Project A9: Coarse grained non-equilibrium dynamics of active soft matter

Active colloids can self-propel in an unbiased solvent and provide a paradigmatic example of non-equilibrium soft matter. They have received enormous attention in recent years, partly for their rich ability to form dynamic structures such as living crystals, self-organized super-rotor assemblies, and travelling wave patterns. To a large extent, these dynamic structures are now known to hinge on the unusual hydrodynamic interactions among active colloids as well as on the phoretic cross-interactions which hinge on the action of a phoretic field (concentration, temperature) gradient due to a certain colloid on other colloids in the system. These interactions are in general long-ranged, confinement-dependent, non-reciprocal, non-instantaneous and non-pair-wise. However, despite their importance in generic experiments with active colloids, many key aspects of these interactions are still not well understood. To improve our corresponding understanding, the overarching goal of the present project is to develop a conceptually new and generic multiscale simulation method which describes large ensembles of active colloids including their full near- and far-field interactions at a resolution beyond existing continuum approaches.

To reach this goal, the project develops highly detailed simulations combined with coarse-graining techniques for which it exploits the TRR 146 framework. In particular, it

  1. generalizes the Bounded Support Spectral Solver (BoSSS) solver, which serves as a generic simulation platform within the TRR and at the TU Darmstadt for solving Partial Differential Equations (PDE), and extends its applicability regime to account for the full phoretic, hydrodynamic and confinement-induced cross-interactions of active colloids leading to close interactions with C7.
  2. concretely exploits previous achievements within the TRR regarding the modelling of memory effects (A3).
  3. cooperates with B8 where complementary DPD simulations will be performed to resolve details of the interactions of small active colloids with walls at comparatively fine scales.
  4. complements existing coarse-graining activities within the TRR which focus either on (near) equilibrium (A2, A3) and kinetically arrested (A6) states or require a steady state (A7) to persistent non-equilibrium dynamical situations.

The project has started mid-2020 and has so far managed to develop the conceptual framework to model active colloids including their full interactions, generalize the BoSSS-simulation platform to account for phoretic interactions and to conceptually develop the coarse-graining procedure for phoretic interactions in 2D, the implementation of which would successfully complete the objectives of the present funding period. Ultimately reaching the overarching project goal – which is our target in the next funding period -- requires, however, to advance the developed simulation method to account for generic active colloids by meeting the following key challenges:

  1. To account for 3D confinement, memory and hydro-phoretic cross-coupling effects which play a key role in most experiments on the collective behaviour of active colloids, we need to generalize our fine-grained simulation approach and its implementation in the BoSSS-platform accordingly.
  2. Obtaining an effective coarse-grained interacting particle-based model which incorporates the full phoretic and hydrodynamic cross-interactions among active particles in 3D (rather than just the phoretic ones in 2D as in the present funding period), which requires a generalized coarse-graining approach, similar to force-matching.

Besides its role in the TRR, a success of the present project would create a unique method allowing for the first time to simulate very large ensembles of active colloids including their full hydrodynamic and phoretic many body interactions, which could shine light on various still-mysterious phenomena in active matter such as the mechanisms behind the dynamical breaking up of living crystals.

Interactions in active colloids
Benno Liebchen, Aritra K Mukhopadhyay
Journal of Physics: Condensed Matter 34 (8), 083002 (2021)
see publication

Active droploids
Jens Grauer, Falko Schmidt, Jesús Pineda, Benjamin Midtvedt, Hartmut Löwen, Giovanni Volpe, Benno Liebchen
Nature Communications 12 (1), (2021)
see publication