GAS BUBBLE FORMATION 333 served this type of entrainment from a perfectly smooth, viscous jet at a Reynolds number as low as 10. Furthermore, a study on such laminar jets indicated that bubble entrainment could occur only when the linear velocity of the jet exceeded a critical value termed "minimum entrain- ment velocity." By keeping the jet velocity below this value, laminar jet entrainment by the film breakup mechanism can be eliminated. The minimum entrainment velocity is a [unction of the jet diameter as well as the physical properties of the jetting fluid. For Newtonian jets having a uniform velocity profile, the following correlation was found by the author (5): We = 10 Re ø'74 or L • J where We = Weber number Re = Reynolds number D = jet diameter at the point where jet meets the receiving fluid Ve = minimmn entrainment velocity p = density of the liquid 3' = surface tension of the liquid • = viscosity of the liquid By solving the equation for minimum entrainment velocity, the fol- lowing equation is obtained: 6.22 •yo.794 •)0.206 •00.206 •0.587 From this equation, it can be seen that a fluid with low surface tension and high viscosity will have a low minimum entrainment velo- city and will be likely to trap air by this mechanism. A solution to this problem is then to use a nozzle and filling rate such that the linear jet velocity is always below the minimum entrainment velocity. In some instances, a reduction of jet velocity may not be possible or desirable and it may be necessary to solve the problem by redesigning the filling nozzle. Ideally, the filling nozzle should be submerged into the receiving fluid at all times to avoid air entrainment however, this is not always possible in modern filling machines. Some filling nozzles

334 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS are designed so that the jets do not hit the receiving fluid vertically, but rather they are to flow along the wall of the bottle being filled (Fig. 8). Among those illustrated, (B) and (C) are usually the better types from the aeration viewpoint. The type (D) with multiple pinhole orifices can sometimes introduce more air than a vertical nozzle because of the high jetting velocity. (A) (B) (C) (D} Figure 8. Various types of filling nozzles (A) Vertical nozzle (B) J-shaped nozzle (C) Double-orifice nozzle (D) Pinhole nozzle Incorporation of Powdered Material In cosmetic processing, as in the preparation of a liquid eyeliner or fiuid make-up, it is often necessary to add powdered materials such as pigments or zinc stearate into a liquid. During such addition, the powders can carry into the liquid bulk an appreciable amount of air which may remain in the product. This is a very common problem but not always easy to solve. Often a slow and uniform addition or a sprinkling of the powders rather dumping them into the batch will ease the problem. If the batch under- goes viscosity changes during the manufacturing process, the powdered material should be added when the batch is at its lowest viscosity (e.g., while the batch is hot) so that any entrained air bubbles can be freed.