|Institution:||Illinois Institute of Technology|
|Keywords:||M.S. in Applied Mathematics, December 2013|
|Full text PDF:||http://hdl.handle.net/10560/3242|
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.