Kim, Minsu2014-12-192014-12-192014-09https://hdl.handle.net/11299/168244University of Minnesota Ph.D. dissertation. September 2014. Major: Mathematics. Advisor: Yoichiro Mori. 1 computer file (PDF); vii, 63 pages.In this thesis, a model of polymer gels on thermal effects is developed and analyzed, and numerical simulations for a one-dimensional geometry is performed. Gels are useful materials in many manufacturing as well as biomedicine, by use of which a variety of apparatus such as drug delivery devices are designed. It is important in physics to observe how gels change under different temperature, and in particular, we examine how gels respond to the gradient of temperature. Even though temperature is a key factor to be considered, no physical theory with thermal gradients has been presented. That becomes a motivation for this work, and we construct a thermodynamic theory of gels and apply it to investigate several phenomena in the one-dimensional geometry, such as the evolution of the interface between the gel and the environmental fluid.enMathematicsThesis or Dissertation