AmericanChemicalSociety.com

Applications of drop formation are legion and range from inkjet printing to separations.  A particularly important application of drop formation in the petrochemical industries is the formation of emulsions, which are dispersions of drops of one fluid in a second fluid.  A common way of producing emulsions is to inject the drop fluid from a tube into a bath of a second fluid with which it is immiscible.  Previous researchers have used coflowing, electric fields, and surfactants to control the dynamics of drop formation and the sizes of the resulting drops.  In particular, previous studies by us and others have shown that drops can be formed by a number of mechanisms, including dripping, jetting, and tip streaming.  During the course of this research, we have focused our attention on purely hydrodynamic means of drop formation that uses neither electric fields nor surfactants.

In the computations as well as the experiments, the tube is immersed into an open container filled with the ambient fluid.  The tube has radius R, the container has cross sectional area d squared, the container is filled with the ambient fluid to a height H, and the tube is immersed into the ambient fluid from the top to a height L.  These dimensions are such that H>>R and H>>L.  Moreover, computations are used to determine values of R/H and L/H that are small enough so that a further increase in the value of H would have a negligible effect on the dynamics.

In the experiments, water and solutions of glycerol in water (45, 50, and 76 weight percent glycerol) have been employed as the inner or drop liquids, and 0.65, 1, 10, and 20 cSt Polydimethyl siloxane (PDMS or silicone oil) have been used as the outer liquid to achieve different values of the ratio of the viscosity of the ambient fluid to that of drop fluid, m.  At a given value of m, experiments are carried out by varying the dimensionless flow rate of the inner fluid, or the Weber number We (which is the ratio of inertial to interfacial tension force).  At each value of We, drops are continuously formed to determine whether a steady state is reached or a more complex response results.  At low values of We, the process of drop formation is periodic and drops form by the dripping mode, as also occurs in the oft studied situation when drops of the same liquid are formed in a passive ambient fluid like air.  After the formation of each primary drop, a much smaller satellite droplet is also formed.  This regime of drop formation is called simple period-1 dripping with satellites or P1S.  For certain values of the governing dimensionless groups, the formation of satellites may cease once a certain value of We is exceeded.   This regime of drop formation is called simple period-1 dripping without satellites or P1.  As We is further increased, however, a critical value of We is reached beyond which the dripping dynamics becomes complex.  In this regime of drop formation, as We is varied, the dynamics may exhibit period-2 dripping with satellites P2S, exhibit P1S response once again, revert back to P2S response, and possibly exhibit other period-n, where n=3, 4, …, responses.  For certain values of the dimensionless groups, these complex dripping phenomena may take place without the occurrence of satellite droplets.  It is noteworthy that when drops are formed in a passive ambient fluid like air, complex dripping always takes place without the occurrence of satellite droplets.  As Weber number continues to be increased, the dripping becomes chaotic.  At yet higher values of We, the dynamics finally transitions from dripping to jetting.  For each fluid pair, these responses are succinctly summarized by means of bifurcation diagrams that show either the limiting length L of drops, which is the distance measured from the tube outlet to the drop tip at the instant of drop pinch off, or the volume V of drops that detach from the tube as a function of Weber number We.

Aside from We and m, the dynamics of drop formation depends on the Ohnesorge number Oh (which is the ratio of viscous force to interfacial tension force), the ratio d of the density of the outer fluid to that of the inner fluid, and the Bond number G (which measures the relative importance of gravitational force to interfacial tension force).  Experiments have been carried out to determine the effect of all these dimensionless groups on the dynamics.  A quantity of engineering importance in drop formation studies is the volume V of primary drops that are formed.  While the dependence of V on the various dimensionless drops is quite complicated, it is noteworthy that when the Weber number is small, the drop volume V varies roughly inversely with the Bond number G.