1,074 research outputs found
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
Diffuse interface models of locally inextensible vesicles in a viscous fluid
We present a new diffuse interface model for the dynamics of inextensible
vesicles in a viscous fluid. A new feature of this work is the implementation
of the local inextensibility condition in the diffuse interface context. Local
inextensibility is enforced by using a local Lagrange multiplier, which
provides the necessary tension force at the interface. To solve for the local
Lagrange multiplier, we introduce a new equation whose solution essentially
provides a harmonic extension of the local Lagrange multiplier off the
interface while maintaining the local inextensibility constraint near the
interface. To make the method more robust, we develop a local relaxation scheme
that dynamically corrects local stretching/compression errors thereby
preventing their accumulation. Asymptotic analysis is presented that shows that
our new system converges to a relaxed version of the inextensible sharp
interface model. This is also verified numerically. Although the model does not
depend on dimension, we present numerical simulations only in 2D. To solve the
2D equations numerically, we develop an efficient algorithm combining an
operator splitting approach with adaptive finite elements where the
Navier-Stokes equations are implicitly coupled to the diffuse interface
inextensibility equation. Numerical simulations of a single vesicle in a shear
flow at different Reynolds numbers demonstrate that errors in enforcing local
inextensibility may accumulate and lead to large differences in the dynamics in
the tumbling regime and differences in the inclination angle of vesicles in the
tank-treading regime. The local relaxation algorithm is shown to effectively
prevent this accumulation by driving the system back to its equilibrium state
when errors in local inextensibility arise.Comment: 25 page
Global minimizers for axisymmetric multiphase membranes
We consider a Canham-Helfrich-type variational problem defined over closed
surfaces enclosing a fixed volume and having fixed surface area. The problem
models the shape of multiphase biomembranes. It consists of minimizing the sum
of the Canham-Helfrich energy, in which the bending rigidities and spontaneous
curvatures are now phase-dependent, and a line tension penalization for the
phase interfaces. By restricting attention to axisymmetric surfaces and phase
distributions, we extend our previous results for a single phase
(arXiv:1202.1979) and prove existence of a global minimizer.Comment: 20 pages, 3 figure
Stability of MultiComponent Biological Membranes
Equilibrium equations and stability conditions are derived for a general class of multicomponent biological membranes. The analysis is based on a generalized Helfrich energy that
accounts for geometry through the stretch and curvature, the composition, and the interaction between geometry and composition. The use of nonclassical differential operators and related integral theorems in conjunction with appropriate composition and mass conserving variations simplify the derivations. We show that instabilities of multicomponent membranes are significantly different from
those in single component membranes, as well as those in systems undergoing spinodal decomposition in flat spaces. This is due to the intricate coupling between composition and shape as well as the nonuniform tension in the membrane. Specifically, critical modes have high frequencies unlike single component vesicles and stability depends on system size unlike in systems undergoing spinodal
decomposition in flat space. An important implication is that small perturbations may nucleate localized but very large deformations. We show that the predictions of the analysis are in qualitative agreement with experimental observations
Conditions for extreme sensitivity of protein diffusion in membranes to cell environments
We study protein diffusion in multicomponent lipid membranes close to a rigid
substrate separated by a layer of viscous fluid. The large-distance, long-time
asymptotics for Brownian motion are calculated using a nonlinear stochastic
Navier-Stokes equation including the effect of friction with the substrate. The
advective nonlinearity, neglected in previous treatments, gives only a small
correction to the renormalized viscosity and diffusion coefficient at room
temperature. We find, however, that in realistic multicomponent lipid mixtures,
close to a critical point for phase separation, protein diffusion acquires a
strong power-law dependence on temperature and the distance to the substrate
, making it much more sensitive to cell environment, unlike the logarithmic
dependence on and very small thermal correction away from the critical
point.Comment: 19 pages, 4 figure
Recent advances in the simulation of particle-laden flows
A substantial number of algorithms exists for the simulation of moving
particles suspended in fluids. However, finding the best method to address a
particular physical problem is often highly non-trivial and depends on the
properties of the particles and the involved fluid(s) together. In this report
we provide a short overview on a number of existing simulation methods and
provide two state of the art examples in more detail. In both cases, the
particles are described using a Discrete Element Method (DEM). The DEM solver
is usually coupled to a fluid-solver, which can be classified as grid-based or
mesh-free (one example for each is given). Fluid solvers feature different
resolutions relative to the particle size and separation. First, a
multicomponent lattice Boltzmann algorithm (mesh-based and with rather fine
resolution) is presented to study the behavior of particle stabilized fluid
interfaces and second, a Smoothed Particle Hydrodynamics implementation
(mesh-free, meso-scale resolution, similar to the particle size) is introduced
to highlight a new player in the field, which is expected to be particularly
suited for flows including free surfaces.Comment: 16 pages, 4 figure
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