Overview
My MSc project at Imperial College London studied gyrotactic swimming microorganisms in a vertical pipe. Gravity and shear affect their swimming direction, while the cells also influence the flow through buoyancy. This coupling can produce nonuniform concentration profiles and bifurcations.
I worked under the supervision of Prof. Yongyun Hwang and Lloyd Fung.
Gyrotactic cell distributions in upward and downward pipe flow.
Numerical model
I developed an unsteady finite-volume solver in MATLAB for the coupled cell-conservation and momentum equations. The implementation used a semi-implicit first-order scheme for cell conservation and an implicit scheme for momentum.
The study considered fixed flow rate, prescribed pressure gradient, and time-periodic pressure forcing. Conservation and boundary conditions mattered when comparing behavior across different flow directions and initial conditions.
Coupled cell-conservation and momentum equations.
Bifurcation analysis
At fixed flow rate, the calculations reproduced a bifurcation at a Richardson number of 8 and showed a qualitative match near 25 with the reference results discussed in my thesis.
Centerline concentration under fixed-flow-rate conditions.
For prescribed pressure gradients, I examined how the initial flow rate affected the final concentration and velocity profiles. Some cases exhibited an interval of divergence before convergence, whose extent depended on the forcing and initial condition.
Oscillatory forcing
I also derived a linearized state-space system to study the response to sinusoidal pressure gradients and investigated how the parameters affected its frequency response.
Centerline-velocity frequency response to periodic pressure forcing.
Report and background
Background literature: Fung, L., Bearon, R. N., and Hwang, Y. (2020). Bifurcation and stability of downflowing gyrotactic micro-organism suspensions in a vertical pipe. Journal of Fluid Mechanics, 902, A26. DOI: 10.1017/jfm.2020.614.