Patches of patches: Spatial fluctuations of elastic turbulence in
porous media
Sujit Datta,
Princeton
University, New Jersey, USA
Abstract
Polymer
solutions are often injected in porous media for applications such as oil
recovery and groundwater remediation. As the fluid navigates the tortuous pore
space, elastic stresses build up, causing the flow to become unstable at
sufficiently large flow rates—a phenomenon often known as “elastic turbulence”.
However, what physical factors determine the onset of this instability, and
what its spatial and temporal characteristics are, remain unknown. Here, we use
direct visualization in model porous media to address this gap in knowledge.
First, we show that the spacing between pores strongly influences the flow:
when the pore spacing is sufficiently small, the unstable flow in the different
pores exhibits a surprising bistability due to the
interplay between elongation and relaxation of polymers as they are advected
through the pore space [1]. Second, using full three-dimensional porous media,
we show that the onset of unstable flow in each pore is akin to a second-order
phase transition, arising due to the persistence of discrete patches of instability.
Thus, unstable flow is patchy across the different pores of the medium. Guided
by these findings, we directly link the energy dissipated by pore-scale
fluctuations to the flow resistance through the entire medium, enabling
prediction of the macroscopic transport behavior [2]. Together, these results
reveal the rich array of behaviors that can arise during the unstable flow of
polymer solutions through porous media, and provide a general framework by
which flow fluctuations can be predicted and controlled.
[1] C. A.
Browne, A. Shih, S. S. Datta, Journal of Fluid Mechanics, 890, A2 (2020).
[2] C. A.
Browne and S. S. Datta, arxiv:2011.06036 (2020).
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