Microhydrodynamics & fluctuations 1100-MHF
1. Introduction. Microscale flows in soft matter, biophysics, and technology.
2. Stokes flows
a) properties of Stokes equations (properties, general theorems, Lorentz reciprocal theorem)
b) Green's functions and fundamental solutions,
c) integral representations of Stokes flows,
d) Friction and mobility – application to spherical particles
e) Multipole expansion of Stokes equations
f) Faxén laws
g) Hydrodynamic interactions
h) Unsteady Stokes flows
i) Swimming in microscale
3. Diffusion
a) Fluctuation-dissipation theorem
b) Self-diffusion vs. collective diffusion
c) Short- and long-time diffusion coefficients
d) Influence of hydrodynamic interactions
e) Effective viscosity (Einstein formula)
4. Particle transport in external fields. Phoretic flows (electrophoresis, diffusiophoresis and others)
Main fields of studies for MISMaP
Prerequisites (description)
Course coordinators
Learning outcomes
1. Knowledge
After completing the course, the student:
– knows and understands the fundamental laws and concepts of microhydrodynamics in the low-Reynolds-number regime, including the properties and physical consequences of the Stokes equations,
– knows and understands methods for describing Stokes flows, including Green’s functions, integral representations, multipole expansions, and Faxén laws,
– knows and understands the physical origin of hydrodynamic interactions, as well as the concepts of friction and mobility in colloidal suspensions,
– knows and understands the connection between dissipation and fluctuations expressed by the fluctuation–dissipation theorem, and the role of hydrodynamic interactions in diffusion,
– knows and understands mechanisms of particle transport in external fields and the physics of phoretic flows (e.g. electrophoresis, diffusiophoresis).
2. Skills
After completing the course, the student:
– is able to formulate and analyse the Stokes equations for simple physical systems and apply appropriate boundary conditions,
– is able to use Green’s functions, Faxén laws, and multipole expansions to solve microhydrodynamics problems,
– is able to calculate friction coefficients, mobilities, and single-particle and collective diffusion coefficients,
– is able to account for hydrodynamic interactions in the description of Brownian motion and assess their impact on dynamical properties of suspensions,
– is able to interpret theoretical results in the context of soft matter, biological systems, and microfluidic applications.
3. Social competences
After completing the course, the student:
– is ready to independently study advanced research literature in microhydrodynamics and colloidal dynamics,
– is ready to critically assess theoretical models and understand the limitations of their applicability,
– is ready to clearly communicate physical reasoning, calculations, and conclusions.
Assessment criteria
Hand-in exercises and final written exam.
Bibliography
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 in the course website & discussed in classes
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: