139 research outputs found
Boundary elements method for microfluidic two-phase flows in shallow channels
In the following work we apply the boundary element method to two-phase flows
in shallow microchannels, where one phase is dispersed and does not wet the
channel walls. These kinds of flows are often encountered in microfluidic
Lab-on-a-Chip devices and characterized by low Reynolds and low capillary
numbers.
Assuming that these channels are homogeneous in height and have a large
aspect ratio, we use depth-averaged equations to describe these two-phase flows
using the Brinkman equation, which constitutes a refinement of Darcy's law.
These partial differential equations are discretized and solved numerically
using the boundary element method, where a stabilization scheme is applied to
the surface tension terms, allowing for a less restrictive time step at low
capillary numbers. The convergence of the numerical algorithm is checked
against a static analytical solution and on a dynamic test case. Finally the
algorithm is applied to the non-linear development of the Saffman-Taylor
instability and compared to experimental studies of droplet deformation in
expanding flows.Comment: accepted for publication, Computers and Fluids 201
Viscous Taylor droplets in axisymmetric and planar tubes: from Bretherton's theory to empirical models
The aim of this study is to derive accurate models for quantities
characterizing the dynamics of droplets of non-vanishing viscosity in
capillaries. In particular, we propose models for the uniform-film thickness
separating the droplet from the tube walls, for the droplet front and rear
curvatures and pressure jumps, and for the droplet velocity in a range of
capillary numbers, , from to and inner-to-outer viscosity
ratios, , from , i.e. a bubble, to high viscosity droplets.
Theoretical asymptotic results obtained in the limit of small capillary number
are combined with accurate numerical simulations at larger . With these
models at hand, we can compute the pressure drop induced by the droplet. The
film thickness at low capillary numbers () agrees well with
Bretherton's scaling for bubbles as long as . For larger viscosity
ratios, the film thickness increases monotonically, before saturating for
to a value times larger than the film thickness of a
bubble. At larger capillary numbers, the film thickness follows the rational
function proposed by Aussillous \& Qu\'er\'e (2000) for bubbles, with a fitting
coefficient which is viscosity-ratio dependent. This coefficient modifies the
value to which the film thickness saturates at large capillary numbers. The
velocity of the droplet is found to be strongly dependent on the capillary
number and viscosity ratio. We also show that the normal viscous stresses at
the front and rear caps of the droplets cannot be neglected when calculating
the pressure drop for
Edge states control droplet break-up in sub-critical extensional flows
A fluid droplet suspended in an extensional flow of moderate intensity may
break into pieces, depending on the amplitude of the initial droplet
deformation. In subcritical uniaxial extensional flow the non-breaking base
state is linearly stable, implying that only a finite amplitude perturbation
can trigger break-up. Consequently, the stable base solution is surrounded by
its finite basin of attraction. The basin boundary, which separates initial
droplet shapes returning to the non-breaking base state from those becoming
unstable and breaking up, is characterized using edge tracking techniques. We
numerically construct the edge state, a dynamically unstable equilibrium whose
stable manifold forms the basin boundary. The edge state equilibrium controls
if the droplet breaks and selects a unique path towards break-up. This path
physically corresponds to the well-known end-pinching mechanism. Our results
thereby rationalize the dynamics observed experimentally [Stone & Leal, J.
Fluid Mech. 206, 223 (1989)
A unified criterion for the centrifugal instabilities of vortices and swirling jets
Swirling jets and vortices can both be unstable to the centrifugal instability but with a different wavenumber selection: the most unstable perturbations for swirling jets in inviscid fluids have an infinite azimuthal wavenumber, whereas, for vortices, they are axisymmetric but with an infinite axial wavenumber. Accordingly, sufficient condition for instability in inviscid fluids have been derived asymptotically in the limits of large azimuthal wavenumber for swirling jets (Leibovich and Stewartson, J. Fluid Mech., vol. 126, 1983, pp. 335-356) and large dimensionless axial wavenumber for vortices (Billant and Gallaire, J. Fluid Mech., vol. 542, 2005, pp. 365-379). In this paper, we derive a unified criterion valid whatever the magnitude of the axial flow by performing an asymptotic analysis for large total wavenumber . The new criterion recovers the criterion of Billant and Gallaire when the axial flow is small and the Leibovich and Stewartson criterion when the axial flow is finite and its profile sufficiently different from the angular velocity profile. When the latter condition is not satisfied, it is shown that the accuracy of the Leibovich and Stewartson asymptotics is strongly reduced. The unified criterion is validated by comparisons with numerical stability analyses of various classes of swirling jet profiles. In the case of the Batchelor vortex, it provides accurate predictions over a wider range of axial wavenumbers than the Leibovich-Stewartson criterion. The criterion shows also that a whole range of azimuthal wavenumbers are destabilized as soon as a small axial velocity component is present in a centrifugally unstable vorte
A new prediction of wavelength selection in radial viscous fingering involving normal and tangential stresses
We reconsider the radial Saffman-Taylor instability, when a fluid injected
from a point source displaces another fluid with a higher viscosity in a
Hele-Shaw cell, where the fluids are confined between two neighboring flat
plates. The advancing fluid front is unstable and forms fingers along the
circumference. The so-called Brinkman equations is used to describe the flow
field, which also takes into account viscous stresses in the plane and not only
viscous stresses due to the confining plates like the Darcy equation. The
dispersion relation agrees better with the experimental results than the
classical linear stability analysis of radial fingering in Hele-Shaw cells that
uses Darcy's law as a model for the fluid motion
Three-dimensional instability of isolated vortices
International audienceWe study the three-dimensional stability of the family of vortices introduced by Carton and McWilliams [Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence, edited by Nikhoul and Jamart (Elsevier, New York, 1989)] describing isolated vortices. For these vortices, the circulation vanishes outside their core over a distance depending on a single parameter, the steepness a. We proceed to the direct numerical simulation of the linear impulse response to obtain both temporal and spatio-temporal instability results. In the temporal instability framework, growth rates are calculated as a function of the axial wavenumber k and the azimuthal wavenumber m. The stability analysis is performed at a Reynolds number of Re=667. It is shown that the most unstable mode is the axisymmetric mode m=0, regardless of the steepness parameter in the investigated range. When the steepness a is increased the band of unstable azimuthal modes widens, i.e., larger m are destabilized. The study of the spatio-temporal spreading of the wave packet shows that the m=2 mode is always the fastest traveling mode, for all studied values of the steepness parameter. © 2003 American Institute of Physics
Unraveling radial dependency effects in fiber thermal drawing
Fiber-based devices with advanced functionalities are emerging as promising
solutions for various applications in flexible electronics and bioengineering.
Multimaterial thermal drawing, in particular, has attracted strong interest for
its ability to generate fibers with complex architectures. Thus far, however,
the understanding of its fluid dynamics has only been applied to single
material preforms for which higher order effects, such as the radial dependency
of the axial velocity, could be neglected. With complex multimaterial preforms,
such effects must be taken into account, as they can affect the architecture
and the functional properties of the resulting fiber device. Here, we propose a
versatile model of the thermal drawing of fibers, which takes into account a
radially varying axial velocity. Unlike the commonly used cross section
averaged approach, our model is capable of predicting radial variations of
functional properties caused by the deformation during drawing. This is
demonstrated for two effects observed, namely, by unraveling the deformation of
initially straight, transversal lines in the preform and the dependence on the
draw ratio and radial position of the in-fiber electrical conductivity of
polymer nanocomposites, an important class of materials for emerging fiber
devices. This work sets a thus far missing theoretical and practical
understanding of multimaterial fiber processing to better engineer advanced
fibers and textiles for sensing, health care, robotics, or bioengineering
applications
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