# Formation and Breakup of an Immiscible Compound Jet with Density or Viscosity Stratification
## 5 Conclusions  
We have numerically investigated the effects of density and viscosity on the formation and breakup of a compound liquid jet in coflowing outer fluid in an axisymmetric cylindrical tube.  
Figure 11: Snapshots of compound liquid jets for (**a**) \(\mu_{23}\) = 0.18; (**b**) \(\mu_{23}\) = 1 and (**c**) \(\mu_{23}\) = 5. The rest of the parameters are \(\rho_{13}\) = 1, \(\rho_{23}\) = 1 and \(\mu_{13}\) = 1. Graphs (**d–f**) represents the average breakup length, drop diameter and drop formation time for variable intermediate-to-outer viscosity ratios.  
Figure 12: Percent of multi-core compound drops formed vs. intermediate-to-outer viscosity ratio. The horizontal and slant lines depicted in this plot correspond to 1-core and 2-core compound drops formation respectively.  
The study showed the influence of density and viscosity ratios, i.e., \(\rho_{13}\), \(\rho_{23}\), \(\mu_{13}\) and \(\mu_{23}\) on the dynamics of the compound jet. The simulations show that, according to the density and viscosity ratios, the compound jet can transition to jetting or dripping mode. For low values of \(\rho_{13}\) and \(\rho_{23}\), the inner and compound drops favor dripping mode and at higher values, they form in jetting and mixed dripping-jetting mode respectively. At higher values of \(\rho_{13}\) and \(\rho_{23}\), the inertia force increasingly dominates, which causes more instabilities in the system and hence, more multi-core drop formation occurs. By contrast, for variation in \(\mu_{13}\), no jet transition from dripping to jetting was observed. For low values of viscosity ratio \(\mu_{23}\), dripping is more favorable for inner and compound drops, but at higher values of \(\mu_{13}\), both the drops form in the jetting mode. Variations in viscous resistance are the main cause of such behavior. Increasing the values of \(\rho_{13}\) and \(\rho_{23}\) leads to significant variation of average drop diameter, whereas changes in \(\mu_{13}\) and \(\mu_{23}\) yielded less change in the diameter. This shows that compared to viscosity ratios, the system is more sensitive towards density ratios.  
This work provides overviews on the effect of density and viscosity ratios in a coflowing liquid-liquid-liquid system which has specific applications to industrial processes. However, some unresolved questions still exist. There is a need to analyze in detail the non-monotonic nature of the formation of multi-core drops (Figure 6) and the conditions for satellite drops formation during the breakup of a compound jet. The effect of nozzle geometry on the compound jet modes, drop size and formation time also merits further research.  
The supporting videos article are available at doi: [[http://www.mdpi.com/2076-3417/9/22/4817/s1](http://www.mdpi.com/2076-3417/9/22/4817/s1)]([http://www.mdpi.com/2076-3417/9/22/4817/s1](http://www.mdpi.com/2076-3417/9/22/4817/s1)).  
[PERSON], [PERSON] and [PERSON] designed the study. [PERSON] modified the Front Tracking Code and [PERSON] performed the simulations. [PERSON], [PERSON] and [PERSON] wrote the manuscript. All authors discussed the results and contributed to the final manuscript.  
This research received no external funding.  
[PERSON] is thankful to JICA (Japan International Cooperation Agency) for their support under the JICA-Friendship Scholarship Program 2016-2019. [PERSON] is thankful to the Phenikaa University Foundation for Science and Technology Development for their support. The front-tracking code was adapted from a program provided by [PERSON] and [PERSON]  
The authors declare no conflict of interest.