Steady laminar flow of liquid–liquid jets at high Reynolds numbers*

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Abstract
The axisymmetric steady-state laminar flow of a Newtonian liquid jet injected vertically into another immiscible Newtonian liquid is investigated for various Reynolds numbers. The steady-state solution was calculated by solving the axisymmetric transient equations of motion and continuity using a numerical scheme based on the volume of fluid (VOF) method combined with the new continuum surface force (CSF) algorithm. The analysis takes into account pressure, viscous, inertial, gravitational, and surface tension forces. Comparison with previous experimental measurements, performed on a xylene/water system, under conditions where all of these forces are important, shows good agreement over the entire range of conditions studied. Comparisons of the present numerical method with the numerical results of previous boundary-layer methods help establish their range of validity.