The Physics of Dew, Breath Figures and Dropwise Condensation

Foreword
Preface
Contents
About the Author
1 Humid Air
1.1 Humid Air Characteristics
1.1.1 Dalton Law
1.1.2 Humid Air Equation of State
1.1.3 Humid Air Density
1.1.4 Saturated Vapor Pressure
1.2 Specific Quantities
1.2.1 Moisture Content, Humidity Ratio, Mass Mixing Ratio, Absolute and Specific Humidity
1.2.2 Relative Humidity
1.2.3 Dew Point Temperature and Relative Humidity
1.2.4 Dew Point Depression Temperature and Relative Humidity
1.2.5 Degree of Saturation
1.2.6 Specific Volume
1.2.7 Specific Enthalpy
1.2.8 Wet Bulb Temperature and the Psychrometric Constant
1.2.9 Mollier Diagram and the Psychometric Chart
2 Boundary Layers
2.1 Hydrodynamic Boundary Layer
2.1.1 Forced Convection
2.1.2 Free Convection
2.2 Thermal and Mass Diffusion Boundary Layers
2.2.1 Forced Flow
2.2.2 Free Convection
3 Nucleation
3.1 Homogeneous Nucleation
3.2 Heterogeneous Nucleation
3.3 Growth Regimes Overview
4 Single Droplet Growth
4.1 Growth in Pure Vapor
4.2 Growth in Vapor with Non-Condensable Gases
4.2.1 2D Concentration Profile
4.2.2 2D Drop Growth
4.2.3 3D Drop Growth
4.2.4 3D Drop and 3D Concentration Profile
5 Drop Coalescence
5.1 Free Drops
5.1.1 Bridge Nucleation
5.1.2 Bridge Evolution
5.2 Coalescence of Sessile Drops
5.2.1 Perfect Wetting Liquid (θc = 0)
5.2.2 Hydrophobic Liquid (θc > 90°)
5.2.3 Hydrophilic Liquid (θc < 90°)
5.2.4 Short Time Oscillations of Bridge and Drop
5.2.5 Late Time Slow Regime
6 Drop Pattern Evolution
6.1 Individual Drop Growth in a 2D Pattern
6.1.1 3D Drop Growth by 2D Surface Diffusion
6.1.2 3D Drop Growth by 3D Diffusion. Equivalent Film
6.2 Individual 3D Drop Growth in a 1D Pattern
6.3 3D Drop Pattern Evolution with Coalescence
6.3.1 Constancy of Surface Coverage
6.3.2 Mean Radius Growth Law
6.3.3 Droplet Number
6.4 Self-Similar Regime for Any Drop and Substrate Dimensionalities
6.4.1 Scaling
6.4.2 Various Drop and Substrate Dimensionalities
6.5 Contact Angle Dependence of Surface Coverage
6.6 New Drops Generation
6.6.1 Surface Coverage
6.6.2 Effect of Gravity
6.6.3 Late Stage Drop Radius Distribution
6.7 Drop Pattern Evolution in Pure Vapor
6.7.1 Drop Growth
6.7.2 Drop Size Distribution (No Coalescences)
6.7.3 Drop Size Distribution (Coalescences)
6.8 Complete Drop Distribution
7 Humidity Sink and Inhibited Condensation
7.1 Lyophilic Spots
7.2 Hydrogels
7.3 Ice Crystals
7.3.1 Nucleation RIC
7.3.2 Flux RIC
7.4 Salty Drop
7.4.1 General Features
7.4.2 Salty Drop Evolution
7.4.3 Region of Inhibited Condensation
7.4.4 Concentration Profile
7.5 Salty Drops and Ice
7.5.1 Ice-Water, Salt-Water and Salt-Ice RICs
7.5.2 Ice-Salt and Water-Salt RICs Evolution
8 Border Effects
8.1 Geometric and Thermal Discontinuities
8.1.1 General
8.1.2 Linear Discontinuity
8.1.3 Approximation of the Surface Coverage
8.1.4 Corner Discontinuity
8.1.5 Droplet Growth Near a Discontinuity
8.2 Simulations
8.2.1 Model Geometry and Boundary Conditions
8.2.2 Growth Rates
8.3 Competition Edge Effect—Thermal Conduction
9 Spatio-Temporal Dynamics
9.1 Drop Self-Diffusion
9.1.1 Number of Coalescence Events
9.1.2 Mean Drop Displacement
9.2 Visited Surface
9.2.1 Dry Surface Power Law Decay
9.2.2 Dry Surface Fractal Contour
9.2.3 Models and Simulations
9.3 Temporal Noise in Surface Coverage
9.3.1 1D Numerical Study
9.3.2 Analytical Model
10 Micro- and Nano-Patterned Substrates
10.1 Fabrication of Micro-Patterns and Functional Coatings
10.1.1 Functional Coatings
10.1.2 Incompletely Ordered Roughness
10.1.3 Ordered Roughness
10.1.4 Liquid-Infused Microstructures
10.2 Pillars
10.2.1 2R < a, b, c Nucleation and Growth—Stage (i)
10.2.2 2R  a, b, c—Stage (ii)
10.2.3 2R > a, b, c Transition to W or CB State—Stages (iii–iv)
10.3 Long-Range Coalescences
10.3.1 Grooves
10.3.2 Amphiphilic Nanostructures
10.4 Coalescence-Induced Jumping Drops
10.4.1 Jump Velocity
10.4.2 Jump Direction
10.4.3 Ballistic Motion
10.4.4 Effect of Substrate Tilt Angle
11 Liquid, Liquid-Infused and Soft Substrates
11.1 Liquid Substrate
11.1.1 Droplet Nucleation
11.1.2 Droplet Growth for Cloaking Oil
11.1.3 Droplet Growth for Non-cloaking Oil
11.2 Liquid-Imbibed Substrate (LIS)
11.2.1 Water Drop Nucleation
11.2.2 Oil–Water-Solid Interactions
11.2.3 Droplet Growth
11.3 Soft or Deformable Substrates
12 Phase Change Materials
12.1 Observations
12.2 Slip-Stick Process
12.2.1 General Behavior
12.2.2 Drop Evolution
12.3 Substrate Heating and Melting
12.3.1 Bare Substrate
12.3.2 Substrate Under Drops
12.3.3 Melting Time
12.3.4 Surface Temperature Increase
12.4 Stage I: Fast Droplet Motion
12.4.1 Relaxation of Capillary Forces
12.4.2 Thermocapillary Motion
12.4.3 Freezing Time and Jump Length
12.5 Stage II: Contact Line Slow Relaxation
13 Thermal Effects
13.1 Heat Transfer
13.1.1 Heat Transfer Coefficients
13.1.2 Substrate Coating
13.2 Filmwise Condensation
13.3 Interface Heat Transfer
13.3.1 Pure Vapor
13.3.2 Vapor with Non-condensable Gases
13.4 Conductive Cooling: The Nusselt Film
13.4.1 Pure Vapor
13.4.2 Vapor with Non-condensable Gas
13.5 Dropwise Condensation
13.5.1 Effect of Drop Curvature
13.5.2 Interface Heat Transfer—Pure Vapor
13.5.3 Interface Heat Transfer—Vapor with Non-condensable Gases
13.5.4 Drop Conduction and Convection Modes
13.5.5 One Drop Overall Heat Transfer
13.5.6 Heat Transfer with Drop Size Distribution (Pure Vapor)
13.5.7 Heat Transfer with Drop Size Distribution (Vapor with Non-condensable Gases)
13.6 Radiative Cooling
13.6.1 Filmwise Condensation
13.6.2 Dropwise Condensation
14 Gravity Effects
14.1 Smooth Substrates
14.1.1 Filmwise
14.1.2 Dropwise
14.2 Edge Effects
14.3 Textured Substrates
14.3.1 Filmwise
14.3.2 Dropwise
14.4 Other Rough and Porous Substrates
14.4.1 Sand Blasting
14.4.2 Porous Substrates (Fibrocement)
14.5 Effect of Tilt Angle and Condensation Rate
14.5.1 Low Supercooling
14.5.2 Large Supercooling
14.6 Liquid-Imbibed Substrate (LIS)
14.7 Soft Substrates
15 Optical Effects
15.1 Transmitted or Reflected Light
15.1.1 Description
15.1.2 Optical Properties of a Single Drop
15.1.3 Diffraction by a Single Drop
15.1.4 Zero-Order Diffraction by a Dew Pattern
15.2 Scattered Light
15.3 Condensed Volume
15.4 Surface Emissivity Change During Condensation
15.4.1 General
15.4.2 Wet Substrate Emissivity
15.4.3 Wet Surface Emissivity Calculation
15.4.4 Emissivity and Condensed Mass Evolution
Glossary—Acronyms
A The Clausius-Clapeyron Relation
B Relation Between Vapor and Heat Transfer Coefficients
B.1 Vapor Transfer
B.2 Heat Transfer
B.3 Ratio of Transfer Coefficients
C Navier-Stokes Equations
D Volume of a Spherical Cap
E Wetting and Super Wetting Properties
E.1 Ideal Surface
E.1.1 Young-Dupré Relation
E.1.2 Energy of Adhesion
E.1.3 Laplace-Young Equation
E.1.4 Capillary Length
E.2 Rough and Micro-patterned Surfaces
E.2.1 Rough Substrate
E.2.2 Micro-patterned Substrate. Cassie-Baxter and Wenzel States
F Coalescence Bridge Geometry
F.1 Radius of Curvature r in the X, Z Plane
F.2 Large Contact Angle
F.3 Small Contact Angle
G Mean Values
H Drop Pearling Transition
I Frost Propagation
J Raoult Law and Salty Drops
K Error and Gamma Functions
K.1 Error and Complementary Error Functions
K.2 The Gamma Function
L Sand Blasting Roughness
L.1 Roughness Amplitudes
L.2 Wenzel Roughness Factor
M Drop Motion in a Wettability Gradient
N Ballistic Motion
N.1 Trajectory Without Air Resistance
N.2 Trajectory with Air Resistance
O Radiative Cooling
O.1 Radiative Properties of Materials
O.1.1 Definitions
O.1.2 Planck’s Law and Black Body
O.1.3 Stefan-Boltzmann Law
O.1.4 Kirchhoff’s Law of Thermal Radiation
O.1.5 Grey Body
O.2 Atmospheric Radiation
O.2.1 Long-Wave Radiative Transfer in the Atmosphere
O.2.2 Clear Sky Emissivity: Radiation Deficit
P The Kelvin Equation
Q Meniscus in a Groove
R Light Reflection and Transmission
Bibliography
Index
Index