8,585 research outputs found
On the bending algorithms for soft objects in flows
International audienceOne of the most challenging aspects in the accurate simulation of three-dimensional soft objects such as vesicles or biological cells is the computation of membrane bending forces. The origin of this difficulty stems from the need to numerically evaluate a fourth order derivative on the discretized surface geometry. Here we investigate six different algorithms to compute membrane bending forces, including regularly used methods as well as novel ones. All are based on the same physical model (due to Canham and Helfrich) and start from a surface discretization with flat triangles. At the same time, they differ substantially in their numerical approach. We start by comparing the numerically obtained mean curvature, the Laplace-Beltrami operator of the mean curvature and finally the surface force density to analytical results for the discocyte resting shape of a red blood cell. We find that none of the considered algorithms converges to zero error at all nodes and that for some algorithms the error even diverges. There is furthermore a pronounced influence of the mesh structure: Discretizations with more irregular triangles and node connectivity present serious difficulties for most investigated methods. To assess the behavior of the algorithms in a realistic physical application, we investigate the deformation of an initially spherical capsule in a linear shear flow at small Reynolds numbers. To exclude any influence of the flow solver, two conceptually very different solvers are employed: the Lattice-Boltzmann and the Boundary Integral Method. Despite the largely different quality of the bending algorithms when applied to the static red blood cell, we find that in the actual flow situation most algorithms give consistent results for both hydrodynamic solvers. Even so, a short review of earlier works reveals a wide scattering of reported results for, e.g., the Taylor deformation parameter. Besides the presented application to biofluidic systems, the investigated algorithms are also of high relevance to the computer graphics and numerical mathematics communities
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
Slow rotation of a spherical particle inside an elastic tube
In this paper, we present an analytical calculation of the rotational
mobility functions of a particle rotating on the centerline of an elastic
cylindrical tube whose membrane exhibits resistance towards shearing and
bending. We find that the correction to the particle rotational mobility about
the cylinder axis depends solely on membrane shearing properties while both
shearing and bending manifest themselves for the rotational mobility about an
axis perpendicular to the cylinder axis. In the quasi-steady limit of vanishing
frequency, the particle rotational mobility nearby a no-slip rigid cylinder is
recovered only if the membrane possesses a non-vanishing resistance towards
shearing. We further show that for the asymmetric rotation along the cylinder
radial axis, a coupling between shearing and bending exists. Our analytical
predictions are compared and validated with corresponding boundary integral
simulations where a very good agreement is obtained.Comment: 23 pages, 7 figures and 107 references. Revised manuscript
resubmitted to Acta Mec
Particle mobility between two planar elastic membranes: Brownian motion and membrane deformation
We study the motion of a solid particle immersed in a Newtonian fluid and
confined between two parallel elastic membranes possessing shear and bending
rigidity. The hydrodynamic mobility depends on the frequency of the particle
motion due to the elastic energy stored in the membrane. Unlike the
single-membrane case, a coupling between shearing and bending exists. The
commonly used approximation of superposing two single-membrane contributions is
found to give reasonable results only for motions in the parallel, but not in
the perpendicular direction. We also compute analytically the membrane
deformation resulting from the motion of the particle, showing that the
presence of the second membrane reduces deformation. Using the
fluctuation-dissipation theorem we compute the Brownian motion of the particle,
finding a long-lasting subdiffusive regime at intermediate time scales. We
finally assess the accuracy of the employed point-particle approximation via
boundary-integral simulations for a truly extended particle. They are found to
be in excellent agreement with the analytical predictions.Comment: 14 pages, 8 figures and 96 references. Revised version resubmitted to
Phys. Fluid
Multi-Particle Collision Dynamics -- a Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids
In this review, we describe and analyze a mesoscale simulation method for
fluid flow, which was introduced by Malevanets and Kapral in 1999, and is now
called multi-particle collision dynamics (MPC) or stochastic rotation dynamics
(SRD). The method consists of alternating streaming and collision steps in an
ensemble of point particles. The multi-particle collisions are performed by
grouping particles in collision cells, and mass, momentum, and energy are
locally conserved. This simulation technique captures both full hydrodynamic
interactions and thermal fluctuations. The first part of the review begins with
a description of several widely used MPC algorithms and then discusses
important features of the original SRD algorithm and frequently used
variations. Two complementary approaches for deriving the hydrodynamic
equations and evaluating the transport coefficients are reviewed. It is then
shown how MPC algorithms can be generalized to model non-ideal fluids, and
binary mixtures with a consolute point. The importance of angular-momentum
conservation for systems like phase-separated liquids with different
viscosities is discussed. The second part of the review describes a number of
recent applications of MPC algorithms to study colloid and polymer dynamics,
the behavior of vesicles and cells in hydrodynamic flows, and the dynamics of
viscoelastic fluids
The motion of a deforming capsule through a corner
A three-dimensional deformable capsule convected through a square duct with a
corner is studied via numerical simulations. We develop an accelerated boundary
integral implementation adapted to general geometries and boundary conditions.
A global spectral method is adopted to resolve the dynamics of the capsule
membrane developing elastic tension according to the neo-Hookean constitutive
law and bending moments in an inertialess flow. The simulations show that the
trajectory of the capsule closely follows the underlying streamlines
independently of the capillary number. The membrane deformability, on the other
hand, significantly influences the relative area variations, the advection
velocity and the principal tensions observed during the capsule motion. The
evolution of the capsule velocity displays a loss of the time-reversal symmetry
of Stokes flow due to the elasticity of the membrane. The velocity decreases
while the capsule is approaching the corner as the background flow does,
reaches a minimum at the corner and displays an overshoot past the corner due
to the streamwise elongation induced by the flow acceleration in the downstream
branch. This velocity overshoot increases with confinement while the maxima of
the major principal tension increase linearly with the inverse of the duct
width. Finally, the deformation and tension of the capsule are shown to
decrease in a curved corner
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