2,704 research outputs found
The dynamics of a capsule in a wall-bounded oscillating shear flow
The motion of an initially spherical capsule in a wall-bounded oscillating
shear flow is investigated via an accelerated boundary integral implementation.
The neo-Hookean model is used as the constitutive law of the capsule membrane.
The maximum wall-normal migration is observed when the oscillation period of
the imposed shear is of the order of the relaxation time of the elastic
membrane; hence, the optimal capillary number scales with the inverse of the
oscillation frequency and the ratio agrees well with the theoretical prediction
in the limit of high-frequency oscillation. The migration velocity decreases
monotonically with the frequency of the applied shear and the capsule-wall
distance. We report a significant correlation between the capsule lateral
migration and the normal stress difference induced in the flow. The periodic
variation of the capsule deformation is roughly in phase with that of the
migration velocity and normal stress difference, with twice the frequency of
the imposed shear. The maximum deformation increases linearly with the membrane
elasticity before reaching a plateau at higher capillary numbers when the
deformation is limited by the time over which shear is applied in the same
direction and not by the membrane deformability. The maximum membrane
deformation scales as the distance to the wall to the power 1/3 as observed for
capsules and droplets in near-wall steady shear flows
Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method
The deformation of an initially spherical capsule, freely suspended in simple
shear flow, can be computed analytically in the limit of small deformations [D.
Barthes-Biesel, J. M. Rallison, The Time-Dependent Deformation of a Capsule
Freely Suspended in a Linear Shear Flow, J. Fluid Mech. 113 (1981) 251-267].
Those analytic approximations are used to study the influence of the mesh
tessellation method, the spatial resolution, and the discrete delta function of
the immersed boundary method on the numerical results obtained by a coupled
immersed boundary lattice Boltzmann finite element method. For the description
of the capsule membrane, a finite element method and the Skalak constitutive
model [R. Skalak et al., Strain Energy Function of Red Blood Cell Membranes,
Biophys. J. 13 (1973) 245-264] have been employed. Our primary goal is the
investigation of the presented model for small resolutions to provide a sound
basis for efficient but accurate simulations of multiple deformable particles
immersed in a fluid. We come to the conclusion that details of the membrane
mesh, as tessellation method and resolution, play only a minor role. The
hydrodynamic resolution, i.e., the width of the discrete delta function, can
significantly influence the accuracy of the simulations. The discretization of
the delta function introduces an artificial length scale, which effectively
changes the radius and the deformability of the capsule. We discuss
possibilities of reducing the computing time of simulations of deformable
objects immersed in a fluid while maintaining high accuracy.Comment: 23 pages, 14 figures, 3 table
Dynamics of a spherical capsule in a planar hyperbolic flow: influence of bending resistance
International audienceWe consider an initially spherical capsule freely suspended in a planar hyperbolic flow and study the influence of the wall bending resistance on the capsule dynamics. The capsule wall is assumed to be made of a three-dimensional homogeneous elastic material. The fluid-structure interaction between the capsule and the external flow is modeled numerically by coupling a boundary integral method with a shell finite element method. It is found that, for given three-dimensional wall mechanical properties, the capsule deformability is drastically reduced as the bending resistance is increased. But, if one expresses the same results as a function of the two-dimensional mechanical properties of the mid-surface, which is how the capsule wall is modeled in the thin-shell model, the capsule deformed shape is identical to the one predicted for a capsule devoid of bending resistance. The bending rigidity is found to have a negligible influence on the shape and deformation: the capsule main deformation mode is thus solely a function of the elastic stretching of the mid-surface. The wall bending resistance still plays a role locally in the regions where buckling occurs. Its influence is studied in the low flow strength regime, for which wrinkling of the wall is observed to persist at steady state. We show that the wrinkle wavelength only depends on the bending number, which compares the relative importance of bending and shearing phenomena, and provide the correlation law. This result is interesting as it allows bending resistance to be estimated from experiments on capsules in a planar hyperbolic flow at low flow strength
Forced transport of deformable containers through narrow constrictions
We study, numerically and analytically, the forced transport of deformable
containers through a narrow constriction. Our central aim is to quantify the
competition between the constriction geometry and the active forcing,
regulating whether and at which speed a container may pass through the
constriction and under what conditions it gets stuck. We focus, in particular,
on the interrelation between the force that propels the container and the
radius of the channel, as these are the external variables that may be directly
controlled in both artificial and physiological settings. We present
Lattice-Boltzmann simulations that elucidate in detail the various phases of
translocation, and present simplified analytical models that treat two limiting
types of these membrane containers: deformational energy dominated by the
bending or stretching contribution. In either case we find excellent agreement
with the full simulations, and our results reveal that not only the radius but
also the length of the constriction determines whether or not the container
will pass.Comment: 9 pages, 4 figure
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