## Modelling Pinchoff and Reconnection in a Hele-Shaw Cell I: The Models and their Calibration (2000)

Citations: | 10 - 1 self |

### BibTeX

@MISC{Lee00modellingpinchoff,

author = {Hyeong-gi Lee and J. S. Lowengrub and J. Goodman},

title = {Modelling Pinchoff and Reconnection in a Hele-Shaw Cell I: The Models and their Calibration},

year = {2000}

}

### OpenURL

### Abstract

This is the first paper in a two-part series in which we analyze two model systems to study pinchoff and reconnection in binary fluid flow in a Hele-Shaw cell. The systems stem from a simplification of a general system of equations governing the motion of a binary fluid (NSCH model [69]) to flow in a Hele-Shaw cell. The system takes into account the chemical diffusivity between different components of a fluid mixture and the reactive stresses induced by inhomogeneity. In one of the systems we consider (HSCH), the binary fluid may be compressible due to diffusion. In the other system (BHSCH), a Boussinesq approximation is used and the fluid is incompressible. In this paper, we motivate, present and calibrate the HSCH/BHSCH equations so as to yield the classical sharp interface model as a limiting case. We then analyze their equilibria, one dimensional evolution and linear stability. In the second paper (Part II [66]), we analyze the behavior of the models in the fully nonline...