82 research outputs found
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 âcrownâ 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
âof lined cavitiesâ 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
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
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.
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.
Generation and Breakup of Worthington Jets After Cavity Collapse
Helped by the careful analysis of their experimental data, Worthington (1897)
described roughly the mechanism underlying the formation of high-speed jets
ejected after the impact of an axisymmetric solid on a liquid-air interface. In
this work we combine detailed boundary-integral simulations with analytical
modeling to describe the formation and break-up of such Worthington jets in two
common physical systems: the impact of a circular disc on a liquid surface and
the release of air bubbles from an underwater nozzle. We first show that the
jet base dynamics can be predicted for both systems using our earlier model in
Gekle, Gordillo, van der Meer and Lohse. Phys. Rev. Lett. 102 (2009).
Nevertheless, our main point here is to present a model which allows us to
accurately predict the shape of the entire jet. Good agreement with numerics
and some experimental data is found. Moreover, we find that, contrarily to the
capillary breakup of liquid cylinders in vacuum studied by Rayleigh, the
breakup of stretched liquid jets at high values of both Weber and Reynolds
numbers is not triggered by the growth of perturbations coming from an external
source of noise. Instead, the jet breaks up due to the capillary deceleration
of the liquid at the tip which produces a corrugation to the jet shape. This
perturbation, which is self-induced by the flow, will grow in time promoted by
a capillary mechanism. We are able to predict the exact shape evolution of
Worthington jets ejected after the impact of a solid object - including the
size of small droplets ejected from the tip due to a surface-tension driven
instability - using as the single input parameters the minimum radius of the
cavity and the flow field before the jet emerges
Analytic Solution to the Piecewise Linear Interface Construction Problem and its Application in Curvature Calculation for Volume-of-Fluid Simulation Codes
The plane-cube intersection problem has been around in literature since 1984
and iterative solutions to it have been used as part of piecewise linear
interface construction (PLIC) in computational fluid dynamics simulation codes
ever since. In many cases, PLIC is the bottleneck of these simulations
regarding compute time, so a faster, analytic solution to the plane-cube
intersection would greatly reduce compute time for such simulations. We derive
an analytic solution for all intersection cases and compare it to the one
previous solution from Scardovelli and Zaleski (Ruben Scardovelli and Stephane
Zaleski. "Analytical relations connecting linear interfaces and volume
fractions in rectangular grids". In: Journal of Computational Physics 164.1
(2000), pp. 228-237.), which we further improve to include edge cases and
micro-optimize to reduce arithmetic operations and branching. We then extend
our comparison regarding compute time and accuracy to include two different
iterative solutions as well. We find that the best choice depends on the
employed hardware platform: on the CPU, Newton-Raphson is fastest with
vectorization while analytic solutions perform better without. The reason for
this is that vectorization instruction sets do not include trigonometric
functions as used in the analytic solutions. On the GPU, the fastest method is
our optimized version of the analytic SZ solution. We finally provide details
on one of the applications of PLIC: curvature calculation for the
Volume-of-Fluid model used for free surface fluid simulations in combination
with the lattice Boltzmann method.Comment: 18 pages, 6 figure
Cross-stream transport of asymmetric particles driven by oscillating shear
We study the dynamics of asymmetric, deformable particles in oscillatory,
linear shear flow. By simulating the motion of a dumbbell, a ring polymer, and
a capsule we show that cross-stream migration occurs for asymmetric elastic
particles even in linear shear flow if the shear rate varies in time. The
migration is generic as it does not depend on the particle dimension.
Importantly, the migration velocity and migration direction are robust to
variations of the initial particle orientation, making our proposed scheme
suitable for sorting particles with asymmetric material properties.Comment: 5 pages, 4 figure
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