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 9:15-11:00
Tutorials: Thursdays 12:15-14:00

Exam:

17 June, 09:00-13:00, room 1.03

Course materials

Lectures
[Lecture 1 slides]
[Lecture 9 slides]

Tutorials
[Tutorial 1 problems]
[Tutorial 2 problems]
[Tutorial 3 problems]
[Tutorial 4 problems]
[Tutorial 5 problems]
[Tutorial 6 problems]
[Tutorial 7 problems]
[Tutorial 8 problems]
[Tutorial 9 problems]
[Tutorial 10 problems]


[True vs. pseudo (scalars, vectors, tensors) – note]

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)

Rules of course completion:

Midterm exam (40%), Final exam (60%) (dates TBA) To pass the course >50% of total amount of attainable points

• To pass the course >50% of total amount of attainable points from:
  • Midterm exam – weight 40%
  • Final exam – weight 60%
• In retake session: written exam and possibility to replace your result of the midterm by an oral exam.

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
1. Masoud, H., & Stone, H. A. (2019). The reciprocal theorem in fluid dynamics and transport phenomena. Journal of Fluid Mechanics, 879, P1–P6. DOI: 10.1017/jfm.2019.553
2. E. J. Hinch. Small particles in a viscous fluid [pdf]
3. E. Klaseboer, D.Y.C. Chan. On the derivation of the Smoluchowski result of electrophoretic mobility, J. Coll. Interf. Sci. 568, 179 (2020). [pdf]
4. M. Smoluchowski A Contribution to the Theory of Electric Endosmosis and a Few Related Phenomena, Rozprawy wydziału matematyczno-przyrodniczego Akademji Umiejętności w Krakowie. T. XLIII. Serja A.; 110–127 (1903). (translated from Polish) [pdf]
5. J.T. Ault, S. Shin Physicochemical Hydrodynamics of Particle Diffusiophoresis Driven by Chemical Gradients, Annu. Rev. Fluid Mech 57, 227–55 (2025). [pdf]
6. M. Smoluchowski, Über die Wechselwirkung von Kugeln die sich in einer zähen Flüssigkeit bewegen, Bulletin de l'Académie des Sciences de Cracovie, Janivier 1911, 28. [pdf]
7. M. Smoluchowski, O oddziaływaniu wzajemnem kul poruszających się w ośrodku lepkim, Rozprawy Wydziału matematyczno-przyrodniczego Akademii Umiejętności w Krakowie, Ser. A , T. 51 (1911), s. 1-5. [pdf]
8. S. G. Brush, A History of Random Processes: I. Brownian Movement from Brown to Perrin, Archive for History of Exact Sciences, 6.8.1968, Vol. 5, No. 1 (6.8.1968), pp. 1-36 [pdf]
9. B. Cichocki, articles in Delta (in Polish): ["Ruchy Browna", 04/1983] ["Ruchy Browna (II)", 05/1983] ["Siła argumentów", 12/1997]
10. R. B. Jones, Rotational diffusion in dispersive media (2003). [pdf]
11. G. Nägele, The physics of colloidal soft matter (2004). [pdf]