94 research outputs found
Self propulsion of droplets driven by an active permeating gel
We discuss the flow field and propulsion velocity of active droplets, which
are driven by body forces residing on a rigid gel. The latter is modelled as a
porous medium which gives rise to permeation forces. In the simplest model, the
Brinkman equation, the porous medium is characterised by a single length scale
--the square root of the permeability. We compute the flow fields inside
and outside of the droplet as well as the energy dissipation as a function of
. We furthermore show that there are optimal gel fractions, giving rise
to maximal linear and rotational velocities. In the limit ,
corresponding to a very dilute gel, we recover Stokes flow. The opposite limit,
, corresponding to a space filling gel, is singular and not
equivalent to Darcy's equation, which cannot account for self-propulsion
Towards finite-dimensional gelation
We consider the gelation of particles which are permanently connected by
random crosslinks, drawn from an ensemble of finite-dimensional continuum
percolation. To average over the randomness, we apply the replica trick, and
interpret the replicated and crosslink-averaged model as an effective molecular
fluid. A Mayer-cluster expansion for moments of the local static density
fluctuations is set up. The simplest non-trivial contribution to this series
leads back to mean-field theory. The central quantity of mean-field theory is
the distribution of localization lengths, which we compute for all
connectivities. The highly crosslinked gel is characterized by a one-to-one
correspondence of connectivity and localization length. Taking into account
higher contributions in the Mayer-cluster expansion, systematic corrections to
mean-field can be included. The sol-gel transition shifts to a higher number of
crosslinks per particle, as more compact structures are favored. The critical
behavior of the model remains unchanged as long as finite truncations of the
cluster expansion are considered. To complete the picture, we also discuss
various geometrical properties of the crosslink network, e.g. connectivity
correlations, and relate the studied crosslink ensemble to a wider class of
ensembles, including the Deam-Edwards distribution.Comment: 18 pages, 4 figures, version to be published in EPJ
Friction-induced Shear thickening: a microscopic perspective
We develop a microscopic picture of shear thickening in dense suspensions
which emphasizes the role of frictional forces, coupling rotational and
translational degrees of freedom. Simulations with contact forces and viscous
drag only, reveal pronounced shear thickening with a simultaneous increase in
contact number and energy dissipation by frictional forces. At high densities,
when the translational motion is severely constrained, we observe liquid-like
gear-states with pronounced relative rotations of the particles coexisting with
solid-like regions which rotate as a whole. The latter are stabilised by
frustrated loops which become more numerous and persistent with increasing
pressure, giving rise to an increasing lengthscale of this mosaique-like
structure and a corresponding increase in viscosity.Comment: 7 pages, 12 figures, accepted in EP
Anisotropic Random Networks of Semiflexible Polymers
Motivated by the organization of crosslinked cytoskeletal biopolymers, we
present a semimicroscopic replica field theory for the formation of anisotropic
random networks of semiflexible polymers. The networks are formed by
introducing random permanent crosslinks which fix the orientations of the
corresponding polymer segments to align with one another. Upon increasing the
crosslink density, we obtain a continuous gelation transition from a fluid
phase to a gel where a finite fraction of the system gets localized at random
positions. For sufficiently stiff polymers, this positional localization is
accompanied by a {\em continuous} isotropic-to-nematic (IN) transition occuring
at the same crosslink density. As the polymer stiffness decreases, the IN
transition becomes first order, shifts to a higher crosslink density, and is
preceeded by an orientational glass (statistically isotropic amorphous solid)
where the average polymer orientations freeze in random directions.Comment: 5 pages, 2 figures; final version with expanded discussion to appear
in PR
- …