Dynamics of Circular Contact Lines

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Dynamics of Circular Contact Lines
Shomeek Mukhopadhyay Department of Physics ,
Duke University
with
Bob Behringer , Duke Physics Mihaela Froelich ,
Duke Math Tom Witelski , Department of
Mathematics , Oxford
Duke Math Andreas Munch and Pete Evans, Humboldt
U, Berlin Andrea Bertozzi, UCLA Karen Daniels (
NC State ) , Rachel Levy ( Harvey-Mudd)
---- Cha Cha Days 2007 --- October 19 21
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Basic Idea of Wetting
Drop on a solid
Youngs Relation
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Fingers
Starbursts
Kinks
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Lubrication equation for film thickness
Introduce dimensionless variables
Rescaled dimensionless equation
where
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Solutions (thin initial film)
a compressive shock (CS) unstable to transverse
perturbations
t
CS
x
Initial state
3000 seconds
6000 seconds
a pair of compressive and undercompressive shock
(UCS)
t
CS
UCS
x
Initial state
900 seconds
1800 seconds
Physical Review Letters,2003 2004
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What about a single finger ?
Fingering Instability of the gravitationally
driven flows has been the subject of long
investigations.
Huppert (1982) showed that the position of the
tip versus time follows a t 1/3 law neglecting
surface tension
Our experiment follows small droplets over long
times to check the domain of validity of Huppert
scaling and the effect of long range van der
Waals forces.
Haskett and Mukhopadhyay Dynamics of perfectly
wetting drops under gravity ( cond-mat 0612266 )
Phys. Rev. E,August 2007
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Physical Review Letters , September 2007
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Driven Circular Contact lines
CCD Camera
Beamsplitter
The Post Modern Newtons Bucket
Sodium Vapor Lamp
Experimental Set up
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Top view of the central spot
Interference fringes in 589nm Sodium light.
Classical Solution
Classical Solution neglects surface Tension ,
Viscosity and disjoining Pressure
Parabolic otherwise
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Movie of an evolving thin film 37 rad/sec
Rossby 0.85
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Movie of another evolving thin film. Same Rossby
No. Different Initial Conditions
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Centrifugal forces combined with Marangoni stress.
Steel Substrate and silicon wafer , embedded
thermistors and annular heater.
Slip Ring.
Cooling water lines to reservoir.
Stepper Motor.
Imaging done with 589 nm Sodium Vapor .
Interferometry.
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Temp K
Position of Thermistor
Instantaneous Temperature Profile
Long Term Temperature Record
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Governing Equations and Dimensionless Groups
Governing Equation
Five Dimensionless Numbers
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Retracting Drop ( no rotation ) only radial
temperature gradient .
The temperature gradient changed from 4K/cm to 10
K/cm . The two images are taken 1000 seconds
apart.T
Central Part of the drop .
Timescales for the Retracting drop.
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Fingering Instability of a spinning microdroplet
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Height microns
Decay of Height
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Spin Coating Plane
Isothermal Rotation of a constant volume droplet
Drops with Radial Heating Plane
Volume
Angular Velocity
Marangoni vs Centrifugal plane
Surface Tension gradient
Constant Volume Parameter Space
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Conclusions and Future Work

• Spreading Drops on Viscoelastic substrates create
  fracturing instabilities or random walk motion.
• The effect of centrifugal force on a wetting
  fluid never causes it to dewet.
• Effect of Marangoni and Centrifugal forces
  changes the thinning dynamics and gives rise to
  (experimentally observed) scaling laws.
• The effect of a radial temperature gradient on a
  perfectly wetting drop, causes it to retract.

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Thank You