A mathematical model of emulsion polymerization
- Gajewski, Herbert
- Zacharias, Klaus
2010 Mathematics Subject Classification
- 35F25 35Q80 80A30 82D60
- emulsion polymerization, nonlinear nonlocal first-order partial integro-differential equation
We consider a mathematical model of polymerization which in the language of chemistry is called emulsion polymerization. Roughly speaking, polymerization is the formation of huge molecules (-the molecules of the polymer-) from smaller ones (-the molecules of the monomer). In the case of emulsion polymerization this process takes place in an aqueous medium in the presence of appropriate auxiliary substances. As an example we mention that the well-known polymer polyvinyl chloride (PVC) can be produced in this way starting from the monomer vinyl chloride. There are different possibilities to operate a polymerization reactor. One distinguishes batch (or discontinuous) and continuous reactors. The batch reactor is one where all ingredients are charged at the beginning of the polymerization and the reaction proceeds over a certain interval of time. Continuous reactors run with a continuous inflow and outflow of material. Mixed types of reactor operating are possible, e.g. the semibatch mode where part of the ingredients are added during the polymerization process. A general assumption is that the content of the reaction vessel is well stirred so that local inhomogeneities can be neglected. The mathematical model presented here was proposed in the seventies by Min and Ray (, , ). It has been modified and extended in the research group of Dr. Tauer (,  , ) at the (former) Institute of Polymer Chemistry (Teltow-Seehof). At the (former) Karl Weierstrass Institute of Mathematics (Berlin) the model has been investigated from the mathematical and numerical point of view during several years (, , , ).
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