GAS BUBBLE FORMATION 329 (A) (B) (c) Figure 4. Air entrainment by jetting and pouring To explain the basic mechanism of air entrainment by jets, Fig. 5 illustrates the discharge of a fluid through a small nozzle into a ves- sel containing the same fluid. The jet in (A) is perfectly smooth and there is no air in the receiving fluid. The jet in (B) is discharged at a much higher rate and the jet surface is irregular and the surrounding air is trapped by the jet surface and carried into the bulk. The jet in (A) is evidently in a laminar flow and (B) is in a turbulent flow. DV• R e - • (A) (B) LAMINAR TURBULENT Figure 5. Laminar and turbulent jets

330 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS In fluid mechanics, transition from a laminar flow to turbulent flow is related to a dimensionless parameter, Reynolds number defined as follows: where Re = Reynolds number D = diameter of the jet V = linear velocity of lhe jet 0 = density of the fluid /• = viscosity of the fluid When the nozzle is perfectly smooth and sufficiently long the transi- tion from a laminar flow to turbulent flow normally occurs at a Reynolds number above 1000. However, if the nozzle is not smooth, straight, or too short, the jet may be in a turbulent flow at a lower Reynolds num- ber. The turbulent jets can often be the cause of bubble problems in cosmetic processing. For example, if a hot lipstick is tooured from a kettle into a mold through a valve with a short exit pipe, the product may become aerated. This is because, in flowing through the valve and elbow, the velocity distribution in the pipe becomes irregular causing uneven stream sur- face which traps the sun-ounding air as the liquid plunges into the mold. By lengthening the exit with a smooth pipe, it is possible to smooth the jet stream and reduce the chance of air entrapment by turbu- lence. The length o[ the tube required to smooth the flow of a jet is dependent on the jet velocity as well as the physical properties of the fluid. Generally, the lower the viscosity, the longer the pipe length should be to achieve a smooth laminar flow. A similar troublesome bubble entrainment problem can occur in the filling of cosmetic preparations using a straight circular nozzle. The modern filling machines generally operate at a very high speed and the discharged fluid can easily be in turbulent flow depending on the nozzle design and fluid properties. Often the lengthening of the filling nozzle alone will not solve the problem completely. Reduction in the filling rate is a possible solntion but it will affect the production rate. One possible way to minimize the turbulent en- trainment is to use a filling nozzle with a larger dimneter. For example, 1)y doubling the jet diameter, D, while keeping the volnmetric flow rate