Sedimentation of point particles in Stokes flow
Simulation written for Computer Simulations in Soft Matter Physics course with Piotr Szymczak. The three-body problem of sedimenting particles is investigated numerically, involving reversible and non-reversible algorithms. Three point particles sedimenting in viscous liquid exhibit interesting behaviour stemming from hydrodynamic interactions between them. The flow field is modelled by the Oseen tensor approximation. A certain class of initial conditions (horizontal alignment) is investigated to analyse chaotic mixing behaviour in the first phase of particles' motion. [available on request]
Four approaches to hydrodynamic Green's functions - the Oseen tensors
Prepared for Microworld Hydrodynamics course with Maria Ekiel - Jeżewska.
Four ways of deriving the flow field generated by a force concentrated in one point in low Reynolsd number flow regime are presented, basing on the books by Zapryanov & Tabakova, Kim & Karilla, Dhont and Pozrikidis. We find a fundamental solution of Stokes equations for infinite fluid which can be used to construct solutions with more complex forces. [pdf], also available at ArXiV: preprint no. 1312.6231
Stokes flow generated by a point force in various geometries. I. Pressure field
Materials made for Microhydrodynamics course with Maria Ekiel - Jeżewska.
Fundamental pressure solutions of Stokes equations in presence of a free boudary or rigid wall are constructed using the method of images. The subsequent steps of the construction are presented. [pdf]
Fresnel and Fraunhofer Diffraction - a lecture experiment
Patterns presenting a dynamic transition between Fresnel and Fraunhofer diffraction patterns using a moving diverging lens. See the photographs and the preprint of our paper here:
Fresnel and Fraunhofer diffraction patterns