96 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
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
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.
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
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