Fracturing instability in interfacial Hele-Shaw flows involving complex fluids

Fracturing instability has been observed in experiments on interfacial Hele-Shaw flows involving at least one complex fluid but there has not been much theoretical work on the origin of this instability. In this talk, we will discuss this problem by setting it up as a linear stability problem where a viscous Newtonian fluid (or air) displaces an Oldroyd-B (OB) fluid in a rectilinear Hele-Shaw cell. Results of such an analysis shows that compared to upper convected maxwell (UCM) case, a certain regularizing effect of the Newtonian contribution of the stress from OB is found, (i) at least one of the singular behaviors found in UCM case is removed, and (ii) less unstable than the UCM case. This is a joint work with Zhiying Hai.

Note: A similar version of this talk was scheduled in the program of last year for remote delivery in Indianapolis but could not be delivered because of internet problems.