638 research outputs found
Dual mechanism model for fluid particle breakup in the entire turbulent spectrum
This work provides an in-depth understanding of different breakup mechanisms for fluid particles in turbulent flows. All the disruptive and cohesive stresses are considered for the entire turbulent energy spectrum and their contributions to the breakup are evaluated. A new modeling framework is presented that bridges across turbulent subranges. The model entails different mechanisms for breakup by abandoning the classical limitation of inertial models. The predictions are validated with experiments encompassing both breakup regimes for droplets stabilized by internal viscosity and interfacial tension down to the micrometer length scale, which covers both the inertial and dissipation subranges. The model performance ensures the reliability of the framework, which involves different mechanisms. It retains the breakup rate for inertial models, improves the predictions for the transition region from inertia to dissipation, and bridges seamlessly to Kolmogorov-sized droplets
Concurrent factors determine toughening in the hydraulic fracture of poroelastic composites
Brittle materials fail catastrophically. In consequence of their limited flaw-tolerance, failure occurs by localized fracture and is typically a dynamic process. Recently, experiments on epithelial cell monolayers have revealed that this scenario can be significantly modified when the material susceptible to cracking is adhered to a hydrogel substrate. Thanks to the hydraulic coupling between the brittle layer and the poroelastic substrate, such a composite can develop a toughening mechanism that relies on the simultaneous growth of multiple cracks. Here, we study this remarkable behaviour by means of a detailed model, and explore how the material and loading parameters concur in determining the macroscopic toughness of the system. By extending a previous study, our results show that rapid loading conveys material toughness by promoting distributed cracking. Moreover, our theoretical findings may suggest innovative architectures of flaw-insensitive materials with higher toughness. ArXI
Efficient Mixing at low Reynolds numbers using polymer additives
Mixing in fluids is a rapidly developing field of fluid mechanics
\cite{Sreen,Shr,War}, being an important industrial and environmental problem.
The mixing of liquids at low Reynolds numbers is usually quite weak in simple
flows, and it requires special devices to be efficient. Recently, the problem
of mixing was solved analytically for a simple case of random flow, known as
the Batchelor regime \cite{Bat,Kraich,Fal,Sig,Fouxon}. Here we demonstrate
experimentally that very viscous liquids at low Reynolds number, . Here we
show that very viscous liquids containing a small amount of high molecular
weight polymers can be mixed quite efficiently at very low Reynolds numbers,
for a simple flow in a curved channel. A polymer concentration of only 0.001%
suffices. The presence of the polymers leads to an elastic instability
\cite{LMS} and to irregular flow \cite{Ours}, with velocity spectra
corresponding to the Batchelor regime \cite{Bat,Kraich,Fal,Sig,Fouxon}. Our
detailed observations of the mixing in this regime enable us to confirm sevearl
important theoretical predictions: the probability distributions of the
concentration exhibit exponential tails \cite{Fal,Fouxon}, moments of the
distribution decay exponentially along the flow \cite{Fouxon}, and the spatial
correlation function of concentration decays logarithmically.Comment: 11 pages, 5 figure
Monolithic simulation of convection-coupled phase-change - verification and reproducibility
Phase interfaces in melting and solidification processes are strongly
affected by the presence of convection in the liquid. One way of modeling their
transient evolution is to couple an incompressible flow model to an energy
balance in enthalpy formulation. Two strong nonlinearities arise, which account
for the viscosity variation between phases and the latent heat of fusion at the
phase interface.
The resulting coupled system of PDE's can be solved by a single-domain
semi-phase-field, variable viscosity, finite element method with monolithic
system coupling and global Newton linearization. A robust computational model
for realistic phase-change regimes furthermore requires a flexible
implementation based on sophisticated mesh adaptivity. In this article, we
present first steps towards implementing such a computational model into a
simulation tool which we call Phaseflow.
Phaseflow utilizes the finite element software FEniCS, which includes a
dual-weighted residual method for goal-oriented adaptive mesh refinement.
Phaseflow is an open-source, dimension-independent implementation that, upon an
appropriate parameter choice, reduces to classical benchmark situations
including the lid-driven cavity and the Stefan problem. We present and discuss
numerical results for these, an octadecane PCM convection-coupled melting
benchmark, and a preliminary 3D convection-coupled melting example,
demonstrating the flexible implementation. Though being preliminary, the latter
is, to our knowledge, the first published 3D result for this method. In our
work, we especially emphasize reproducibility and provide an easy-to-use
portable software container using Docker.Comment: 20 pages, 8 figure
Time-Energy Tradeoffs for Evacuation by Two Robots in the Wireless Model
Two robots stand at the origin of the infinite line and are tasked with
searching collaboratively for an exit at an unknown location on the line. They
can travel at maximum speed and can change speed or direction at any time.
The two robots can communicate with each other at any distance and at any time.
The task is completed when the last robot arrives at the exit and evacuates. We
study time-energy tradeoffs for the above evacuation problem. The evacuation
time is the time it takes the last robot to reach the exit. The energy it takes
for a robot to travel a distance at speed is measured as . The
total and makespan evacuation energies are respectively the sum and maximum of
the energy consumption of the two robots while executing the evacuation
algorithm.
Assuming that the maximum speed is , and the evacuation time is at most
, where is the distance of the exit from the origin, we study the
problem of minimizing the total energy consumption of the robots. We prove that
the problem is solvable only for . For the case , we give an
optimal algorithm, and give upper bounds on the energy for the case .
We also consider the problem of minimizing the evacuation time when the
available energy is bounded by . Surprisingly, when is a
constant, independent of the distance of the exit from the origin, we prove
that evacuation is possible in time , and this is optimal up
to a logarithmic factor. When is linear in , we give upper bounds
on the evacuation time.Comment: This is the full version of the paper with the same title which will
appear in the proceedings of the 26th International Colloquium on Structural
Information and Communication Complexity (SIROCCO'19) L'Aquila, Italy during
July 1-4, 201
The numerical control of the motion of a passive particle in a point vortex flow
This work reports numerical explorations in the advection of one passive tracer by point vortices
living in the unbounded plane. The main objective is to find the energy-optimal displacement
of one passive particle (point vortex with zero circulation) surrounded by N point vortices. The
direct formulation of the corresponding control problems is presented for the case of N = 1, N = 2,
N = 3 and N = 4 vortices. The restrictions are due to (i) the ordinary differential equations that
govern the displacement of the passive particle around the point vortices, (ii) the available time
T to go from the initial position z0 to the final destination zf; and (iii) the maximum absolute
value umax that is imposed on the control variables. The resulting optimization problems are
solved numerically. The numerical results show the existence of nearly/quasi-optimal control.info:eu-repo/semantics/publishedVersio
Forces between clustered stereocilia minimize friction in the ear on a subnanometre scale
The detection of sound begins when energy derived from acoustic stimuli
deflects the hair bundles atop hair cells. As hair bundles move, the viscous
friction between stereocilia and the surrounding liquid poses a fundamental
challenge to the ear's high sensitivity and sharp frequency selectivity. Part
of the solution to this problem lies in the active process that uses energy for
frequency-selective sound amplification. Here we demonstrate that a
complementary part involves the fluid-structure interaction between the liquid
within the hair bundle and the stereocilia. Using force measurement on a
dynamically scaled model, finite-element analysis, analytical estimation of
hydrodynamic forces, stochastic simulation and high-resolution interferometric
measurement of hair bundles, we characterize the origin and magnitude of the
forces between individual stereocilia during small hair-bundle deflections. We
find that the close apposition of stereocilia effectively immobilizes the
liquid between them, which reduces the drag and suppresses the relative
squeezing but not the sliding mode of stereociliary motion. The obliquely
oriented tip links couple the mechanotransduction channels to this least
dissipative coherent mode, whereas the elastic horizontal top connectors
stabilize the structure, further reducing the drag. As measured from the
distortion products associated with channel gating at physiological stimulation
amplitudes of tens of nanometres, the balance of forces in a hair bundle
permits a relative mode of motion between adjacent stereocilia that encompasses
only a fraction of a nanometre. A combination of high-resolution experiments
and detailed numerical modelling of fluid-structure interactions reveals the
physical principles behind the basic structural features of hair bundles and
shows quantitatively how these organelles are adapted to the needs of sensitive
mechanotransduction.Comment: 21 pages, including 3 figures. For supplementary information, please
see the online version of the article at http://www.nature.com/natur
Fluid Particle Accelerations in Fully Developed Turbulence
The motion of fluid particles as they are pushed along erratic trajectories
by fluctuating pressure gradients is fundamental to transport and mixing in
turbulence. It is essential in cloud formation and atmospheric transport,
processes in stirred chemical reactors and combustion systems, and in the
industrial production of nanoparticles. The perspective of particle
trajectories has been used successfully to describe mixing and transport in
turbulence, but issues of fundamental importance remain unresolved. One such
issue is the Heisenberg-Yaglom prediction of fluid particle accelerations,
based on the 1941 scaling theory of Kolmogorov (K41). Here we report
acceleration measurements using a detector adapted from high-energy physics to
track particles in a laboratory water flow at Reynolds numbers up to 63,000. We
find that universal K41 scaling of the acceleration variance is attained at
high Reynolds numbers. Our data show strong intermittency---particles are
observed with accelerations of up to 1,500 times the acceleration of gravity
(40 times the root mean square value). Finally, we find that accelerations
manifest the anisotropy of the large scale flow at all Reynolds numbers
studied.Comment: 7 pages, 4 figure
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