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Modeling Wormlike Micellar Solutions
註釋Wormlike micellar solutions are composed of long flexible structures that result from self-assembly processes of surfactant molecules. At high enough concentration, these wormlike micelles can entangle and give viscoelastic properties to the solution just like typical polymers. Micellar solutions, in contrast to polymeric solutions, have two different relaxation mechanisms. One is the reptation of the micelles out of their entanglements and the second mechanism comes from their ability to break and reform continuously. Applications of wormlike micellar solutions are found in a wide range of industries and hence the importance of understanding and predict their behavior under different geometries and deformation conditions. Here we construct and analyze mathematical models of wormlike micellar solutions. The motivation for this work derives not only from the industrial need to predict the behavior of such solutions, but also from the challenges arising in the modeling of wormlike micellar solutions in even simple experimental systems. The main goal of this dissertation is the formulation of a new scission/reforming model of wormlike micellar solutions. This new model is an interacting species network model that incorporates the scission and reforming processes of wormlike micellar systems and thus can be directly linked to their physical behaviors. In the model, the micelles are modeled as elastic segments consisting of Hookean springs connected to form an elastic network. The breaking and reforming dynamics were introduced as a simplified version of the reaction kinetics proposed by Cates [Macromolecules, 1987].