creator Zhao, Meng advisor Li, Shuwang In this paper, we study a moving interface problem in a Hele-Shaw cell, where two immiscible reactive fluids meet at the interface and initiate chemical reactions. A new gel-like phase is produced at the interface and may modify the elastic bending property there. We model the interface as an elastic membrane with a local curva- ture dependent bending rigidity. In the first part of this paper, we review the linear stability analysis on a curvature weakening model, and derive critical flux conditions such that a Hele-Shaw bubble can develop unstable fingering pattern and self-similar morphology. In the second part of this report, we develop a boundary integral nu- merical algorithm to perform nonlinear simulations. Preliminary numerical results show that in the nonlinear regime, there also exist stable self-similar solutions. Submitted by Liana Khananashvili (khananashvili@iit.edu) on 2014-05-13T17:01:31Z No. of bitstreams: 1 Thesis.pdf: 1790134 bytes, checksum: df36cef24b753b3c50956681d3993f77 (MD5) Made available in DSpace on 2014-05-13T17:01:31Z (GMT). No. of bitstreams: 1 Thesis.pdf: 1790134 bytes, checksum: df36cef24b753b3c50956681d3993f77 (MD5) Previous issue date: 2013-12 M.S. in Applied Mathematics, December 2013 2013 2013-12 http://hdl.handle.net/10560/3242 en Thesis born digital application/pdf In Copyright http://rightsstatements.org/page/InC/1.0/ Restricted Access MATH / Applied Mathematics Illinois Institute of Technology Affiliated department