Motion of drops on a surface

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Motion of drops on a surface induced by Bias and
Noise
Srinivas Mettu Department of Chemical
Engineering Lehigh University Bethlehem, PA 18015
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Outline

• Motivation
• Background
• Experimental Results
• Simulation Results

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Part I
Motion of drops on a surface induced by
temperature gradient
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• Macro-scale flow
• pressure driven

• Micro-scale flow
• discrete flow
• driven by temperature, concentration or
  wettability gradient

• Applications
• Micro Fluidics

Temperature Gradient

• Advantages
• Programmable
• Reversible

Splitting
Propulsion
Turning
Ref Darhuber, A. A. Valentino, J. P. Davis, J.
M. Troian, S. M. Wagner, S. Appl. Phys. Lett.
2003, 82, 657.
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Contact angle hysteresis
Contact Angle Hysteresis
How to overcome the effect of contact angle
hysteresis?
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Schematic of Experimental Setup
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High Speed Videos of drops
No Temperature Gradient

• Drop oscillates back and forth, no net drift

Temperature Gradient

• Drop oscillates asymmetrically and drifts
  towards cold side

Hot side
Cold side
Temperature Gradient
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Drift Velocity
Forcing Frequency
Resonance Frequency
Rayleigh's Modes
Ref H. Lamb, Hydrodynamics, Cambridge University
Press Cambridge, U.K., 1932.
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Theory
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Drift velocity

• Velocity increases with increase in amplitude

• Velocity peaks at resonance frequencies

Ref S. Mettu, M. K. Chaudhury, Langmuir. 24,
10833 (2008).
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Numerical Simulation of motion of contact line
Temperature Gradient
No Temperature Gradient
Ao Amplitude of oscillation

• Experiment
• High speed video at 2000 fps

T Time period of oscillation
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CFD Simulations (FLUENT)
Volume force
(1)
(2)
(3)
(4)
Ref J. U. Brackbill, D. B. Kothe, C. Zemach, J.
Comput. Phys. 100, 335 (1992).
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Results from CFD Simulations
Phase Contours
Air
Water Drop
Frequency
Thermal Gradient
Temperature Contours
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Conclusions

• Water drops remain pinned on a temperature
  gradient
• surface due to hysteresis
• Water drops move towards the cold side of
  surface
• when subjected to periodic vibration
• Drop velocity reaches maximum at resonance
  frequencies
• Simple model has been developed to predict the
  drift velocity
• as a function of frequency and amplitude of
  vibration

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Part II
Motion of drops induced by White Noise
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Daniel, Chaudhury
And Chen,
Science
2002

• Rapid Rate of Condensation
• Drift velocity is high

• Slow Rate of Condensation
• Drift velocity is small

• Noise arising
• from random coalescence
• from contact line fluctuation

Simple Model
Biased Random Motion
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Modified Langevin Equation
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Solution for drift velocity
Ref M. K. Chaudhury, S. Mettu, Langmuir. 24,
6128 (2008).
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Analogy with condensation on gradient surface
Degree of subcooling (Tv-Ts)
Power of noise (K)
enthalpy of vaporization (J/kg)
surface tension
gradient
density
friction prefactor
degree of subcooling
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Conclusions

• Drift velocity of drop under external noise is a
  strong function
• of power of noise (K)
• For large values of K, drift velocity saturates
  to classical
• Einstein limit of
• An analogy is drawn between drops drifting under
  the
• influence of noise arising from rapid rate of
  condensation and
• drops drifting under the influence external
  white noise

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Thank You