Microhydrodynamics & Fluctuations 2025/2026

Sea urchin larva uses microscale hair-like beating cilia to push fluid near their bodies. The flows generated this way are beautiful and complex [Shrestha et al., U. Miami]

Jeffrey Everts & Maciej Lisicki

Lectures: Tuesdays
Tutorials: Thursdays

Rules of course completion: TBA

Course Outline

1. Introduction. Microscale flows in soft matter, biophysics, and technology.
2. Stokes flows
   1. Properties of Stokes equations (properties, general theorems, Lorentz reciprocal theorem)
   2. Green's functions and fundamental solutions
   3. Integral representations of Stokes flows
   4. Friction and mobility – application to spherical particles
   5. Multipole expansion of Stokes equations
   6. Faxén laws
   7. Hydrodynamic interactions
   8. Unsteady Stokes flows
   9. Swimming in microscale
3. Diffusion
   1. Fluctuation-dissipation theorem
   2. Self-diffusion vs. collective diffusion
   3. Short- and long-time diffusion coefficients
   4. Influence of hydrodynamic interactions
   5. Effective viscosity (Einstein formula)
4. Particle transport in external fields. Phoretic flows (electrophoresis, diffusiophoresis, and others)

Literature

• E. Guazzelli and J. Morris – A Physical Introduction to Suspension Dynamics
• S. Kim and S. J. Karrila – Microhydrodynamics: Principles and Selected Applications
• J. K. G. Dhont – An Introduction to the Dynamics of Colloids
• J. Happel and H. Brenner – Low Reynolds Number Hydrodynamics
• H. Ohshima – Theory of Colloid and Interfacial Electrokinetic Phenomena
• S. R. de Groot and P. Mazur – Non-equilibrium Thermodynamics
• Research articles referenced on the course website & discussed in classes