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

GAS BUBBLE FORMATION 331 constant, the linear flow rate, V, will be reduced to one-fourth. There- fore, the Reynolds number for the larger jet will be only one-half of the smaller jet and this might bring the jet to the laminar flow region to avoid turbulent bubble entrainment. The above calculation assumes no change in the fluid viscosity as the jet nozzle is enlarged. This will be true only with a Newtonian fluid, the viscosity of which is independent of the rate of shear. Many cos- metic preparations are non-Newtonian and particularly emulsion prod- ucts are generally pseudoplastic or thixotropic, i.e., shear-thinning. Shear-thinning means that the viscosity decreases with increasing rate of shear. Because of the high linear velocity, the shear stress on the fluid while it flows through the nozzle is much greater in the smaller nozzle than in the larger nozzle. Therefore, if the fluid is shear-thinning, the viscosity of the fluid in the smaller jet may be much smaller than the viscosity of the same fluid flowing through a larger nozzle. Nat- ura]ly, this will make the Reynolds number even greater in the smaller jet and increase the chance of aeration when the filling material is thixotropic. For these reasons, filling nozzles with very small discharg- ing holes should be avoided. In addition to the bubble problem, dis- charging of a thixotropic emulsion through very small openings can sometimes cause a permanent viscosity breakdown. At times, the turbulent bubble entrainment problem can be solved by varying the filling temperature. Many cosmetic creams are filled at an elevated temperature for practical or aesthetic reasons. Since the viscosity of an emulsion is usually low at a high temperature, reduction of filling temperature may increase the fluid viscosity and hence reduce the Reynolds number at which the product is filled. The mechanism of bubble formation by jet discussed above involves turbulent entrainment. However, depending on the physical proper- ties of the fluid, the discharging rate, and the geometry of the nozzle, air can be entrained even when the jet is perfectly smooth and in laminar flow (4). The author investigated the bubble entrainment by such laminar jets using high-speed photography and, as illustrated in Fig. 6, this is due to the formation of a very thin film of gas which breaks away to form air bubbles in the product. Figure 7 is a photograph taken by the author showing formation and breakup of such a cylindrical air film. This type of bubble entrainment by a laminar jet is quite common in the filling of viscous cosmetic preparations. The author has ob-