(132e) Drop Breakage By Shear Tip Speed

Many products produced in the process industries involve emulsification where the drop size distribution affects the processing and the product properties, e.g. food, cosmetic, pharmaceutical, and health care products. For example, in a two-phase process, the mass transfer rate between the phases is proportional to the interfacial area. This interfacial area changes with the drop size distribution, which varies with the conditions inside the vessel and time. Therefore, an understanding of the mechanisms for drop break-up is key for any design process. For inviscid systems, there are two main mechanisms that are thought to break drops: break-up due to turbulent eddies, i.e. energy dissipation rate; and break-up due to the agitator shear rate.

Break-up due to turbulent eddies is generally based on the work of Kolmogorov (1949) and Hinze (1955) which utilises the concept of eddy turbulence to define a limiting drop size. It is usually assumed that drop break-up occurs due to the interactions of drops with the turbulent eddies of sufficient energy to break the drop. Therefore, for a given fluid system the effective equilibrium drop size (this is the drop size after a sensible processing time, when the drop size reduction with time is very small and almost unmeasurable) is dependent on the energy per unit mass and thus should scale-up with this value when using geometrically similar vessels.

Break-up due to the agitator shear rate is based on a balance between the external viscous stresses and the surface tension forces (Liao and Lucas, 2009). If the break-up is due to the agitator shear rate then the effective equilibrium drop size is related to the maximum shear rate. This would mean that lower power number agitators can produce smaller drops than higher power number agitators, as low power number agitators may have a higher shear rate, which has been seen experimentally by Zhou and Kresta (1998).

This paper presents the shear tip speed, KsND, and shows it how drop size data for a wide variety of agitators can be correlated against the shear tip speed, which is proportional to the maximum shear rate generated by the agitator. This paper continues with analysis of the drop sizes produced by a variety of turbines and modified turbine impellers showing better correlation with the shear tip speed.

Hinze, J. O. 1955. AIChE Journal 1, 289-295.

Kolmogorov, A.M. 1949. Doklady Akademii Nauk 66, 825-828.

Liao, Y. and Lucas, D. 2009. Chem. Eng. Sci. 64, 3389-3406.

Rodgers, T. L. and Cooke, M. 2012. Chem. Eng. Res. Des., 90, 323-327.

Zhou, G. and Kresta, S. M. 1998. Chem. Eng. Sci. 53, 2063-2079.