334 research outputs found
Hydrodynamic Theories for Flows of Active Liquid Crystals and the Generalized Onsager Principle
We articulate and apply the generalized Onsager principle to derive transport equations for active liquid crystals in a fixed domain as well as in a free surface domain adjacent to a passive fluid matrix. The Onsager principle ensures fundamental variational structure of the models as well as dissipative properties of the passive component in the models, irrespective of the choice of scale (kinetic to continuum) and of the physical potentials. Many popular models for passive and active liquid crystals in a fixed domain subject to consistent boundary conditions at solid walls, as well as active liquid crystals in a free surface domain with consistent transport equations along the free boundaries, can be systematically derived from the generalized Onsager principle. The dynamical boundary conditions are shown to reduce to the static boundary conditions for passive liquid crystals used previously
Hydrodynamic Theories for Flows of Active Liquid Crystals and the Generalized Onsager Principle
We articulate and apply the generalized Onsager principle to derive transport equations for active liquid crystals in a fixed domain as well as in a free surface domain adjacent to a passive fluid matrix. The Onsager principle ensures fundamental variational structure of the models as well as dissipative properties of the passive component in the models, irrespective of the choice of scale (kinetic to continuum) and of the physical potentials. Many popular models for passive and active liquid crystals in a fixed domain subject to consistent boundary conditions at solid walls, as well as active liquid crystals in a free surface domain with consistent transport equations along the free boundaries, can be systematically derived from the generalized Onsager principle. The dynamical boundary conditions are shown to reduce to the static boundary conditions for passive liquid crystals used previously
Generic theory of active polar gels: a paradigm for cytoskeletal dynamics
We develop a general theory for active viscoelastic materials made of polar
filaments. This theory is motivated by the dynamics of the cytoskeleton. The
continuous consumption of a fuel generates a non equilibrium state
characterized by the generation of flows and stresses. Our theory can be
applied to experiments in which cytoskeletal patterns are set in motion by
active processes such as those which are at work in cells.Comment: 28 pages, 2 figure
Active nematic gels as active relaxing solids
I put forward a continuum theory for active nematic gels, defined as fluids
or suspensions of orientable rodlike objects endowed with active dynamics, that
is based on symmetry arguments and compatibility with thermodynamics. The
starting point is our recent theory that models (passive) nematic liquid
crystals as relaxing nematic elastomers. The interplay between viscoelastic
response and active dynamics of the microscopic constituents is naturally taken
into account. By contrast with standard theories, activity is not introduced as
an additional term of the stress tensor, but it is added as an external
remodeling force that competes with the passive relaxation dynamics and drags
the system out of equilibrium. In a simple one-dimensional channel geometry, we
show that the interaction between non-uniform nematic order and activity
results in either a spontaneous flow of particles or a self-organization into
sub-channels flowing in opposite directions
A Second Order Fully-discrete Linear Energy Stable Scheme for a Binary Compressible Viscous Fluid Model
We present a linear, second order fully discrete numerical scheme on a
staggered grid for a thermodynamically consistent hydrodynamic phase field
model of binary compressible fluid flow mixtures derived from the generalized
Onsager Principle. The hydrodynamic model not only possesses the variational
structure, but also warrants the mass, linear momentum conservation as well as
energy dissipation. We first reformulate the model in an equivalent form using
the energy quadratization method and then discretize the reformulated model to
obtain a semi-discrete partial differential equation system using the
Crank-Nicolson method in time. The numerical scheme so derived preserves the
mass conservation and energy dissipation law at the semi-discrete level. Then,
we discretize the semi-discrete PDE system on a staggered grid in space to
arrive at a fully discrete scheme using the 2nd order finite difference method,
which respects a discrete energy dissipation law. We prove the unique
solvability of the linear system resulting from the fully discrete scheme. Mesh
refinements and two numerical examples on phase separation due to the spinodal
decomposition in two polymeric fluids and interface evolution in the gas-liquid
mixture are presented to show the convergence property and the usefulness of
the new scheme in applications
Hydrodynamic theory for nematic shells: the interplay among curvature, flow and alignment
We derive the hydrodynamic equations for nematic liquid crystals lying on
curved substrates. We invoke the Lagrange-Rayleigh variational principle to
adapt the Ericksen-Leslie theory to two-dimensional nematics in which a
degenerate anchoring of the molecules on the substrate is enforced. The only
constitutive assumptions in this scheme concern the free-energy density, given
by the two-dimensional Frank potential, and the density of dissipation which is
required to satisfy appropriate invariance requirements. The resulting
equations of motion couple the velocity field, the director alignment and the
curvature of the shell. To illustrate our findings, we consider the effect of a
simple shear flow on the alignment of a nematic lying on a cylindrical shell
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