752 research outputs found
Compressible air flow through a collapsing liquid cavity
We present a multiscale approach to simulate the impact of a solid object on
a liquid surface: upon impact a thin liquid sheet is thrown upwards all around
the rim of the impactor while in its wake a large surface cavity forms. Under
the influence of hydrostatic pressure the cavity immediately starts to collapse
and eventually closes in a single point from which a thin, needle-like jet is
ejected. Existing numerical treatments of liquid impact either consider the
surrounding air as an incompressible fluid or neglect air effects altogether.
In contrast, our approach couples a boundary-integral method for the liquid
with a Roe scheme for the gas domain and is thus able to handle the fully
\emph{compressible} gas stream that is pushed out of the collapsing impact
cavity. Taking into account air compressibility is crucial, since, as we show
in this work, the impact crater collapses so violently that the air flow
through the cavity neck attains supersonic velocities already at cavity
diameters larger than 1 mm. Our computational results are validated through
corresponding experimental data.Comment: Submitted to Comput Mec
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
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
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
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.
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.
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
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.
Impact on liquids : void collapse and jet formation
A spectacular example of free surface flow is the impact of a solid object on a liquid: At\ud
impact a “crown” splash is created and a surface cavity (void) emerges which\ud
immediately starts to collapse due to the hydrostatic pressure of the surrounding liquid.\ud
Eventually the cavity closes in a single point about halfway down its length and shoots\ud
out a fast and extremely slender water jet. Here we impact thin circular discs a few\ud
centimeters in radius with velocities of a few meters per second. Combining high-speed\ud
imaging with sophisticated boundary-integral simulations we elucidate various aspects of\ud
this fascinating process.\ud
First we show that the mechanism behind the formation of the fast, almost needle-like\ud
liquid jet is reminiscent of the violent jets of fluidized metal created during the explosion\ud
“of lined cavities” in military and mining operations. We obtain quantitative agreement\ud
between our simulations, experiments, and analytical model.\ud
Next we use visualization experiments to measure the air flow as it is squeezed out of\ud
the shrinking impact cavity. Together with numerical simulations we show that even in\ud
our simple system of a 2 cm disc impacting at merely 1 m/s the air flow easily attains\ud
supersonic velocities.\ud
A long-standing controversy in the fluid dynamics community has been until recently the\ud
pinch-off behavior of a bubble inside a liquid. Our observation of different time scales for\ud
the onset of the predicted final regime reconciles the different views expressed in recent literature about bubble pinch-off.\ud
Next we replace the impacting disc by a long, smooth cylinder and find that the closure\ud
position of the cavity displays distinct regimes separated by discrete jumps which are\ud
consistently observed in experiment and numerical simulations.\ud
Finally, we simulate the collapse of nanobubbles nucleating from small (50 nm) pits\ud
drilled into a silicon wafer. We find that just prior to final collapse a jet very similar in\ud
appearance to those after solid object impact forms and penetrates deep into the hole
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