Breakup and Coalescence in Complex Flows

There have been several attempts at models incorporating breakup and coalescence. Two concepts underlie many of these models binary breakup and a flow subdivision into weak and strong flows. These ideas were first used by Manas-Zloczower, Nir, and Tadmor (1982, 1984) in modeling the dispersion of carbon black in an elastomer in a Banbury internal mixer. A similar approach was taken by Janssen and Meijer (1995) to model blending of two polymers in an extruder. In this case the extruder was divided into two types of zones, strong and weak. The strong zones correspond to regions 

The basic procedure of the VILM model is to send an initial distribution of drops through a specified number of strong and weak zones. With each pass through the strong and weak zones, the evolution of the drop distribution is determined based on the fundamentals of breakup and coalescence. 

Size distributions from a typical simulation produced by the VILM model. After six cycles a steady size is reached. Smaller sizes are obtained after live cycles as compared to the Anal distribution. The conditions for the simulation are = fia = 100 Pa s, f = 0.2, and t = 5 x 10 3 N/m. 

Average steady-state size of the dispersed phase at different viscosity ratios. The solid and dashed lines represent simulations in which /xj and jUc are held constant. Other process parameters are the same as used for Fig. 28 (except t = 0.05). It is clear that the magnitudes of both viscosities must be considered rather than just the viscosity ratio. The lowest viscosity in each case is 1 Pa-s and the highest 1000 Pa - s. The curves are equally spaced on a logarithmic scale for viscosity. 

Hence it is the values of each viscosity, dispersed and continuous, and not just the viscosity ratio that is important in determining the average size. The average size increases with a decrease in either continuous or dispersed phase viscosity for fixed operating conditions. 

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