13 research outputs found
Long-lived anomalous thermal diffusion induced by elastic cell membranes on nearby particles
The physical approach of a small particle (virus, medical drug) to the cell
membrane represents the crucial first step before active internalization and is
governed by thermal diffusion. Using a fully analytical theory we show that the
stretching and bending of the elastic membrane by the approaching particle
induces a memory in the system which leads to anomalous diffusion, even though
the particle is immersed in a purely Newtonian liquid. For typical cell
membranes the transient subdiffusive regime extends beyond 10 ms and can
enhance residence times and possibly binding rates up to 50\%. Our analytical
predictions are validated by numerical simulations.Comment: 13 pages and 5 figures. The Supporting Information is included.
Manuscript accepted for publication in Phys. Rev.
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
Numerical-experimental observation of shape bistability of red blood cells flowing in a microchannel
Red blood cells flowing through capillaries assume a wide variety of
different shapes owing to their high deformability. Predicting the realized
shapes is a complex field as they are determined by the intricate interplay
between the flow conditions and the membrane mechanics. In this work we
construct the shape phase diagram of a single red blood cell with a
physiological viscosity ratio flowing in a microchannel. We use both
experimental in-vitro measurements as well as 3D numerical simulations to
complement the respective other one. Numerically, we have easy control over the
initial starting configuration and natural access to the full 3D shape. With
this information we obtain the phase diagram as a function of initial position,
starting shape and cell velocity. Experimentally, we measure the occurrence
frequency of the different shapes as a function of the cell velocity to
construct the experimental diagram which is in good agreement with the
numerical observations. Two different major shapes are found, namely croissants
and slippers. Notably, both shapes show coexistence at low (<1 mm/s) and high
velocities (>3 mm/s) while in-between only croissants are stable. This
pronounced bistability indicates that RBC shapes are not only determined by
system parameters such as flow velocity or channel size, but also strongly
depend on the initial conditions.Comment: 13 pages, 9 figures (main text). 13 pages, 31 figures (SI
Coexistence of stable branched patterns in anisotropic inhomogeneous systems
A new class of pattern forming systems is identified and investigated:
anisotropic systems that are spatially inhomogeneous along the direction
perpendicular to the preferred one. By studying the generic amplitude equation
of this new class and a model equation, we show that branched stripe patterns
emerge, which for a given parameter set are stable within a band of different
wavenumbers and different numbers of branching points (defects). Moreover, the
branched patterns and unbranched ones (defect-free stripes) coexist over a
finite parameter range. We propose two systems where this generic scenario can
be found experimentally, surface wrinkling on elastic substrates and
electroconvection in nematic liquid crystals, and relate them to the findings
from the amplitude equation.Comment: 7 pages, 4 figure
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
Vortical flow structures induced by red blood cells in capillaries
Objective
Knowledge about the flow field of the plasma around the red blood cells in capillary flow is important for a physical understanding of blood flow and the transport of micro- and nanoparticles and molecules in the flowing plasma. We conducted an experimental study on the flow field around red blood cells in capillary flow that is complemented by simulations of vortical flow between red blood cells.
Methods
Red blood cells were injected in a 10 × 12 µm rectangular microchannel at a low hematocrit, and the flow field around one or two cells was captured by a high-speed camera that tracked 250 nm nanoparticles in the flow field, acting as tracers.
Results
While the flow field around a steady “croissant” shape is found to be similar to that of a rigid sphere, the flow field around a “slipper” shape exhibits a small vortex at the rear of the red blood cell. Even more pronounced are vortex-like structures observed in the central region between two neighboring croissants.
Conclusions
The rotation frequency of the vortices is to a good approximation, inversely proportional to the distance between the cells. Our experimental data are complemented by numerical simulations
Vortical flow structures induced by red blood cells in capillaries
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