Impact of Microdrops on Solids

1
Impact of Microdrops on Solids
James Sprittles Yulii Shikhmurzaev
Typical microdrop simulation (blue) compared to
experiment (black).
Interface formation - qualitatively Fluid
particles are advected through the contact line
from the liquid-gas to the liquid-solid
interface. Near the contact line the interface
is out of equilibrium and, notably, the surface
tension takes finite time/distance to relax to
its new equilibrium value see figure 6.

• Recent experiments show that all current models
  of drop impact and spreading
  are fundamentally flawed.
• The error will be considerable for the micron
  scale drops encountered in ink-jet printing.
• We are developing a universal computational
  platform, implementing a new model, to describe
  such experiments.

Liquid
Gas
Solid
6. Sketch of flow in the contact line region
showing how surface tension relaxes over a finite
distance.
To model this process surface variables are
introduced, the surface density and the
surface velocity .
Governing equations
Problem formulation
In the bulk
Incompressible Navier-Stokes
On free surfaces
On liquid-solid interfaces
Kinematic
Normal and tangential stress
Generalised Navier
Normal velocity
Surface equation of state
Darcy type eqn.
U, m/s
1. Sketch of a spreading droplet.
Surface mass continuity
At contact lines
2. Contact angle-speed plot for 2 mm water
droplets impacting at different Weber number
based on impact speed (Bayer Megaridis 06) .
Mass balance
Failure of conventional models All existing
models are based on the contact angle being a
function of the contact line speed and material
properties The experimental investigations of
both Bayer Megaridis 06 and Sikalo et al 02
using millimetre sized drops have shown this
assumption incorrect see figure 2.
Additionally, conventional models predict an
infinite pressure at the contact line and/or the
incorrect kinematics there, see Shikhmurzaev
2007.
Young equation
Computational We are developing a multi-purpose
finite element code extending the spine method
devised by Ruschak then improved by Scriven and
co-workers. This is capable of simulating
flows where the standard approach fails, such as
pinch-off of liquid drops and coalescence of
drops. Results from a drop impact and spreading
simulation are shown in figure 5. A snapshot of
the finite element mesh during a simulation can
be seen in figure 7.
7. Computational mesh of nodes on triangular
elements.

• Extensions
• The development mode provides a conceptual
  framework for additional physical/chemical
  effects including thermal effects and contact
  angle hysteresis.
• Substrates of Variable Wettability
• Such chemically altered solids are naturally
  incorporated into the IFM and can have a
  considerable impact on the flow field (Sprittles
  Shikhmurzaev 07).
• Porous Substrates
• One of the many possible generalisations of our
  work is the extension of the solid from
  impermeable to porous.

4. Dynamic contact angle as a function of coating
speed for different flow rates (Blake
Shikhmurzaev 02).
3. Curtain coating geometry in a frame moving
with the contact line.
Contact angle dependence on the flow
field Experiments of Blake Shikhmurzaev 02 and
Clarke Stattersfield 06 demonstrated that in
curtain coating the contact angle is dependent on
the flow field and, in particular, the flow rate
see figure 4. The only model to predict this
effect is the Interface Formation Model (IFM),
see Shikhmurzaev 2007, which we are applying to
drop impact and spreading.
5. Qualitative agreement between a simulation
using the conventional model with experiments of
Dong 06. Water drops of radius 25 microns at
impact speed 12.2m/s with equilibrium contact
angle of 88 degrees.
References Bayer Megaridis, J. Fluid Mech.,
558, 2006. Shikhmurzaev, Capillary Flows with
Forming Interfaces, 2007. Blake Shikhmurzaev,
J. Coll. Int. Sci., 253, 2002. Sikalo et al,
Exper. Therm. Fluid Sci., 25, 2002. Clarke
Stattersfield, Phy. Fluids, 18, 2006. Sprittles
Shikhmurzaev, Phy. Rev. E., 76, 2007. Dong,
PhD, 2006.