455 research outputs found
Theory of the collapsing axisymmetric cavity
We investigate the collapse of an axisymmetric cavity or bubble inside a
fluid of small viscosity, like water. Any effects of the gas inside the cavity
as well as of the fluid viscosity are neglected. Using a slender-body
description, we show that the minimum radius of the cavity scales like , where is the time from collapse. The exponent
very slowly approaches a universal value according to . Thus, as observed in a number of recent experiments, the
scaling can easily be interpreted as evidence of a single non-trivial scaling
exponent. Our predictions are confirmed by numerical simulations
Additive Equivalence in Turbulent Drag Reduction by Flexible and Rodlike Polymers
We address the "Additive Equivalence" discovered by Virk and coworkers: drag
reduction affected by flexible and rigid rodlike polymers added to turbulent
wall-bounded flows is limited from above by a very similar Maximum Drag
Reduction (MDR) asymptote. Considering the equations of motion of rodlike
polymers in wall-bounded turbulent ensembles, we show that although the
microscopic mechanism of attaining the MDR is very different, the macroscopic
theory is isomorphic, rationalizing the interesting experimental observations.Comment: 8 pages, PRE, submitte
Experimental and numerical investigations of flow structure and momentum transport in a turbulent buoyancy-driven flow inside a tilted tube.
Buoyancy-driven turbulent mixing of fluids of slightly different densities [At = Δρ/(2〈ρ〉) = 1.15×10−2] in a long circular tube tilted at an angle θ = 15° from the vertical is studied at the local scale, both experimentally from particle image velocimetry and laser induced fluorescence measurements in the vertical diametrical plane and numerically throughout the tube using direct numerical simulation. In a given cross section of the tube, the axial mean velocity and the mean concentration both vary linearly with the crosswise distance z from the tube axis in the central 70% of the diameter. A small crosswise velocity component is detected in the measurement plane and is found to result from a four-cell mean secondary flow associated with a nonzero streamwise component of the vorticity. In the central region of the tube cross section, the intensities of the three turbulent velocity fluctuations are found to be strongly different, that of the streamwise fluctuation being more than twice larger than that of the spanwise fluctuation which itself is about 50% larger than that of the crosswise fluctuation. This marked anisotropy indicates that the turbulent structure is close to that observed in homogeneous turbulent shear flows. Still in the central region, the turbulent shear stress dominates over the viscous stress and reaches a maximum on the tube axis. Its crosswise variation is approximately accounted for by a mixing length whose value is about one-tenth of the tube diameter. The momentum exchange in the core of the cross section takes place between its lower and higher density parts and there is no net momentum exchange between the core and the near-wall regions. A sizable part of this transfer is due both to the mean secondary flow and to the spanwise turbulent shear stress. Near-wall regions located beyond the location of the extrema of the axial velocity (|z|≳0.36 d) are dominated by viscous stresses which transfer momentum toward (from) the wall near the top (bottom) of the tube
Void elimination in screen printed thick film dielectric pastes
The problem is to understand the mechanisms for the formation and evolution of defects in wet screen printed layers. The primary objective is to know how best to alter the properties of the paste (rather than the geometry of the screen printing process itself) in order to eliminate the defects.
With these goals in mind the work done during the Study Group reported here was as follows; to describe a simple model for the closure of craters, a model for the partial closure of vias, a possible mechanism for the formation of pinholes and finally a more detailed consideration of the screen printing process
Stress balance in nano-patterned N/Cu(001) surfaces
We employ helium atom scattering (HAS) and density functional theory (DFT)
based on the ultrasoft pseudopotential scheme and the plane-wave basis set to
investigate the strain and stress balance in nano-patterned N/Cu(001) surfaces.
HAS shows that, with increasing N coverage (and decreasing stripe widths), the
stress-relief-driven lateral expansion of the averaged lattice parameter within
finite-sized N-containing patches reduces from 3.5% to 1.8% and that, beyond a
critical exposure, the lateral expansion of the patches increases again
slightly, to 2.4%. The latter implies that in this higher coverage range the
compressive stress is partially relieved via another mechanism, which turns out
to be nucleation of Cu-vacancy trenches. In full agreement with the above and
previous experimental observations, DFT calculations show that an optimized
N-induced c(2\times2) structure has a net surface stress level of 4.2 N/m and
such stress is effectively relieved when stripes of clean Cu(001) form along
the direction or when trench-like steps of Cu atoms form along the
direction. Additionally, the calculations demonstrate that (contrary to earlier
suggestions) rumpling displacements within the outermost Cu layer do not act to
relieve the compressive surface stress levels and that, while clock-like
displacements could relieve stress levels, such displacements are energetically
unstable
Micro-Capsules in Shear Flow
This paper deals with flow-induced shape transitions of elastic capsules. The
state of the art concerning both theory and experiments is briefly reviewed
starting with dynamically induced small deformation of initially spherical
capsules and the formation of wrinkles on polymerized membranes. Initially
non-spherical capsules show tumbling and tank-treading motion in shear flow.
Theoretical descriptions of the transition between these two types of motion
assuming a fixed shape are at variance with the full capsule dynamics obtained
numerically. To resolve the discrepancy, we expand the exact equations of
motion for small deformations and find that shape changes play a dominant role.
We classify the dynamical phase transitions and obtain numerical and analytical
results for the phase boundaries as a function of viscosity contrast, shear and
elongational flow rate. We conclude with perspectives on timedependent flow, on
shear-induced unbinding from surfaces, on the role of thermal fluctuations, and
on applying the concepts of stochastic thermodynamics to these systems.Comment: 34 pages, 15 figure
A new model for simulating colloidal dynamics
We present a new hybrid lattice-Boltzmann and Langevin molecular dynamics
scheme for simulating the dynamics of suspensions of spherical colloidal
particles. The solvent is modeled on the level of the lattice-Boltzmann method
while the molecular dynamics is done for the solute. The coupling between the
two is implemented through a frictional force acting both on the solvent and on
the solute, which depends on the relative velocity. A spherical colloidal
particle is represented by interaction sites at its surface. We demonstrate
that this scheme quantitatively reproduces the translational and rotational
diffusion of a neutral spherical particle in a liquid and show preliminary
results for a charged spherical particle. We argue that this method is
especially advantageous in the case of charged colloids.Comment: For a movie click on the link below Fig
Brewing of filter coffee
We report progress on mathematical modelling of coffee grounds in a drip filter coffee machine. The report focuses on the evolution of the shape of the bed of coffee grounds during extraction with some work also carried out on the chemistry of extraction. This work was sponsored by Philips who are interested in understanding an observed correlation between the final shape of the coffee grounds and the quality of the coffee. We used experimental data gathered by Philips and ourselves to identify regimes in the coffee brewing process and relevant regions of parameter space. Our work makes it clear that a number of separate processes define the shape of the coffee bed depending on the values of the parameters involved e.g. the size of the grains and the speed of fluid flow during extraction. We began work on constructing mathematical models of the redistribution of the coffee grounds specialised to each region and on a model of extraction. A variety of analytic and numerical tools were used. Furthermore our research has progressed far enough to allow us to begin to exploit connections between this problem and other areas of science, in particular the areas of sedimentology and geomorphology, where the processes we have observed in coffee brewing have been studied
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