, 15, 24, 25, 30) of the length of liquid jets in immiscible liquid systems have been made, but agreement with Equation (1) is not necessarily good in the linear region even when the appropriate values for a given by Meister and Scheele (16) are employed.In both liquid-gas and liquid-liquid systems, the jet length-nozzle velocity curve displays a maximum. In liquid-gas systems, this maximum is generally very sharp and is followed immediately by jet disruption, which is characterized by the appearance of random waves, a broad drop size distribution and a sharp decrease in jet length. If

A new constitutive equation for concentrated polymer solutions and melts is presented that is based on the entanglement theory of Lodge. The strain rate dependence of the memory function is determined using a physical hypothesis of interacting spheres where the spheres represent spheres of influence of the network junctions. The resulting equation has one constant that can be estimated theoretically in addition to the natural relaxation spectrum. At high strain rates, a second empirical constant is introduced to account for the orientation of the spheres of influence. Predictions of the equation and the equations of Bogue, Bird-Carreau, and Tanner were compared to steady and transient shear stress and normal stress data obtained on a Weissenberg rheogoniometer. The new equation fits nonlinear transient data more satisfactorily than other equations of similar complexity.