10,242 research outputs found
Bridging the computational gap between mesoscopic and continuum modeling of red blood cells for fully resolved blood flow
We present a computational framework for the simulation of blood flow with
fully resolved red blood cells (RBCs) using a modular approach that consists of
a lattice Boltzmann solver for the blood plasma, a novel finite element based
solver for the deformable bodies and an immersed boundary method for the
fluid-solid interaction. For the RBCs, we propose a nodal projective FEM
(npFEM) solver which has theoretical advantages over the more commonly used
mass-spring systems (mesoscopic modeling), such as an unconditional stability,
versatile material expressivity, and one set of parameters to fully describe
the behavior of the body at any mesh resolution. At the same time, the method
is substantially faster than other FEM solvers proposed in this field, and has
an efficiency that is comparable to the one of mesoscopic models. At its core,
the solver uses specially defined potential energies, and builds upon them a
fast iterative procedure based on quasi-Newton techniques. For a known
material, our solver has only one free parameter that demands tuning, related
to the body viscoelasticity. In contrast, state-of-the-art solvers for
deformable bodies have more free parameters, and the calibration of the models
demands special assumptions regarding the mesh topology, which restrict their
generality and mesh independence. We propose as well a modification to the
potential energy proposed by Skalak et al. 1973 for the red blood cell
membrane, which enhances the strain hardening behavior at higher deformations.
Our viscoelastic model for the red blood cell, while simple enough and
applicable to any kind of solver as a post-convergence step, can capture
accurately the characteristic recovery time and tank-treading frequencies. The
framework is validated using experimental data, and it proves to be scalable
for multiple deformable bodies
Fluid Vesicles in Flow
We review the dynamical behavior of giant fluid vesicles in various types of
external hydrodynamic flow. The interplay between stresses arising from
membrane elasticity, hydrodynamic flows, and the ever present thermal
fluctuations leads to a rich phenomenology. In linear flows with both
rotational and elongational components, the properties of the tank-treading and
tumbling motions are now well described by theoretical and numerical models. At
the transition between these two regimes, strong shape deformations and
amplification of thermal fluctuations generate a new regime called trembling.
In this regime, the vesicle orientation oscillates quasi-periodically around
the flow direction while asymmetric deformations occur. For strong enough
flows, small-wavelength deformations like wrinkles are observed, similar to
what happens in a suddenly reversed elongational flow. In steady elongational
flow, vesicles with large excess areas deform into dumbbells at large flow
rates and pearling occurs for even stronger flows. In capillary flows with
parabolic flow profile, single vesicles migrate towards the center of the
channel, where they adopt symmetric shapes, for two reasons. First, walls exert
a hydrodynamic lift force which pushes them away. Second, shear stresses are
minimal at the tip of the flow. However, symmetry is broken for vesicles with
large excess areas, which flow off-center and deform asymmetrically. In
suspensions, hydrodynamic interactions between vesicles add up to these two
effects, making it challenging to deduce rheological properties from the
dynamics of individual vesicles. Further investigations of vesicles and similar
objects and their suspensions in steady or time-dependent flow will shed light
on phenomena such as blood flow.Comment: 13 pages, 13 figures. Adv. Colloid Interface Sci., 201
Active elastohydrodynamics of vesicles in narrow, blind constrictions
Fluid-resistance limited transport of vesicles through narrow constrictions
is a recurring theme in many biological and engineering applications. Inspired
by the motor-driven movement of soft membrane-bound vesicles into closed
neuronal dendritic spines, here we study this problem using a combination of
passive three-dimensional simulations and a simplified semi-analytical theory
for active transport of vesicles that are forced through such constrictions by
molecular motors. We show that the motion of these objects is characterized by
two dimensionless quantities related to the geometry and the strength of
forcing relative to the vesicle elasticity. We use numerical simulations to
characterize the transit time for a vesicle forced by fluid pressure through a
constriction in a channel, and find that relative to an open channel, transport
into a blind end leads to the formation of an effective lubrication layer that
strongly impedes motion. When the fluid pressure forcing is complemented by
forces due to molecular motors that are responsible for vesicle trafficking
into dendritic spines, we find that the competition between motor forcing and
fluid drag results in multistable dynamics reminiscent of the real system. Our
study highlights the role of non-local hydrodynamic effects in determining the
kinetics of vesicular transport in constricted geometries
Computational studies of biomembrane systems: Theoretical considerations, simulation models, and applications
This chapter summarizes several approaches combining theory, simulation and
experiment that aim for a better understanding of phenomena in lipid bilayers
and membrane protein systems, covering topics such as lipid rafts, membrane
mediated interactions, attraction between transmembrane proteins, and
aggregation in biomembranes leading to large superstructures such as the light
harvesting complex of green plants. After a general overview of theoretical
considerations and continuum theory of lipid membranes we introduce different
options for simulations of biomembrane systems, addressing questions such as:
What can be learned from generic models? When is it expedient to go beyond
them? And what are the merits and challenges for systematic coarse graining and
quasi-atomistic coarse grained models that ensure a certain chemical
specificity
Viscous regularization and r-adaptive remeshing for finite element analysis of lipid membrane mechanics
As two-dimensional fluid shells, lipid bilayer membranes resist bending and
stretching but are unable to sustain shear stresses. This property gives
membranes the ability to adopt dramatic shape changes. In this paper, a finite
element model is developed to study static equilibrium mechanics of membranes.
In particular, a viscous regularization method is proposed to stabilize
tangential mesh deformations and improve the convergence rate of nonlinear
solvers. The Augmented Lagrangian method is used to enforce global constraints
on area and volume during membrane deformations. As a validation of the method,
equilibrium shapes for a shape-phase diagram of lipid bilayer vesicle are
calculated. These numerical techniques are also shown to be useful for
simulations of three-dimensional large-deformation problems: the formation of
tethers (long tube-like exetensions); and Ginzburg-Landau phase separation of a
two-lipid-component vesicle. To deal with the large mesh distortions of the
two-phase model, modification of vicous regularization is explored to achieve
r-adaptive mesh optimization
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