Dispersion of Melts, Liquid Droplets, and Gas Bubbles

As described in the previous section, solid particles can be broken up if the applied shear stresses are sufficiently large. In contrast, however, liquid droplets cannot be dispersed under certain conditions, even in shear fields with very large shear stresses. The Weber number We is often used to characterize the dispersion of droplets (another notation often used instead 

In the opposite case, i. e., for a viscosity ratio of X 1, it is also not possible for the droplet to break up in a pure shear field f 1 ]. Low viscosity ratios like these occur, for instance, when incorporating low-viscosity additives such as plasticizers or when dispersing gases. Thus, just as there is an upper limit for the viscosity ratio, there is a lower limit below which it is not possible to break up droplets in a pure shear field [1,10]. 

If an extensional force is also applied in addition to the pure shear force (for types of flow, see Fig. 9.2), the critical value of the Weber number is considerably lower. It is possible to break up droplets in an extensional flow even when the viscosity ratios are very high. Thus, extensional flow is significantly more effective than pure shear flow when attempting to disperse droplets and break up high-viscosity gels or polymer particles. 

In extensional flow, droplets or high-viscosity particles are drawn out into filaments that ultimately break up into smaller droplets. For the droplets to break up, the load must be maintained for a certain period of time. It can also be beneficial to deform the droplet, allow it to relax briefly and then apply the load again. This enables elastic restoring forces in high-viscosity droplets to be overcome. 

A characteristic time can also be defined for a droplet which, like the Weber number, is obtained from the ratio of the external force to the restoring force. 

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