Investigation of the dynamics of geometrically restricted soft matter systems with long-ranged interactions
Final Report Abstract
We investigate the evolution of a system of colloidal particles in confinement, both with theory and experiments. Such a colloidal quasi–monolayer, e.g., formed at a fluid interface or by means of a suitable confining potential, exhibits interesting properties since the trapping may induce long–ranged interactions between the particles. Suitably large colloids trapped at a fluid interface deform the latter due to external forces (e.g. gravity) acting on them perpendicular to the interface. This induces so–called capillary interactions, with which the system constitutes a colloidal analog to a self–gravitating fluid, with the important difference that the range of the interaction may be tuned by varying the so–called capillary length of the system of interface and particles. We extend an existing model for the dynamics of the quasi–monolayer by introducing hydrodynamic interactions for the system of colloidal particles and both in theory and simulations. Hydrodynamic interactions are approximated by their far–field limit at the two–body level in both methods. Within this approximation, hydrodynamic interactions are described with a position–dependent diffusion tensor and become long–ranged themselves, typically being rather repulsive at large distances. The system with capillary interactions thus exhibits a speed–up of the dynamics, the qualitative phenomenology summarized earlier in the dynamical phase diagram however, remains unchanged. These “accelerated” dynamics are further investigated without any additional interactions. We consider a system of non–interacting particles (an ideal gas) confined by means of a suitable potential. Such a confined colloidal monolayer exhibits anomalously fast collective diffusion. This effect is also observed experimentally via a strong increase of the wavenumber–dependent diffusion coefficient for large scales, and is a consequence of the hydrodynamic interactions mediated by the three–dimensional (3D) ambient fluid acting on the confined (e.g. to 2D) particles. Upon varying the width of the confinement we can always identify a regime of length scales where the collective diffusion is anomalous. These length scales are larger than the width of the confinement. An important consequence is that all collective diffusion processes of quasi–monolayers in an ambient fluid may become anomalous at long times, provided the lateral system size may become larger than the width of the confinement. This applies to interfacially trapped colloids in particular, but also e.g. to Marangoni flow of surfactants. The complete dynamics of colloidal particles in confinement may be cast into a diffusion– like evolution equation for the density of the particles, i.e. a generalized diffusion equation. This approach allows one to encode all interactions into the wavenumber dependent diffusion coefficient, which can be expressed in terms of a series expansion with respect to the wavenumber. Clustering instabilities and anomalous behavior then appear as non–zero coefficients for negative powers of the wavenumber, whereas normal collective diffusion is characterized by the absence of all negative powers in this series expansion. An experimental realization of the capillary system has been designed and set up. First tests provide promising insights in the dynamics, but demand for future testing and investigations in order to obtain more quantitative results and compare them to our model.
Publications
- “3D hydrodynamic interactions lead to divergences in 2D diffusion” J. Phys.: Condensed Matter 27, 194113 (2015)
J. Bleibel, A. Domínguez, M. Oettel
(See online at https://doi.org/10.1088/0953-8984/27/19/194113) - “A dynamic DFT approach to generalized diffusion equations in a system with long– ranged and hydrodynamic interactions” J. Phys.: Condensed Matter: 28, 244021 (2016)
J. Bleibel, A. Domínguez, M. Oettel
(See online at https://doi.org/10.1088/0953-8984/28/24/244021) - “Onset of anomalous diffusion in colloids confined to quasi–monoayers” Phys. Rev. E 95, 032604 (2017)
J. Bleibel, A. Domínguez, M. Oettel
(See online at https://doi.org/10.1103/PhysRevE.95.032604)
