467 research outputs found
Modeling of control forces for kinematical constraints in the dynamics of multibody systems: A new approach
Conventionally kinematical constraints in multibody systems are treated similar to geometrical constraints and are modeled by constraint reaction forces which are perpendicular to constraint surfaces. However, in reality, one may want to achieve the desired kinematical conditions by control forces having different directions in relation to the constraint surfaces. The conventional equations of motion for multibody systems subject to kinematical constraints are generalized by introducing general direction control forces. Conditions for the selections of the control force directions are also discussed. A redundant robotic system subject to prescribed end-effector motion is analyzed to illustrate the methods proposed
Brownian motion near an elastic cell membrane: A theoretical study
Elastic confinements are an important component of many biological systems
and dictate the transport properties of suspended particles under flow. In this
chapter, we review the Brownian motion of a particle moving in the vicinity of
a living cell whose membrane is endowed with a resistance towards shear and
bending. The analytical calculations proceed through the computation of the
frequency-dependent mobility functions and the application of the
fluctuation-dissipation theorem. Elastic interfaces endow the system with
memory effects that lead to a long-lived anomalous subdiffusive regime of
nearby particles. In the steady limit, the diffusional behavior approaches that
near a no-slip hard wall. The analytical predictions are validated and
supplemented with boundary-integral simulations.Comment: 16 pages, 7 figures and 161 references. Contributed chapter to the
flowing matter boo
Hydrodynamic interaction between particles near elastic interfaces
We present an analytical calculation of the hydrodynamic interaction between
two spherical particles near an elastic interface such as a cell membrane. The
theory predicts the frequency dependent self- and pair-mobilities accounting
for the finite particle size up to the 5th order in the ratio between particle
diameter and wall distance as well as between diameter and interparticle
distance. We find that particle motion towards a membrane with pure bending
resistance always leads to mutual repulsion similar as in the well-known case
of a hard-wall. In the vicinity of a membrane with shearing resistance,
however, we observe an attractive interaction in a certain parameter range
which is in contrast to the behavior near a hard wall. This attraction might
facilitate surface chemical reactions. Furthermore, we show that there exists a
frequency range in which the pair-mobility for perpendicular motion exceeds its
bulk value, leading to short-lived superdiffusive behavior. Using the
analytical particle mobilities we compute collective and relative diffusion
coefficients. The appropriateness of the approximations in our analytical
results is demonstrated by corresponding boundary integral simulations which
are in excellent agreement with the theoretical predictions.Comment: 16 pages, 7 figures and 109 references. Manuscript accepted for
publication in J. Chem. Phy
Rotation Rate of Particle Pairs in Homogeneous Isotropic Turbulence
Understanding the dynamics of particles in turbulent flow is important in
many environmental and industrial applications. In this paper, the statistics
of particle pair orientation is numerically studied in homogeneous isotropic
turbulent flow, with Taylor microscale Reynolds number of 300. It is shown that
the Kolmogorov scaling fails to predict the observed probability density
functions (PDFs) of the pair rotation rate and the higher order moments
accurately. Therefore, a multifractal formalism is derived in order to include
the intermittent behavior that is neglected in the Kolmogorov picture. The PDFs
of finding the pairs at a given angular velocity for small relative separations
reveals extreme events with stretched tails and high kurtosis values.
Additionally, The PDFs are found to be less intermittent and follow a
complementary error function distribution for larger separations.Comment: 16 pages, 3 figures, accepted for publication in European Journal of
Mechanics / B Fluid
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
Creeping motion of a solid particle inside a spherical elastic cavity
On the basis of the linear hydrodynamic equations, we present an analytical
theory for the low-Reynolds-number motion of a solid particle moving inside a
larger spherical elastic cavity which can be seen as a model system for a fluid
vesicle. In the particular situation where the particle is concentric with the
cavity, we use the stream function technique to find exact analytical solutions
of the fluid motion equations on both sides of the elastic cavity. In this
particular situation, we find that the solution of the hydrodynamic equations
is solely determined by membrane shear properties and that bending does not
play a role. For an arbitrary position of the solid particle within the
spherical cavity, we employ the image solution technique to compute the
axisymmetric flow field induced by a point force (Stokeslet). We then obtain
analytical expressions of the leading order mobility function describing the
fluid-mediated hydrodynamic interactions between the particle and confining
elastic cavity. In the quasi-steady limit of vanishing frequency, we find that
the particle self-mobility function is higher than that predicted inside a
rigid no-slip cavity. Considering the cavity motion, we find that the
pair-mobility function is determined only by membrane shear properties. Our
analytical predictions are supplemented and validated by fully-resolved
boundary integral simulations where a very good agreement is obtained over the
whole range of applied forcing frequencies.Comment: 15 pages, 5 figures, 90 references. To appear in Eur. Phys. J.
Hydrodynamic mobility of a solid particle nearby a spherical elastic membrane. II. Asymmetric motion
In this paper, we derive analytical expressions for the leading-order
hydrodynamic mobility of a small solid particle undergoing motion tangential to
a nearby large spherical capsule whose membrane possesses resistance towards
shearing and bending. Together with the results obtained in the first part
(Daddi-Moussa-Ider and Gekle, Phys. Rev. E {\bfseries 95}, 013108 (2017)) where
the axisymmetric motion perpendicular to the capsule membrane is considered,
the solution of the general mobility problem is thus determined. We find that
shearing resistance induces a low-frequency peak in the particle self-mobility,
resulting from the membrane normal displacement in the same way, although less
pronounced, to what has been observed for the axisymmetric motion. In the zero
frequency limit, the self-mobility correction near a hard sphere is recovered
only if the membrane has a non-vanishing resistance towards shearing. We
further compute the particle in-plane mean-square displacement of a nearby
diffusing particle, finding that the membrane induces a long-lasting
subdiffusive regime. Considering capsule motion, we find that the correction to
the pair-mobility function is solely determined by membrane shearing
properties. Our analytical calculations are compared and validated with fully
resolved boundary integral simulations where a very good agreement is obtained.Comment: 17 pages, 9 figures and 64 references. Manuscript accepted for
publication in Phys. Rev.
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.
Axisymmetric flow due to a Stokeslet near a finite-sized elastic membrane
Elastic confinements play an important role in many soft matter systems and
affect the transport properties of suspended particles in viscous flow. On the
basis of low-Reynolds-number hydrodynamics, we present an analytical theory of
the axisymmetric flow induced by a point-force singularity (Stokeslet) directed
along the symmetry axis of a finite-sized circular elastic membrane endowed
with resistance toward shear and bending. The solution for the viscous
incompressible flow surrounding the membrane is formulated as a mixed boundary
value problem, which is then reduced into a system of dual integral equations
on the inner and outer sides of the domain boundary. We show that the solution
of the elastohydrodynamic problem can conveniently be expressed in terms of a
set of inhomogeneous Fredholm integral equations of the second kind with
logarithmic kernel. Basing on the hydrodynamic flow field, we obtain
semi-analytical expressions of the hydrodynamic mobility function for the
translational motion perpendicular to a circular membrane. The results are
valid to leading-order in the ratio of particle radius to the distance
separating the particle from the membrane. In the quasi-steady limit, we find
that the particle mobility near a finite-sized membrane is always larger than
that predicted near a no-slip disk of the same size. We further show that the
bending-related contribution to the hydrodynamic mobility increases
monotonically upon decreasing the membrane size, whereas the shear-related
contribution displays a minimum value when the particle-membrane distance is
equal to the membrane radius. Accordingly, the system behavior may be shear or
bending dominated, depending on the geometric and elastic properties of the
system. Our results may find applications in the field of nanoparticle-based
sensing and drug delivery systems near elastic cell membranes
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
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