Non-Newtonian drops

Keywords Impact, Wetting, Filtration, Non-Newtonian Drop, Power-Law Model... 

The order of contents in this chapter is as follows In Section 2 the governing equations and numerical methodology are given. Validation of the obtained results for Newtonian fluids in comparison with experimental observations presented by Lorenceau et al. [1] is provided in Section 3.1. A general description of the observations for non-Newtonian droplets captured by horizontal fiber is presented in Section 3.2, and the behavior of non-Newtonian drops affecting thin fibers is explained. Finally, a summary of the results and conclusions is provided. 

Keywords Bag breakup Breakup mode Breakup time Catastrophic breakup Fragments Fragment size distribution Initiation time Multimode breakup Newtonian drops Non-Newtonian drops Ohnesorge number (Oh) Secondary atomization Secondary breakup Sheet-thinning breakup Total breakup time Vibrational breakup Weber number (We)... 

It also remains unclear as to which dimensionless groups play dominant roles in the purely viscous and viscoelastic cases of non-Newtonian drop breakup. As such, dependence of transition We on other nondimensional parameters is unavailable. 

The initial and total breakup times also need to be determined, as well as fragment size distribution information. Unanswered questions include Does Simmons scaling rule (MMD/D32 1.2) hold for non-Newtonian drop secondary breakup and Will non-Newtonian drop secondary breakup produce a root-normal fragment size distribution ... 

The few studies focused on secondary breakup of non-Newtonian drops are reviewed below. 

The sheet-thinning mechanism observed for non-Newtonian drops resembles that observed for Newtonian liquids in some aspects. For instance, it is found at... 

Non-Newtonian liquids also exhibit a transitional multimode regime between bag and sheet-thinning breakup. It is important to note that only bag/plume-type breakup has been observed. Other breakup structures discussed in the Newtonian section have not been observed for non-Newtonian drops. It is unclear if this is due to a lack of available data or some rheological difference. 

In the multimode case, non-Newtonian drops form a much more pronounced stamen that has a much longer lifetime. This stamen eventually forms many large fragments when it finally breaks up. In the sheet-thinning case, non-Newtonian breakup proceeds through two steps - the thinning of the sheet followed by the drop core forming a bag that experiences multimode breakup. 

The microrheology was developed for Newtonian systems, whereas molten polymers are viscoelastic. Thus, in later systems the droplets shape is determined not only by viscosity, but by the elasticity as well. The characteristics of drop deformation and breakup in viscoelastic systems are different from those in Newtonian ones. The initial rate of non-Newtonian drop deformation is higher than for Newtonian, but it takes longer to break — elasticity has a stabilizing effect [Utracki and Shi, 1992]. 

For an axisymmetric creeping flow of a single non-Newtonian drop suspended in another non-Newtonian fluid in the entrance region of a cylindrical tube, as schematically shown in Figure 11.34, let us assume that a spherical drop is placed in the upstream end of the reservoir section and this drop moves along the centerline of the tube. Using... 

We have presented the results of numerical computation via FEM, demonstrating that large deformations of a single non-Newtonian drop suspended in another non-Newtonian liquid can be predicted in a complex flow field, namely, the entrance... 

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