The Effects of Motile Bacteria on Viscous Fingering

Abstract:

Viscous fingering is a hydrodynamic instability that occurs when a less viscous fluid displaces a more viscous one. Instead of progressing as a uniform front, the displacing fluid forms fingers that vary in size and shape to form complex patterns. The interface created from these patterns affects mixing between the two fluids, and therefore understanding how these patterns evolve in time is essential in applications such as enhanced oil recovery, bioremediation, and microfluidics.

Although bacteria can be found virtually everywhere viscous fingering occurs, there are no studies on the effects of their presence on the displacement dynamics. Here, we seek to begin filling this knowledge gap by using as invading fluid an active suspension of fluorescent motile E. coli, and observing how bacteria motility affects the interface and mixing zone between the two fluids. We start by characterizing how viscous environments affect the rheology of these dense suspensions capable of collective swimming (and therefore effective viscosity reductions) using a Couette rheometer. Remarkably, we find that for the entire range of solvent viscosities tested (1-17 mPa·s) we recover superfluidic regimes, in which the effective suspension viscosity is reduced to almost zero. We use these experimental results to formulate a constitutive model for the rheology of bacteria superfluids under flow as a function of the bacteria concentration and the solvent viscosity.

To visualize the motile bacteria both individually and collectively under viscous fingering conditions, we design and fabricate a mesofluidic Hele-Shaw cell that is large enough to accommodate viscous fingering instabilities and small enough to be used with fluorescent microscopy. Surprisingly, we observe a textured interface between the two fluids, in addition to the larger-scale viscous fingering pattern. This interface consists of four distinct regions: monodisperse, filamentous, “rafting,” and diffuse. These unexpected observations are a first step towards understanding how the interplay between active suspensions of motile bacteria and fluid-mechanical instabilities, such as viscous fingering, affects overall mixing under these complex flow conditions which are found in both natural and engineered environments.