Theory and Simulation of Soft Matter, Hydrodynamics, and Biophysics Joost de Graaf

Dimos' Interactive Demonstration Fluid & Colloidal Particles

Explore the motion of colloidal particles suspended in a simple fluid. Drag a large particle to apply a force, or use the controls to change the number and speed of the particles in the system. By hiding the fluid particles, you can place yourself in the position of Robert Brown, who in 1827 observed the irregular motion of tiny particles released from pollen grains into water. Although the surrounding molecules were far too small for him to see, their continual collisions caused the visible particles to wander unpredictably; a phenomenon now known as Brownian motion. In 1905, Albert Einstein showed that this apparently random motion could be explained quantitatively by the thermal motion of molecules. His theory connected the average displacement of a colloidal particle to temperature, fluid viscosity, particle size, and time. A few years later, Jean Perrin tested Einstein's predictions through careful experiments, providing compelling evidence that atoms and molecules are real physical objects and obtaining an estimate of Avogadro's number. When the small fluid particles are made visible, you can observe the microscopic collisions that produce the seemingly random motion seen at larger scales. Lastly, dragging the colloids allows you to see how the fluid particles influence the motion of colloids that are far away, this effect is referred to as hydrodynamic interaction.

Solvent molecules Colloidal particles

Master's Course Microhydrodynamics & Non-Equilibrium Physics

By the end of this lecture series, you will be able to derive basic hydrodynamic equations and perform the necessary frame transformations. You will understand how these transformations come about and what properties of a fluid give rise to certain flow behaviors. You will have familiarity with rheological analysis and understand how to characterize complex fluids. In addition, you will have become proficient in analytically solving fluid dynamical equations for (certain) complex fluids in simple geometries in the linear regime. You will also be able to solve analytically using Green's functions the behavior of (an)isotropic particles in a Newtonian fluid. Lastly, you will have a basic understanding of how microorganisms self-propel and how this influences their interaction with each other and their environment.

If you are interested in self-studying the material, I have provided the course schedule of 2025.

Master's Course Soft and Active Matter Theory

These lecture notes build upon the course taught by R. van Roij, in which classical density functional theory (DFT) is introduced. Here, I cover the essentials of dynamic DFT, topological defects, and active matter in three separate notes. The first set of notes focuses on non-equilibrium order-parameter fields and works toward deriving Cahn-Hilliard and Phase-Field Crystal (PFC) theory. The second set of notes starts by considering the classical XY model and the appropriate continuum form. This is then built upon to describe topological defects and give a flavor of the phase transition induced by defect unbinding. The third set of notes describes several aspects of active systems, before considering active topological defects in pattern-forming PFC theories like Swift-Hohenberg.

Bachelor's Course Advanced Statistical Physics

This course explores the principles and applications of thermodynamics and statistical physics, emphasizing the description of classical many-body systems and touching upon a few simple quantum gasses. We cover the following topics: phase transitions (gas-liquid condensation, magnetic ordering, crystallization, phase separation, and liquid-crystalline order), critical phenomena (exponents, divergent length scales, and fluctuations), and the structure and thermodynamic properties of non-ideal gasses, classical fluids, and liquid crystals. The theoretical framework comprises mean-field theory, a simple renormalization group of spin systems, Landau theory for first- and second-order phase transitions, nucleation theory, the virial expansion for non-ideal atomic gasses, and Onsager theory for anisotropic particles. In addition, the formal relationship of the various thermodynamic potentials (energy, free energy, enthalpy, Gibbs free energy, and grand potential) are related to each other via Legendre transformations; universal thermodynamic identities are also derived.

The notes were originally put together by R. van Roij and later extended and reworked by L. Filion. I subsequently modified these to account for changes in the content and structure of the course. This includes the repartitioning of material between academic years 2021-22 and 2022-23 to accommodate the topic of ideal quantum gases. If you are interested in self-studying the material, I have provided the course schedule of 2024.