Thinfilms flows over microtextured surfaces: Polygonal water sheets

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Thin-films flows over microtextured surfaces
Polygonal water sheets
Adrian P. Delancy , Emilie Dressaire , Laurent
Courbin , and Howard A. Stone School of
Engineering and Applied Sciences, Harvard
University Purdue University, 2008 REU Program,
Materials for BRIDGE APS DFD 2008
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Liquid films and sheets Production use
Taylor 1959
Bremond et al. 2003
Liquid atomization
http//graphics.stanford.edu/lucasp/pictures/ital
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Main point

• Regularly patterned substrates at a micron-scale
  influence the size and shape of liquid sheets

5 mm
5 mm
5 mm
Eight-corner star
Hexagon
Circle
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Experimental set-up
Water
Jet diameter Flow rate
Hexagonal arrays
Square arrays
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Sample result
Smooth Substrate
5 mm
5 mm
5 mm
Circle
Eight-corner star
Hexagon
Hexagonal lattice, Q1.2L/min
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Evolution with Q and surface properties
Smooth Surface
Hexagonal Lattice
Square Lattice
Q 0.5L/min
Q 1.0L/min
Q 1.4L/min
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Mean radius vs flow rate
Mean radius R (mm)
Q (L/min)
Roughness induces Reduction of mean radius at
given flow rate Increase of critical
flow rate for sheet formation
Interpretation Momentum losses caused by
roughness
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Taylor radius
Mass conservation in the sheet at radial position
r Using Bernoulli approximation For
, inertia is balanced by surface tension
effects Radius of the jump
with
R
r
Taylor, PRS, 1959 Clanet, HDR, 2002
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Additional friction of the substrate

For small pressure losses (
) Classical argument not valid
for rough substrates friction losses
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Accounting for the roughness

• Lattice distance

• Posts height

Mean radius, R (mm)
Mean radius, R (mm)
l 100 µm l 200 µm l 300 µm
Q (L/min)
Q (L/min)
Friction losses depend on geometrical features of
lattices
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Towards a model Friction from substrate
Estimate of the film thickness
Pressure drop mostly due to losses/leakage in
porous medium
non-trivial function of Reynolds number (Ergun
flow )
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Conclusions
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