Motion of bacteria in anisotropic fluid, from liquid crystal to visco-elastic liquid crystal
Restricted (Penn State Only)
- Author:
- Chi, Hai
- Graduate Program:
- Mathematics (PHD)
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 14, 2022
- Committee Members:
- Alberto Bressan, Major Field Member
Anna Mazzucato, Major Field Member
Igor Aronson, Outside Unit & Field Member
Xiantao Li, Major Field Member
Leonid Berlyand, Chair & Dissertation Advisor
Alexei Novikov, Professor in Charge/Director of Graduate Studies - Keywords:
- Liquid Crystal
Active suspensions
visco-elastic media
Beris-Edwards Model
existence of solution
homogenization - Abstract:
- Microscopic swimmers, both living (e.g bacteria) and synthetic (e.g. Janus particles), often dwell in anisotropic environments. The most representative realization of such an environment is liquid crystals and even visco-elastic liquid crystals like mucus. In this dissertation, I first present a numerical study of the well-validated Beris-Edwards model. In this work, my collaborators and I show that the microswimmer's shape and its surface anchoring strength affect the swimming direction and can lead to a reorientation transition. Furthermore, there exists a critical surface anchoring strength for non-spherical bacteria-like microswimmers, such that swimming occurs perpendicular in a sub-critical case and parallel in a super-critical case. Finally, we demonstrate that for large propulsion speeds, active microswimmers generate topological defects in the bulk of the liquid crystal. Next, I present an analytical study of the model for suspension in liquid crystal to obtain the existence of the steady motion of the swimmer. The local-in-time existence for the time-dependent model is established. Furthermore, my collaborators and I perform formal two-scale expansion to the model and derive a homogenized model similar to Darcy's Law, which could help us to build a simplified model for bacteria suspension in liquid crystals. The third part of this dissertation is a numerical study on how individual microswimmers (e.g., bacteria) interact in a mucus-like environment modeled by a visco-elastic liquid crystal. My collaborators and I have explained that an individual swimmer moves faster along the same track after the direction reversal, in faithful agreement with the experiment. This behavior is attributed to the formation of the transient tunnel due to the visco-elastic medium memory. We observed in the situation of two swimmers traveling along the same track that the aft swimmer has a higher velocity for two swimmers traveling along the same track and catches up with the leading swimmer. Multiple swimmers launched at different angles form a ``train'': after some transient time, the following swimmers repeat the path of the ``leader''. Overall, our numerical and analytical results can guide experimental works on control of bacteria transport in complex anisotropic environments and shed light on bacteria penetration in mucus and colonization of heterogeneous liquid environments.