Research Summary
I am working on a coupled chemotaxis-fluid model aimed to describe swimming bacteria, which are able exert bio-convective flow patterns on length scales much larger than the bacteria size.
More info.
Moreover, I investigate the delay of blow-up in the Keller-Segel-Fluid system
More info.
Chemotaxis-fluid model
We consider a coupled chemotaxis-fluid model aimed to describe swimming bacteria, which are able exert bio-convective flow patterns on length scales much larger than the bacteria size.
Experimental set-up:
Swimming bacteria are suspended in a drop of water confined within two (vertical and invisible) glass plates 1 mm apart. The bacteria suspension, initially almost homogeneously distributed, evolves as some bacteria swim upwards the oxygen gradient, while other bacteria run out of oxygen and remain immobile. The oxygen itself diffuses into the water through the water surface.
(Click on the picture to start the video!)
Since the bacteria are a bit denser than water, instabilities develop at the high concentration layer close to the water surface. Bacteria-rich plumes form and start to move sideways along the curved surface. Due to these large scale fluid motions formerly inactive bacteria are reoxygenated and participate in the established large scale convection pattern.
Videos courtesy of Goldstein Lab, who also performed the experiments. See their PNAS paper.
In this paper, they suggested a PDE model for the experiment just described. I am working on that model.
Keller-Segel-fluid model
We study a system consisting of the elliptic-parabolic Keller-Segel equations coupled to Stokes equations by transport and gravitational forcing. We show global-in-time existence of solutions for small initial mass in 2D. In 3D we establish global existence assuming that the initial $L^{3/2}$-norm is small. Moreover, we give numerical evidence that for this extension of the Keller-Segel system in 2D, solutions exist with mass above $8\pi$, which is the critical mass for the system without fluid.
