Diffusion Limited Aggregation and Saffman-Taylor Instability in Non-Newtonian Hele-Shaw Flow
Supported by NSF Grant No. DMS-1211713
Two-phase flow in quasi 2D
geometry is relevant to a number of applications, in particular related
to the flow in porous media. This relevance serves as
one important motivation for considering fluid instabillities in the
so-called Hele-Shaw geometry (flow between two glass plates). The
participating students have carried out experimental, theoretical, and
computational study of flow stability in such geometry, focusing in
particular on the setup where a less viscous fluid is injected into a
more viscous one, in a setup known to lead to instability carrying the
name of Saffman-Taylor. The aim of this project has been to study
the instability when the more viscous fluid is non-Newtonian, with
viscosity that depends on shear rate. To
characterize the properties of the emerging patterns, the students have
used several methods to calculate the fractal dimension based on the
data collected from experimental trials and extensive simulations of
diffusion limited aggregation type. Both experimental and
computational results suggest that the fractal dimensions between
Newtonian and non-Newtonian setups differ. This results, if
confirmed, will be of relevance to further work in this field.
Figure 1: Experimental realizations of Saffman-Taylor instability: Newtonian (top/left) and non-Newtonian (bottom/right)
Figure 2: Diffusion limited aggregation method for
simulating Saffman-Taylor instability: Newtonian (top/left) and
non-Newtonian (bottom/right)
