Biomedical Engineering Reference
In-Depth Information
14
Spatial Pattern Formation of Motile
Microorganisms: From Gravitactic
Bioconvection to Protozoan Culture
Dynamics
Tri Nguyen-Quang, Frederic Guichard
Department of Biology, McGill University, Montreal, Canada
The Hung Nguyen
Department of Mechanical Engineering, Polytechnic, University of
Montreal, Montreal, Canada
CONTENTS
14.1 Description and Literature Review of Bioconvection ....................... 536
14.1.1 Overview ............................................................ 536
14.1.2 Review of Literature ................................................ 538
14.2 Onset and Evolution of Gravitactic Bioconvection: Linear Stability
Analysis and Numerical Simulation ........................................ 541
14.2.1 Mathematical Formulation of Gravitactic Bioconvection
in a Porous Medium ................................................ 541
14.2.1.1 Description and Formulation of the Problem ............. 541
14.2.1.2 Initial and Boundary Conditions .......................... 543
14.2.2 Diffusion State ...................................................... 543
14.2.2.1 Nondimensional Equations ................................ 544
14.2.2.2 Linearized Equations ...................................... 545
14.2.3 Numerical Results ................................................... 546
14.2.3.1 Linear Stability Analysis .................................. 546
14.2.3.2 Evolution of Bioconvection ................................ 548
14.2.3.2.1 Critical Threshold and Subcritical Regime..... 548
14.2.3.2.2 Supercritical State .............................. 549
14.3 Experimental Study of the Pattern Formation in a Suspension
of Gravitactic Microorganisms ............................................. 551
14.3.1 Introduction ......................................................... 551
14.3.2 Hele-Shaw Apparatus and Darcy's Law ............................ 553
14.3.3 Geometrical and Physicobiological Parameters ..................... 553
535
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