111 research outputs found

### Stokes flow near the contact line of an evaporating drop

The evaporation of sessile drops in quiescent air is usually governed by
vapour diffusion. For contact angles below $90^\circ$, the evaporative flux
from the droplet tends to diverge in the vicinity of the contact line.
Therefore, the description of the flow inside an evaporating drop has remained
a challenge. Here, we focus on the asymptotic behaviour near the pinned contact
line, by analytically solving the Stokes equations in a wedge geometry of
arbitrary contact angle. The flow field is described by similarity solutions,
with exponents that match the singular boundary condition due to evaporation.
We demonstrate that there are three contributions to the flow in a wedge: the
evaporative flux, the downward motion of the liquid-air interface and the
eigenmode solution which fulfils the homogeneous boundary conditions. Below a
critical contact angle of $133.4^\circ$, the evaporative flux solution will
dominate, while above this angle the eigenmode solution dominates. We
demonstrate that for small contact angles, the velocity field is very
accurately described by the lubrication approximation. For larger contact
angles, the flow separates into regions where the flow is reversing towards the
drop centre.Comment: Journal of Fluid Mechanics 709 (2012

### Stokes flow in a drop evaporating from a liquid subphase

The evaporation of a drop from a liquid subphase is investigated. The two
liquids are immiscible, and the contact angles between them are given by the
Neumann construction. The evaporation of the drop gives rise to flows in both
liquids, which are coupled by the continuity of velocity and shear-stress
conditions. We derive self-similar solutions to the velocity fields in both
liquids close to the three-phase contact line, where the drop geometry can be
approximated by a wedge. We focus on the case where Marangoni stresses are
negligible, for which the flow field consists of three contributions: flow
driven by the evaporative flux from the drop surface, flow induced by the
receding motion of the contact line, and an eigenmode flow that satisfies the
homogeneous boundary conditions. The eigenmode flow is asymptotically
subdominant for all contact angles. The moving contact-line flow dominates when
the angle between the liquid drop and the horizontal surface of the liquid
subphase is smaller than $90^\circ$, while the evaporative-flux driven flow
dominates for larger angles. A parametric study is performed to show how the
velocity fields in the two liquids depend on the contact angles between the
liquids and their viscosity ratio.Comment: submitted to Physics of Fluid

### Droplet deformation by short laser-induced pressure pulses

When a free-falling liquid droplet is hit by a laser it experiences a strong
ablation driven pressure pulse. Here we study the resulting droplet deformation
in the regime where the ablation pressure duration is short, i.e. comparable to
the time scale on which pressure waves travel through the droplet. To this end
an acoustic analytic model for the pressure-, pressure impulse- and velocity
fields inside the droplet is developed in the limit of small density
fluctuations. This model is used to examine how the droplet deformation depends
on the pressure pulse duration while the total momentum to the droplet is kept
constant. Within the limits of this analytic model, we demonstrate that when
the total momentum transferred to the droplet is small the droplet
shape-evolution is indistinguishable from an incompressible droplet
deformation. However, when the momentum transfer is increased the droplet
response is strongly affected by the pulse duration. In this later regime,
compressed flow regimes alter the droplet shape evolution considerably.Comment: Submitted to JF

### Avalanche of particles in evaporating coffee drops

The pioneering work of Deegan et al. [Nature 389, (1997)] showed how a drying
sessile droplet suspension of particles presents a maximum evaporating flux at
its contact line which drags liquid and particles creating the well known
coffee stain ring. In this Fluid Dynamics Video, measurements using micro
Particle Image Velocimetry and Particle Tracking clearly show an avalanche of
particles being dragged in the last moments, for vanishing contact angles and
droplet height. This explains the different characteristic packing of the
particles in the layers of the ring: the outer one resembles a crystalline
array, while the inner one looks more like a jammed granular fluid. Using the
basic hydrodynamic model used by Deegan et al. [Phys. Rev. E 62, (2000)] it
will be shown how the liquid radial velocity diverges as the droplet life comes
to an end, yielding a good comparison with the experimental data.Comment: This entry contains a Fluid Dynamics Video candidate for the Gallery
of Fluid Motion 2011 and a brief article with informatio

### Order-to-disorder transition in ring-shaped colloidal stains

A colloidal dispersion droplet evaporating from a surface, such as a drying
coffee drop, leaves a distinct ring-shaped stain. Although this mechanism is
frequently used for particle self-assembly, the conditions for crystallization
have remained unclear. Our experiments with monodisperse colloidal particles
reveal a structural transition in the stain, from ordered crystals to
disordered packings. We show that this sharp transition originates from a
temporal singularity of the flow velocity inside the evaporating droplet at the
end of its life. When the deposition speed is low, particles have time to
arrange by Brownian motion, while at the end, high-speed particles are jammed
into a disordered phase.Comment: accepted for PR

### Laser-to-droplet alignment sensitivity relevant for laser-produced plasma sources of extreme ultraviolet light

We present and experimentally validate a model describing the sensitivity of
the tilt angle, expansion and propulsion velocity of a tin micro-droplet
irradiated by a 1 {\mu}m Nd:YAG laser pulse to its relative alignment. This
sensitivity is particularly relevant in industrial plasma sources of extreme
ultraviolet light for nanolithographic applications. Our model has but a single
parameter: the dimensionless ratio of the laser spot size to the effective size
of the droplet, which is related to the position of the plasma critical density
surface. Our model enables the development of straightforward scaling arguments
in turn enabling precise control the alignment sensitivity.Comment: 7 pages, 5 figure

### Oscillations of a gas pocket on a liquid-covered solid surface

The dynamic response of a gas bubble entrapped in a cavity on the surface of
a submerged solid subject to an acoustic field is investigated in the linear
approximation. We derive semi-analytical expressions for the resonance
frequency, damping and interface shape of the bubble. For the liquid phase, we
consider two limit cases: potential flow and unsteady Stokes flow. The
oscillation frequency and interface shape are found to depend on two
dimensionless parameters: the ratio of the gas stiffness to the surface tension
stiffness, and the Ohnesorge number, representing the relative importance of
viscous forces. We perform a parametric study and show, among others, that an
increase in the gas pressure or a decrease in the surface tension leads to an
increase in the resonance frequency until an asymptotic value is reached

- …