@misc{9238097,
  abstract     = {{This thesis investigates the fluid dynamics and phase behaviour of active microswimmers in unbounded two-dimensional suspensions. The first part derives analytical expressions for fluid correlations, fluid velocity variance, and energy spectra of non-interacting swimmers. While expressions derived from the Stokes equations, hence ignoring inertial effects, capture qualitative trends, they show quantitative discrepancies. This work demonstrates that these deviations mostly originate from the neglect of inertia, which in 2 dimensions is required to regularise the solutions at long distances. By instead employing the Oseen equations, which incorporate the leading-order effect of fluid inertia, these discrepancies are largely resolved. This indicates that, even at low Reynolds numbers, inertia is an essential regularisation factor in 2D systems, as it is required to govern the far-field flow behaviour.
The second part examines interacting swimmers via lattice Boltzmann (LB) simulations, which undergo a transition from disordered swimming to a quasi-stationary steady state characterised by system-spanning fluid correlations and mesoscopic, nematically ordered swimmer patches. A theoretical expression for the critical density is derived, specifically accounting for finite-size effects. Simulations reveal that the transition occurs only above the critical density and for a sufficiently large persistence length $l_p$. Further investigation suggests a complex interplay between density, system size, and persistence length, and show that the observed transition is broadly reminiscent of a continuous, second order phase transition. While a similar transition occurs in 3D LB and 2D continuum models, the 2D LB transition investigated here is uniquely distinguished by a different transition behaviour for high and low lp values.}},
  author       = {{Hoffmann, Judith}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{Collective Behaviour in 2D Microswimmer Suspensions}},
  year         = {{2026}},
}