1,707 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 , 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 , 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
Fluid flow in drying drops
When a suspension drop evaporates, it leaves behind a drying stain. Examples of these drying stains encountered in daily life are coffee or tea stains on a table top, mineral rings on glassware that comes out of the dishwasher, or the salt deposits on the streets in winter. Drying stains are also present in industrial processes, for example in the printing and coating industry, where the non-uniform drying of drops can be a problem. Pattern formation by evaporation of colloidal suspension drops can however also be used as a tool to manufacture tiny structures on a scale where direct manipulation is not possible.\ud
In order to either prevent ring-stain formation or control the type of stains that are formed, one needs to understand the basic physics of evaporating drops and their internal fluid flow. In this thesis we focused on the fundamentals of drop evaporation, evaporation-driven flow in drying drops, and the subsequent particle transport and deposition. We used a simple model system: a macroscopic sessile water drop that evaporates under atmospheric conditions and contains spherical polystyrene particles. By evaporation of these colloidal suspension drops remarkable, highly-ordered drying patterns were obtained. The particle arrangement inside these patterns originates from a competition between particle diffusion and convection and therefore depends on the evaporation rate of the drop and the particle size
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 , 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
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
Drop deformation by laser-pulse impact
A free-falling absorbing liquid drop hit by a nanosecond laser-pulse
experiences a strong recoil-pressure kick. As a consequence, the drop propels
forward and deforms into a thin sheet which eventually fragments. We study how
the drop deformation depends on the pulse shape and drop properties. We first
derive the velocity field inside the drop on the timescale of the pressure
pulse, when the drop is still spherical. This yields the kinetic-energy
partition inside the drop, which precisely measures the deformation rate with
respect to the propulsion rate, before surface tension comes into play. On the
timescale where surface tension is important the drop has evolved into a thin
sheet. Its expansion dynamics is described with a slender-slope model, which
uses the impulsive energy-partition as an initial condition. Completed with
boundary integral simulations, this two-stage model explains the entire drop
dynamics and its dependance on the pulse shape: for a given propulsion, a
tightly focused pulse results in a thin curved sheet which maximizes the
lateral expansion, while a uniform illumination yields a smaller expansion but
a flat symmetric sheet, in good agreement with experimental observations.Comment: submitted to J. Fluid Mec
Solidification of liquid metal drops during impact
Hot liquid metal drops impacting onto a cold substrate solidify during their
subsequent spreading. Here we experimentally study the influence of
solidification on the outcome of an impact event. Liquid tin drops are impacted
onto sapphire substrates of varying temperature. The impact is visualised both
from the side and from below, which provides a unique view on the
solidification process. During spreading an intriguing pattern of radial
ligaments rapidly solidifies from the centre of the drop. This pattern
determines the late-time morphology of the splat. A quantitative analysis of
the drop spreading and ligament formation is supported by scaling arguments.
Finally, a phase diagram for drop bouncing, deposition and splashing as a
function of substrate temperature and impact velocity is provided
Drop Shaping by Laser-Pulse Impact
We show how the deposition of laser energy induces propulsion and strong
deformation of an absorbing liquid body. Combining high speed with stroboscopic
imaging, we observe that a millimeter-sized dyed water drop hit by a millijoule
nanosecond laser pulse propels forward at several meters per second and deforms
until it eventually fragments. The drop motion results from the recoil momentum
imparted at the drop surface by water vaporization. We measure the propulsion
speed and the time-deformation law of the drop, complemented by
boundary-integral simulations. The drop propulsion and shaping are explained in
terms of the laser-pulse energy, the drop size, and the liquid properties.
These findings are, for instance, crucial for the generation of extreme
ultraviolet light in nanolithography machines.Comment: Submitted as research article to Physical Review Applied, 6 pages
with 6 figure
- âŚ