Filaments breakup

Although the dominant mixing mechanism of an immiscible liquid polymeric system appears to be stretching the dispersed phase into filament and then form droplets by filament breakup, individual small droplet may also break up at Ca 3> Ca. A detailed review of this mechanism is given by Janssen (34). The deformation of a spherical liquid droplet in a homogeneous flow held of another liquid was studied in the classic work of G. I. Taylor (35), who showed that for simple shear flow, a case in which interfacial tension dominates, the drop would deform into a spheroid with its major axis at an angle of 45° to the how, whereas for the viscosity-dominated case, it would deform into a spheroid with its major axis approaching the direction of how (36). Taylor expressed the deformation D as follows... 

Viscoelasticity, Table 1 Evolution of the mid-filament diameter in a fluid filament undergoing capillary-driven breakup. Note Ac is the characteristic relaxation time of the sample, to is the filament breakup time, and ps is the Newtonian viscosity of the solvent... 

Emulsion microrheology predicts that in a Newtonian system a drop will break when the deformabUity exceeds D > /2, that is, when the reduced capillarity number 1experimental data for viscoelastic systems indicate that the drop elasticity has a stabilizing effect thus, that Ko- and the minimum drop diameter for drop break increase with drop elasticity [284-286]. When conditions are identical for Newtonian and viscoelastic drops, the latter fibrillate easier and upon cessation of flow the filament breakup and formation of satellite drops are retarded by elasticity [287]. 

Two main methods of Vi2-measurements are the so-called filament breakup, and the retraction of deformed drop. The advantages of the latter are (i) simplicity and rapidity of measurements, (ii) possibility of the interfacial tension coefficient measurements in both directions i i and2 -> i, and (iii) ability to study the time dependence of Vi2 [15]. 

The first analyses of draw resonance for an isothermal Newtonian fiuid were done independently by Kase and co-workers and Matovich and Pearson in the mid-1960s. The early work on draw resonance and filament breakup is summarized in Petrie and Denn, cited above. Subsequent work is reviewed in... 

Tjahjadi M, Ottino JM, Stone HA (1994) Estimating interfacial tension via relaxation of drop shapes and filament breakup. AIChE J 40 385-394... 

Fig. 23.25 Also,3/ 50,3,Nozzle and d5o,3/1000 of SE (O/W) plotted as a function of VKeg,Nozzle for INMIX and EXMIX nozzles with exit diameter of 0.5 mm for structure preservation comparison of SE, and corresponding secondary droplet evaluation for INMIX nozzle in the related GLR range. The images of the corresponding filament breakup using the EXMIX nozzle (d = 0.5 mm) at distinct We numbers are illustrated for a flow rate 50 ml/min...

The sheet stretching takes place at the high-shear zones, whereas the filaments breakup occurs at low-shear zones via Rayleigh instabilities. 

Fig. 16. Drop breakup in the journal bearing flow. The drop initially in the chaotic region of the flow deforms into a thin filament that breaks to produce a fine dispersion of droplets. The drop initially in the regular region of the flow (island) remains undeformed (Tjahjadi and Ottino, 1991).

Upon breakup, the filament breaks into a set of primary or mother drops whose sizes are, to a first approximation, proportional to R. The size of drops produced when the filament breaks can then be obtained from the distribution of R. Each mother drop produced upon breakup carries a distribution of satellites of diminishing size for example, each mother drop of radius r has associated with it one large satellite of radius r, two smaller satellites of radius i 2 four satellites of radius r(3), and so on. For breakup at rest, the distribution of smaller drops is a unique function of the viscosity ratio. 

Fig. 21. Formation of satellite drops during the breakup of a filament at rest. A comparison between computations and experimental results is shown (Tjahjadi, Stone, and Ottino, 1992). Numbers refer to dimensionless times with ( = 0 corresponding to Fig (a).

Fig. 23. (a) Distribution of drop sizes for mother droplets and satellite droplets (solid lines) produced during the breakup of a filament (average size = 2 x 10 5 m) in a chaotic flow. The total distribution is also shown (dashed line). A log-normal distribution of stretching with a mean stretch of 10 4 was used, (b) The cumulative distribution of mother droplets and satellite droplets (solid line) approaches a log-normal distribution (dashed line). 

Breakup due to capillary instabilities dominates when the length of the filament is more than 15 times the initial radius of the drop. 

At higher temperatures, out of the typical FT regime, carbon could encapsulate the active metal, thereby blocking access to reactants. In extreme cases carbon filaments can also be formed that can result in the breakup of catalyst particles.42... 

Suddenly exposed to a high-velocity gas stream, a droplet is deformed into a saucer shape with a convex surface to the gas flow. The edges of the saucer shape are drawn out into thin sheets and then fine filaments are sheared from the outer part of the sheets, which subsequently disintegrate into smaller droplets and are swept rapidly downstream by the high-velocity gas. Unstable growth of short wavelength surface waves appears to be involved in the breakup process. 21° This is known as shear breakup (Fig. 3.10)J246f... 

Mixing of Immiscible Liquids, and Filament and Droplet Breakup... 

Next we examine the breakup mechanism of immiscible droplets in a continuous phase and that of liquid filaments (30). 

Figures 7.18(b) and 7.18(c) show the breakup into droplets of an extended filament of high density polyethylene in a polystyrene matrix. In Fig. 7.18(b) the distance between the extruder die and the quenching bath is short and the fiber freezes before breaking up, whereas in Fig. 7.18(c) the distance was increased, giving the filaments sufficient time for breakup. As the filament extends, its diameter is reduced until shear forces no longer dominate the surface tension cohesive forces and the filaments breaks into droplets, just like a stream of water from a faucet breaks up into droplets.

---