Drag Reduction for Flow Across Superhydrophobic and Leidenfrost Surfaces Glen McHale University of Northumbria at Newcastle Michael I. Newton Nottingham Trent University Neil Sandham, Brian Gruncell, Angela Busse University of Southampton

Materials Research Society, Boston, USA 5th December 2013

Public Understanding website: http://www.naturesraincoats.com/

Overview

27 December 2013

1. Perfectly Hydrophobic Sphere

– Experimental Motivation

– Analytical Model for Creeping Flow

2. Computational Fluid Dynamics

– Higher Re

– Solid Surface Fractions

3. Channels and Pipes

– Boundary Conditions for Couette, Channel and Pipe Flows

– Analytical Results for Pipes

27 December 2013

Perfectly Hydrophobic Sphere

Perfectly Hydrophobic Sphere

3

Experimental Motivation

27 December 2013

McHale, G. et al., Appl. Phys. Lett. 94 (2009) art. 064104.

Solid sphere Plastron bearing

sphere

Same sphere

Dr Carl

Evans

Superhydrophobic Sphere with Plastron Sphere with Leidenfrost Effect

Vakarelski et al., Phys. Rev. Lett. (2011) 106

27 December 2013

Creeping Flow – Boundary Conditions

Stokes Drag (Low Re) Hadamard-Rybczynski Encapsulated Droplet

Hadamard-Rybczynski drag is 25% less than Stokes drag

Fundamental boundary condition is not “no-slip”, but is continuity of shear stress

Well-known drag reduction effects for gas bubbles with non-rigid interfaces in water

Fluid, 2

Solid

Fluid, 2

Fluid

, 1

Fluid, 2

Fluid, 1

Fluid

McHale, G., et al., Soft Matter 6 (2010) 714.

Compound Droplet – Air Lubricated Flow

27 December 2013

Sphere

Sphere Sphere

Sphere

Perfectly Hydrophobic Model

Drag Reduction Factor

Air Encapsulated (Plastron) Results

xSH= Drag of sphere with plastron/drag of sphere

gl = ratio of dynamic viscosities extent of air lubrication

e = ratio of b/a extent of obstruction cross-section

Solid, water and air can be replaced

by a combination of any three fluids

McHale, G., Flynn, M.R. & Newton, M.I., Soft Matter (2011) 7 art. 10100.

Drag correction as function of normalized plastron

thickness (various gas-to-liquid viscosity ratios).

Drag Correction Factor

27 December 2013

Drag Reduction and Slip Length

Slip Length

Normalized slip length, ls/b, as a function of

normalized plastron thickness, h/b.

Slip length at low h/b is an order of magnitude larger than plastron thickness

ls(-1+ lg/4)h

CD24xSH/Re

McHale, G., Flynn, M.R. & Newton, M.I., Soft Matter (2011) 7 art. 10100.

27 December 2013

CFD: High Re and Solid Surface Fractions

CFD: High Re and Solid Surface Fractions

8

Drag Reduction with Re and h/b

27 December 2013

CFD (FluentTM) Calculations at Higher Re

Gruncell, B.R.K., et al., Phys. Fluid. (2013) 25 art. 043601.

Backflow and Separation

Stokes flow

drag reduction

Axial vel. at top of sphere

(Re=0.001, h/b=0.1)

Onset of separation

at Re=24

Recirculation within Plastron

Apparent slip 0.4U

CFD Calculations seem reliable

27 December 2013

Suppression of Vortices and Separation

Plastron or Leidenfrost layers can narrow wake and reduce drag

Gruncell, B.R.K., et al., Phys. Fluid. (2013) 25 art. 043601.

Sphere

Modification of separation points and

suppression of vortices.

Separation Suppression (Re=100, h/b=0.1)

Vortex

Plastron

Suppression of attached vortices occurs

for 30<Re<100 (limit of calculation)

Suppression of Vortices

Flow Patterns at Re =100

27 December 2013

Superhydrophobicity – Solid Surface Fraction

Gruncell, B.R.K., et al., Phys. Fluid. (2013) 25 art. 043601.

Solid Surface Fraction (Fs) Effects (h/b=0.1) Axisymmetric

baffles

Without baffles

With baffles

Fs=0.1, Re=100

Drag

increase

Drag

decrease

27 December 2013

Channels and Pipes

Channels and Pipes

12

27 December 2013

Model Systems – Analytical Framework

Busse, A., et al., J. Fluid Mech. (2013) 727 488 (Also see: A.P. Tsai, 736)

Four Flow Cases

1. Couette flow

2. Symmetric pressure-driven channel flow

3. One sided pressure-driven channel flow

4. Pipe flow

Boundary Conditions

1. Simplify to perfectly hydrophobic gas layer boundary

2. Continuity of shear stress across gas-liquid interface

3. Continuity of velocity at gas-liquid interface

4. Zero net mass flow rate in gas layer ( recirculation) rather than

usual assumption of equal pressure gradient

Drag Reduction*

*Apparent slip lengths can also be calculated.

27 December 2013

Results for Pipes

Busse, A., et al., J. Fluid Mech. (2013) 727 488 (Also see: A.P. Tsai, 736)

Flow Profiles

Recirculation within Plastron

Optimum gas

thickness

Optimum thickness of air layer (Plastron) is a competition between increased

lubrication by air and increased obstruction of core cross-sectional area for flow

27 December 2013

1. Developed an analytical model of perfect encapsulating air (or vapour) layers

2. At low Re, air lubrication versus increased cross-section optimum thickness

3. At high Re, vortex suppression even higher drag reduction

4. CFD suggests solid surface fraction rapidly suppresses drag reduction mechanism

5. Drag reduction most effective for higher Re and low solid surface fractions

6. General alternative boundary condition recirculating air (or vapour) layer

7. Applied new boundary condition to channel and pipe flows

8. At low Re, air lubrication versus obstruction of core optimum thickness

The End

Group website and reprints: http://www.naturesraincoats.com/

Summary

Acknowledgements UK EPSRC, UK Sport, Dstl

Dr. Morris Flynn (Alberta)

Mr. Ian Campbell, Dr. Martyn Prince (Southampton)

Dr. Carl Evans, Dr. Neil Shirtcliffe (Nottingham Trent)

Dr Scott Drawer (UK Sport), Dr Stuart Brewer (Dstl),