Biological Fluid Mechanics & Active Suspensions - Elective (PHY 447.5/ BIO 447.5)

Venue: Chern Lecture Hall

Class Timings: Thursdays from 2:00 PM - 3:30 PM

First Meeting: 09 January 2025

Course Syllabus: 

The course will be concerned about the low Reynolds number hydrodynamics, swimming of microorganisms, active matter, and the mechanics of swimming (and flying) at high Reynolds number.

• The governing equations: Hydrodynamics at low Reynolds numbers, integral representation, and solution strategies
• Particles in flows: Sedimentation, pair interactions, slender bodies, Brownian motion
• Kinetic theory: Fokker-Planck description, Stress in a suspension of particles, Doi theory for rod suspensions
• Active matter: Swimming of microorganisms, suspension theory of active particles, generic instabilities, closures
• Ideal flows: 2D potential flows, governing equations, point vortices, vortex sheets
• Swimming: Elongated body theory of Lighthill, vortex shedding, lift generation, flow separation, added mass effects

Textbooks:

• Élisabeth Guazzelli and Jeffrey F. Morris, A Physical Introduction to Suspension Dynamics (Cambridge Texts in Applied Mathematics)
• Michael Graham, Microhydrodynamics, Brownian Motion, and Complex Fluids (Cambridge Texts in Applied Mathematics)
• M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Oxford Science Publications)
• L. Gary Leal, Advanced Transport Phenomena (Cambridge University Press)
• D. J. Acheson, Elementary Fluid Dynamics (Oxford)
• S. Childress, An Introduction to Theoretical Fluid Mechanics (Courant)

Course Evaluation: This is a reading course. Half of the course will be presented by the instructor. The rest half of the course will be a discussion on related material and reading from books and papers. Final evaluation is based on class participation and reading. 

Course Outcome:

• Develop a foundation of micro hydrodynamics and ideal flows
• Explain how organisms swim across various scales
  
• Write down coarse-grained models for both passive and active particles, perform stability analysis, and understand implications for experimental measurements
  
• Understand the basic features of some of the topics in soft matter: liquid crystals, polymers, and complex fluids

Prerequisite: Graduate-level mathematical methods is required. Some background in fluid dynamics is necessary. Introductory statistical mechanics will be helpful but not required.