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Impact and spreading of microdrops on homo- and heterogeneous solids: Modelling and benchmark simulations
This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.The finite element framework developed for the high accuracy computation of dynamic wetting phenomena in Sprittles & Shikhmurzaev, Int. J. Num. Meth. Fluids 2011 is used to develop a code for the simulation of unsteady flows such as microdrop impact and spreading. The accuracy of the code for
describing free-surface flows is tested by comparing its results to those obtained in previous numerical studies for the large amplitude oscillations of free liquid drops in zero gravity. The capability of our code
to produce high resolution benchmark calculations for dynamic wetting flows, using either conventional modelling or the more sophisticated interface formation model, is demonstrated by simulating microdrop impact and spreading on surfaces of greatly differing wettability. The simulations allow one to see features of the drop shape which are beyond the resolution of experiments. Directions of our research programme that follows the presented study are outlined
Coalescence of Liquid Drops
When two drops of radius touch, surface tension drives an initially
singular motion which joins them into a bigger drop with smaller surface area.
This motion is always viscously dominated at early times. We focus on the
early-time behavior of the radius \rmn of the small bridge between the two
drops. The flow is driven by a highly curved meniscus of length 2\pi \rmn and
width \Delta\ll\rmn around the bridge, from which we conclude that the
leading-order problem is asymptotically equivalent to its two-dimensional
counterpart. An exact two-dimensional solution for the case of inviscid
surroundings [Hopper, J. Fluid Mech. , 349 (1990)] shows that
\Delta \propto \rmn^3 and \rmn \sim (t\gamma/\pi\eta)\ln [t\gamma/(\eta
R)]; and thus the same is true in three dimensions. The case of coalescence
with an external viscous fluid is also studied in detail both analytically and
numerically. A significantly different structure is found in which the outer
fluid forms a toroidal bubble of radius \Delta \propto \rmn^{3/2} at the
meniscus and \rmn \sim (t\gamma/4\pi\eta) \ln [t\gamma/(\eta R)]. This basic
difference is due to the presence of the outer fluid viscosity, however small.
With lengths scaled by a full description of the asymptotic flow for
\rmn(t)\ll1 involves matching of lengthscales of order \rmn^2, \rmn^{3/2},
\rmn\rmn^{7/4}$.Comment: 36 pages, including 9 figure
The Dynamics of Liquid Drops and their Interaction with Solids of Varying Wettabilites
Microdrop impact and spreading phenomena are explored as an interface
formation process using a recently developed computational framework. The
accuracy of the results obtained from this framework for the simulation of high
deformation free-surface flows is confirmed by a comparison with previous
numerical studies for the large amplitude oscillations of free liquid drops.
Our code's ability to produce high resolution benchmark calculations for
dynamic wetting flows is then demonstrated by simulating microdrop impact and
spreading on surfaces of greatly differing wettability. The simulations allow
one to see features of the process which go beyond the resolution available to
experimental analysis. Strong interfacial effects which are observed at the
microfluidic scale are then harnessed by designing surfaces of varying
wettability that allow new methods of flow control to be developed
Scaling Navier-Stokes Equation in Nanotubes
On one hand, classical Monte Carlo and molecular dynamics (MD) simulations
have been very useful in the study of liquids in nanotubes, enabling a wide
variety of properties to be calculated in intuitive agreement with experiments.
On the other hand, recent studies indicate that the theory of continuum breaks
down only at the nanometer level; consequently flows through nanotubes still
can be investigated with Navier-Stokes equations if we take suitable boundary
conditions into account. The aim of this paper is to study the statics and
dynamics of liquids in nanotubes by using methods of non-linear continuum
mechanics. We assume that the nanotube is filled with only a liquid phase; by
using a second gradient theory the static profile of the liquid density in the
tube is analytically obtained and compared with the profile issued from
molecular dynamics simulation. Inside the tube there are two domains: a thin
layer near the solid wall where the liquid density is non-uniform and a central
core where the liquid density is uniform. In the dynamic case a closed form
analytic solution seems to be no more possible, but by a scaling argument it is
shown that, in the tube, two distinct domains connected at their frontiers
still exist. The thin inhomogeneous layer near the solid wall can be
interpreted in relation with the Navier length when the liquid slips on the
boundary as it is expected by experiments and molecular dynamics calculations.Comment: 27 page
Minimal formulation of the linear spatial analysis of capillary jets: Validity of the two-mode approach
A rigorous and complete formulation of the linear evolution of harmonically stimulated
capillary jets should include infinitely many spatial modes to account for arbitrary exit
conditions [J. Guerrero et al., J. Fluid Mech. 702, 354 (2012)]. However, it is not rare to
find works in which only the downstream capillary dominant mode, the sole unstable one,
is retained, with amplitude determined by the jet deformation at the exit. This procedure
constitutes an oversimplification, unable to handle a flow rate perturbation without jet
deformation at the exit (the most usual conditions). In spite of its decaying behavior, the
other capillary mode (subdominant) must be included in what can be called a âminimal
linear formulation.â Deformation and mean axial velocity amplitudes at the jet exit are the
two relevant parameters to simultaneously find the amplitudes of both capillary modes.
Only once these amplitudes are found, the calculation of the breakup length may be
eventually simplified by disregarding the subdominant mode. Simple recipes are provided
for predicting the breakup length, which are checked against our own numerical simulations.
The agreement is better than in previous attempts in the literature. Besides, the limits of
validity of the linear formulation are explored in terms of the exit velocity amplitude, the
wave number, the Weber number, and the Ohnesorge number. Including the subdominant
mode extends the range of amplitudes for which the linear model gives accurate predictions,
the criterion for keeping this mode being that the breakup time must be shorter than a
given formula. It has been generally assumed that the shortest intact length happens for the
stimulation frequency with the highest growth rate. However, we show that this correlation
is not strict because the amplitude of the dominant mode has a role in the breakup process
and it depends on the stimulation frequency.Ministerio de EconomĂa, Industria y Competitividad, Spain, under Contract No. FIS2014-25161Junta de AndalucĂa under Contract No. P11-FQM-791
Singularities on charged viscous droplets
We study the evolution of charged droplets of a conducting viscous liquid.
The flow is driven by electrostatic repulsion and capillarity. These droplets
are known to be linearly unstable when the electric charge is above the
Rayleigh critical value. Here we investigate the nonlinear evolution that
develops after the linear regime. Using a boundary elements method, we find
that a perturbed sphere with critical charge evolves into a fusiform shape with
conical tips at time , and that the velocity at the tips blows up as
, with close to -1/2. In the neighborhood of the
singularity, the shape of the surface is self-similar, and the asymptotic angle
of the tips is smaller than the opening angle in Taylor cones.Comment: 9 pages, 6 figure
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