Dynamic breakup of liquid–liquid jets

The axisymmetric, dynamic breakup of a Newtonian liquid jet injected vertically into another immiscible Newtonian liquid at various Reynolds numbers is investigated here. The full transient from jet start‐up to breakup into drops was simulated numerically by solving the time‐dependent axisymmetric equations of motion and continuity using an algorithm based on the Volume of Fluid (VOF) method that was previously proven successful in simulations of steady‐state liquid jets (i.e., of the jet region close to the nozzle before breakup). The algorithm has been further refined here based on its performance on transient problems such as the solution of the free liquid–liquid capillary jet breakup problem. The comparison of the simulation results with previous experimental measurements of jet length under conditions where all forces, i.e., viscous, inertial, buoyancy, and surface tension, are important, can be judged satisfactory given the sensitive dependence of the results on details of the experimental setup th...

[1]  C. W. Hirt,et al.  SOLA-VOF: a solution algorithm for transient fluid flow with multiple free boundaries , 1980 .

[2]  B. J. Meister,et al.  Prediction of jet length in immiscible liquid systems , 1969 .

[3]  B. J. Meister,et al.  Generalized solution of the tomotika stability analysis for a cylindrical jet , 1967 .

[4]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[5]  A. Skelland,et al.  The effects of surface active agents on jet breakup in liquid‐liquid systems , 1989 .

[6]  C. W. Hirt.  Heuristic stability theory for finite-difference equations☆ , 1968 .

[7]  Anne E. Trefethen,et al.  Hydrodynamic Stability Without Eigenvalues , 1993, Science.

[8]  Teruo Takahashi,et al.  Stability of jets in liquid‐liquid systems , 1982 .

[9]  Howard Brenner,et al.  Interfacial transport processes and rheology , 1991 .

[10]  A. Bright.  Minimum drop volume in liquid jet breakup , 1985 .

[11]  R. H. Dettre,et al.  The wettability of low-energy liquid surfaces , 1966 .

[12]  B. J. Meister,et al.  Drop formation at low velocities in liquid‐liquid systems: Part I. Prediction of drop volume , 1968 .

[13]  William D. Harkins,et al.  THE DETERMINATION OF SURFACE TENSION (FREE SURFACE ENERGY), AND THE WEIGHT OF FALLING DROPS: THE SURFACE TENSION OF WATER AND BENZENE BY THE CAPILLARY HEIGHT METHOD. , 1919 .

[14]  J. Brackbill,et al.  A continuum method for modeling surface tension , 1992 .

[15]  R. Donnelly,et al.  Experiments on the capillary instability of a liquid jet , 1966, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[16]  N. Bohr.  Determination of the Surface-Tension of Water by the Method of Jet Vibration , 1909 .

[17]  T. Lundgren,et al.  Satellite formation in capillary jet breakup , 1990 .

[18]  C. C. Addison,et al.  602. The properties of freshly formed surfaces. Part XV. The application of the contracting liquid-jet technique to the measurement of tensions at liquid–liquid interfaces , 1950 .

[19]  B. J. Meister,et al.  Drop formation from cylindrical jets in immiscible liquid systems , 1969 .

[20]  Laminar jet contraction and velocity distribution in immiscible liquid-liquid systems , 1975 .

[21]  Samuel Walter Johnson Smith,et al.  Experiments with mercury jets , 1917 .

[22]  A. Hixson,et al.  Breakup of a Liquid in a Denser Liquid , 1957 .

[23]  Paul Concus,et al.  Static menisci in a vertical right circular cylinder , 1968, Journal of Fluid Mechanics.

[24]  P. Steen,et al.  Shear stabilization of the capillary breakup of a cylindrical interface , 1989 .

[25]  J. R. Richards,et al.  Steady laminar flow of liquid–liquid jets at high Reynolds numbers* , 1993 .

[26]  Joseph B. Keller,et al.  Spatial instability of a jet , 1973 .

[27]  D. B. Kothe,et al.  RIPPLE: A Computer Program for Incompressible Flows with Free Surfaces , 1991 .

[28]  S. Tomotika.  On the Instability of a Cylindrical Thread of a Viscous Liquid Surrounded by Another Viscous Fluid , 1935 .

[29]  L. Rayleigh.  On The Instability Of Jets , 1878 .

[30]  C. Sleicher,et al.  The instability of capillary jets , 1975, Journal of Fluid Mechanics.