mixed Emulsions
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One of the simulations Renardy completed on the Origin2000 was a project for the Polymer Rheology Group at Cambridge University. The rheology group studies the changes in form and flow of polymers. Malcolm Mackley, director of the rheology group, and Sirilak Wannaborworn, a PhD student, performed experiments with an emulsion of Polydimethysiloxane (PDMS) dispersed in Polyisobutene (PIB), two polymers common in many industries. Mackley expressed his enthusiasm in finding a connection between the rheology group and Renardy's projects "I first became aware of Yuriko's work when I visited a research laboratory in Eindhoven, Holland. The professor at Eindhoven showed me a beautiful video sequence of droplet deformation that Yuriko had created and I immediately realized that her numerical work linked with our experimental studies."

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left of Cambridge Cambridge Shearing System
Diagram of the Cambridge
Shearing System. Enlarge image

The rheology group used a micro-optic apparatus called the Cambridge Shearing System to shear the PDMS and PIB emulsion drops. During each run, an emulsion drop was suspended between two horizontal, parallel plates that move back and forth. The scientists performed both simple shear and oscillatory shear measurements on the drop. During the simple shears, the drop was sandwiched between two plates that slide horizontally. Renardy likens the movement to an "infinitely large knife putting mayo on infinitely long bread." The oscillatory shears mimicked the movement of the knife being drawn back and forth across the bread. The scientists sheared the drop by oscillating the plate to the right, then to the left, reversing the direction with a given period, such as every three seconds.

The rheology group then provided Renardy with the experimental data for both types of shears. Through direct numerical simulations, the scientists hoped to obtain corroboration that the empirical measurements were correct. It may sound strange that scientists would seek theoretical corroboration to confirm the accuracy of empirical data. However, experimentalists often worry that the forces they are observing may not be due to the theoretical flow they have in mind. Therefore it is helpful to have their data checked against numerical simulations detailing the proposed theoretical flow. Corroboration gives them some confidence that their data is correct and not due to other forces that they have not considered.


Renardy completed the numerical simulations of drop breakup under oscillatory shear and got quantitative agreement. The good data match means that scientists can use the numerical simulations to accurately predict drop size distribution in simple problems. In large-scale industrial mixing, the flow pattern is much more complicated than the precise calculations performed in the lab simply because there are more drops and more forces working on them. However, the answers gleaned from a model problem for drop size distributions in the lab will serve as a useful "rule of thumb" for drop size distribution in the emulsion industry and eventually will improve the objects we use every day.


This research is supported by the National Science Foundation Division of Chemical and Transport Systems, the NSF Division of Mathematical Sciences, the NSF Division of International Programs, the American Chemical Society Petroleum Research Fund, and Centre National de la Recherche Scientifique.


 
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