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Davide Del Col UIT Summer School 2017

Davide Del Col

Università di Padova – Dipartimento di Ingegneria Industriale

Via Venezia, 1 - 35131 Padova

E-mail: [email protected]

http://stet.dii.unipd.it/

DROPWISE CONDENSATION


Outline

• Surface wettability

• Dropwise condensation over hydrophobic surfaces: experiments

and modeling

• Dropwise condensation over super-hydrophobic surfaces


θ > 90° the surface is defined

hydrophobicSolid

Liquid

Gas

θa > 150° ∧ Δθ < 10° the surface is

defined superhydrophobic

Hydrophobicity: solid surface energy vs liquid surface tension

Solid

Liquid

Gas

θ θ

Static Angles

Dynamic Angles

Wettability

Θ = Static Contact Angle

Θa = Advancing Contact Angle

Θr = Receding Contact Angle

ΔΘ = Θa – Θr =

Contact Angle Hysteresis


• A flat surface is used to define the equilibrium contact

angle.

• The equilibrium contact angle for a droplet is the result of

the force balance at the three-phase contact line (Young,

1805).

Solid

Liquid

Gas

θ

𝜸𝒍𝒈

𝜸𝒍𝒔𝜸𝒈𝒔

Young model:

𝛾𝑔𝑠 − 𝛾𝑙𝑔 cos 𝜃𝑌𝑜𝑢𝑛𝑔 − 𝛾𝑙𝑠 = 0

Wettability


• Wenzel extended the wetting analysis to rough and

porous surfaces.

• For a surface with roughness r defined by the ratio of the

total surface area to the projected area, Wenzel (1936)

showed that the apparent contact angle in the Wenzel

state θW is defined by:

Wettability – Wenzel state

Wenzel model:

𝑐𝑜𝑠𝜃𝑊 = 𝑟 𝑐𝑜𝑠𝜃𝑌𝑜𝑢𝑛𝑔 , 𝑟 =𝑟𝑒𝑎𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒

𝑝𝑟𝑜𝑗𝑒𝑐𝑡𝑒𝑑 𝑠𝑢𝑟𝑓𝑎𝑐𝑒

• The Wenzel state is typically less desired due to the

higher adhesion associated with this wetting state


• Where the droplet rests on the tips of the roughness,

Cassie and Baxter (1944) showed that the apparent

contact angle in the Cassie state θCB is defined by:

Wettability – Cassie and Baxter state

where the solid fraction f is the ratio of the structure or

roughness area contacting the droplet to the projected area.

Cassie-Baxter model:

𝑐𝑜𝑠𝜃𝐶𝐵 = 𝑓 𝑐𝑜𝑠𝜃𝑌𝑜𝑢𝑛𝑔 + 1 − 1

𝑓 = 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑎𝑟𝑒𝑎

• It is important to note that in the case of condensation the

nucleation of droplets can initiate within the roughness,

which may render previous equations non applicable.


Condensation

• In typical industrial systems, the vapor condenses on a

surface forming a liquid film (filmwise condensation). In

fact, the majority of industrial heat exchangers materials

(copper, aluminum, stainless steel…) present high surface

energy.

• During filmwise condensation, the heat transfer

performance is limited by the thickness of the liquid film.

The thermal resistance is mainly due to the heat

conduction though the liquid film.

• The heat transfer coefficient can be enhanced or thinning

the liquid film or promoting a different type of condensation

mechanism: dropwise condensation.


Dropwise

CondensationFilmwise

Condensation

Condensation


Dropwise condensation

• Dropwise condensation (DWC) is a nucleation

phenomenon.

• It is similar to nucleate boiling except that the active

nucleation sites are much smaller and the nucleation site

density is much larger.

• Dropwise condensation, first reported by Schmidt et al.

(1930), occurs when steam and a few other relatively high

surface tension fluids condense on surfaces which are not

wetted by the condensate.


Dropwise condensation:

history of research (Rose, 2002)



• On low surface energy materials, the vapor can condense

forming discrete liquid droplets.

• During DWC, droplets roll off clearing the surface for re-

nucleation. The droplets roll off can be induced by gravity,

vapor shear stress, presence of a wettability gradient on

the surface…

• Since most of the materials used in heat exchangers

present high surface energy, DWC can be achieved

functionalizing the surface with a hydrophobic coating.

• Compared to filmwise condensation, DWC allows heat

transfer coefficients one order of magnitude higher.


Phenomenon:

1. Nucleation radius (rmin)

2. Coalescence radius (re)

3. Departing radius (rmax)


phenomenon



• DWC has been a topic of interest for the past eight

decades. The works focused on the realization of non-

wetting surfaces obtained by applying different coatings.

• However, the realization of robust coating is still a

challenge and further research on this topic is required.

• Recent advancements in nanofabrication and material

science have given further impulse to this field.



• The condensation heat transfer coefficient (HTC) α is the

ratio between the heat flux q’ and the saturation-to-wall

temperature difference:

'

sat wall

q

T T

• Three properties affect the condensation heat transfer

coefficient:

- Nucleation density;

- Advancing/receding contact angle;

- Droplet departure radius.



• The HTC increases with nucleation density. In fact small

droplets have low conduction thermal resistance.

• High apparent contact angle can lead to an increase in

conduction resistance due to the reduced size of the

droplet base.

• Low contact angle hysteresis promote droplet shedding.

• Larger droplet departure size reduce the HTC because

larger droplets have high thermal resistance.


Surface functionalization

• Since most industrial metals, such as aluminum, copper,

titanium and stainless steel have high surface energy,

surface functionalization via a coating that can reduce

surface energy is typically required to obtain DWC.

• Furthermore, the micro- and nanostructured surfaces also

need to be coated to impart low surface energy in order to

take advantage of the benefits offered by the Cassie state.

• This is a particularly active area of research, as no

solution has yet been proposed which satisfactorily

addresses durability, cost and performance.



• Several approaches to obtaining suitably low surface

energies are presented.

• Self-assembled monolayers (SAMs) result from

spontaneous physi- or chemisorption of a thin molecular

film (∼1 nm) comprised of individual molecules on the

condensing surface. These molecules have hydrophobic

tails pointing away from the surface that interact with the

condensate and ligand heads that bind to the surface.

This functionalization method does not introduce a

significant thermal resistance; however, durability is a

primary concern. Exemples are silicon-based ligand

silanes.


Surface functionalization• Polymer coatings such as polytetrafluoroethylene (PTFE)

and silicones have been used as a functional coating to

promote DWC. However, the required coating thickness to

realize satisfactory durability results in an added thermal

resistance which offsets the heat transfer improvement due

to DWC.

• Ion implantation promotes DWC through carbon, nitrogen

and oxygen ion implantation in copper, aluminum, titanium

and steel surfaces.

• Noble metals applied as a thin coating are a robust

approach to achieve DWC. For example, gold, while

intrinsically hydrophilic, rapidly adsorbs hydrocarbons from

air resulting in increased contact angle and DWC.



• Rare earth oxides (REOs) have recently been

demonstrated experimentally to be hydrophobic and

promote DWC of steam. The low cost of REOs relative to

noble metals and high resistance to physical wear offer

promise as a potential candidate for surface coatings, but

REOs have relatively low thermal conductivity


HTC measurement during

dropwise condensation over

hydrophobic surfaces


WATER

IN

VAPOR

OUT

VAPOR

IN

WATER

OUT

VAPORWATER

𝑯𝑻𝑪 =𝑞

∆𝑇

𝒒 = 𝑚𝑐𝑜𝑜𝑙 𝑐𝑐𝑜𝑜𝑙∆𝑇𝑐𝑜𝑜𝑙

𝐴

q𝒒 = 𝜆

Δ𝑇

Δ𝑦

Experimental measurement technique

z

y

𝒒𝒛

𝒒𝒚~ 𝟏%

Del Col et al., 2017


Modeling of DWC on

flat surfaces


Theory of DWC• A theory of heat transfer by dropwise condensation

determines the heat transfer through a drop of given size

and combines this with an expression for the distribution of

drop sizes to obtain the mean surface heat flux.

• Drops range in size from the smallest on which

condensation can take place, “primary drops”, which form

at nucleation sites, to the largest to which drops grow

before the region is swept by a falling drop.

• The drops range in size from nanometer to millimeter scale.

Condensation on the smallest drops is inhibited by the

surface curvature-surface tension effect which necessitates

cooling of the vapor below its normal saturation

temperature.


Theory of DWC

• The primary drops are closely packed (nucleation site

densities exceed 1010 per cm2) and coalescences rapidly

lead to larger drops. New primary drops form in the spaces

that are vacated by coalescences.

• Those drops somewhat larger than primary drops, where

the curvature effect becomes small, experience intense

condensation rates and the temperature drop at the vapor-

condensate interface is important.

• For the largest drops the dominant thermal resistance is

that due to conduction in the drop. A complete theory must

account for all drop sizes.


Theory of DWC

• Drops continue to grow by coalescence and condensation

until a region of the surface is swept by a falling droplet.

• Many thousands of coalescences take place during the

formation of the largest drops.

• In the models here proposed, the detail of the drop growth

process is disregarded and an effective, steady, mean size

distribution function is used.


Twall

Tvapor

𝜑𝑣𝑒 = 𝜑𝑙𝑒 𝑟𝑚𝑖𝑛 =2𝜎𝑇𝑣𝑙𝑖𝑞𝑢𝑖𝑑

ℎ𝑙𝑣(𝑇𝑣𝑎𝑝𝑜𝑟 − 𝑇𝑤𝑎𝑙𝑙

g

Dropwise condensation phenomenon

𝑟𝑒 =1

4𝑁𝑠≈ 1 μm

Nucleation sites (NS)

Khandekar et al., 2014


Dropwise condensation phenomenon

𝐹𝑎𝑑𝑒𝑠𝑖𝑜𝑛 = 𝐹𝑔𝑟𝑎𝑣𝑖𝑡𝑦

𝑟𝑚𝑎𝑥 =6 cos(𝜗𝑟 − cos( 𝜗𝑎)) sin 𝜗

𝜋(2 − 3 cos 𝜗 + 𝑐𝑜𝑠2 𝜗

𝛾

𝜌𝑙𝑔

𝑟𝑚𝑎𝑥 = 𝐾3𝜎

𝜌𝑔

12

Twall

Tvapor

g

Rose, 2002

Abu-Orabi, 1998


1930

Schmidt et al.

1966

Le Fevre & Rose

1998

Abu-Orabi

2011

Kim et al.

Models on hydrophobic surfaces: surface roughness

is not considered

Dropwise condensation model history


1930

Schmidt et al.1966

Le Fevre & Rose

1998

Abu-Orabi

2011

Kim et al.

𝑞 = 𝑟𝑚𝑖𝑛

𝑟𝑚𝑎𝑥

𝑄𝑑(𝑟) ∙ 𝑁 𝑟 𝑑𝑟

𝑄𝑑(𝑟) =𝛥𝑇 −

2𝜎𝑇𝑆𝐴𝑇𝑟 𝜌𝑙ℎ𝑙𝑣

𝐾1𝑟𝜆𝑙+ 𝐾2

0.6270.664

𝑇𝑆𝐴𝑇ℎ𝑙𝑣

2𝜌𝑙

𝛾 + 1𝛾 − 1

𝑅𝑇𝑆𝐴𝑇2𝜋

0.5 𝑁 𝑟 =1

3𝜋𝑟2𝑟𝑚𝑎𝑥

𝑟

𝑟𝑚𝑎𝑥

−23

Resistance through

the drop

Vapor-liquid interface

resistance

Drop curvature

resistance

Le Fevre & Rose model

Rose, 2002


Le Fevre & Rose model

Heat transfer through a drop of given size

• Conduction in a drop. The surface and the base of the drop

have non-uniform temperatures which are equal at the

perimeter of the base. An effective average temperature

between the curved and plane surfaces is used in the

model.

• Surface curvature effect. Surface curvature introduces an

effective resistance to heat transfer which is significant for

very small drops. In order for condensation to occur, the

vapor adjacent to the drop surface must be subcooled.


Le Fevre & Rose modelHeat transfer through a drop of given size

• Interface temperature drop. Because of molecular kinetics

effects during condensation, the interface temperature has

to be slightly lower than the saturation temperature in order

to achieve a finite rate of condensation.

• Heat flux at the base of the drop. It can be obtained

equating the sum of the three temperature differences to

the bulk vapor-surface temperature difference ΔT.

Heat flux for the whole surface

• Knowing the heat exchanged by a single drop and the

number of droplets per unit area, the heat flux can be

calculated through the operation of integration from the

minimum radius to the maximum one.


1930

Schmidt et al.

1966

Le Fevre & Rose1998

Abu-Orabi

2011

Kim et al.


𝑟𝑒

𝑄𝑑 𝑟 ∙ 𝑛 𝑟 𝑑𝑟 + 𝑟𝑒

𝑟𝑚𝑎𝑥

𝑄𝑑 𝑟 ∙ 𝑁 𝑟 𝑑𝑟

𝑄𝑑 𝑟 =4𝜋𝑟2 1 −

𝑟𝑚𝑖𝑛𝑟

𝛥𝑇

𝛿𝜆𝑐𝑜𝑎𝑡

+𝑟𝜆𝑙+2ℎ𝑖

)𝑛 𝑟𝑒 = 𝑁(𝑟𝑒

𝑛 𝑟 = 𝑁(𝑟𝑒))𝑟(𝑟𝑒 − 𝑟𝑚𝑖𝑛)(𝐴2𝑟 + 𝐴3)𝑟𝑒(𝑟 − 𝑟𝑚𝑖𝑛)(𝐴2𝑟𝑒 + 𝐴3𝑒𝐵1+𝐵2

𝑁 𝑟 =1

3𝜋𝑟2𝑟𝑚𝑎𝑥

𝑟

𝑟𝑚𝑎𝑥

−23

Drop curvature resistance

Resistance

through the drop

Vapor-liquid

interface resistanceCoating

resistance

Abu-Orabi model


1930

Schmidt et al.

1966

Le Fevre & Rose

1998

Abu-Orabi2011

Kim et al.


𝑟𝑒

𝑄𝑑 𝑟 ∙ 𝑛 𝑟 𝑑𝑟 + 𝑟𝑒

𝑟𝑚𝑎𝑥

𝑄𝑑 𝑟 ∙ 𝑁 𝑟 𝑑𝑟

𝑞𝑑(𝑟) =𝛥𝑇𝜋𝑟2 1 −

𝑟𝑚𝑖𝑛𝑟

𝛿𝜆𝑐𝑜𝑎𝑡 sin 𝜃

2 +𝑟𝜃

4𝜆𝑙 sin 𝜃+

1)2ℎ𝑖(1 − cos 𝜃

Drop curvature resistance

Resistance

through the drop

Vapor-liquid

interface resistance

Coating

resistance

Kim et al. model


Variable Value Le Fevre

& Rose

Abu-

Orabi

Kim et al.

tSAT [°C] 108 X X X

∆T [°C] 5 X X X

δp [μm] 0.2 X X

λp [W m-1 K-1] 0.2 X X

α [-] 1 X X

NS [m-2] 1012 X X

θ [°] 90 X

θa [°] 88.6 X

θr [°] 63.4 X

LeFevre & Rose : 2

3

𝑟

𝜆𝑙

Abu-Orabi : 𝑟

𝜆𝑙

Kim et al. : 𝑟𝜃

4𝜆𝑙 sin 𝜃

Dropwise condensation model comparison


Dropwise condensation over

superhydrophobic surfaces


Superhydrophobic surfaces

• Superhydrophobic surfaces allow nearly spherical water

droplets to sit on them with high mobility.

• Superhydrophobic surfaces can promote dropwise

condensation and favor droplets shedding (reducing the

droplet departure diameter).

• The high contact angle of droplets can increase the heat

transfer resistance (small portion of the droplet in contact

with the wall).

• Such surfaces can become flooded at low values of heat

flux.



• Superhydrophobic (SH) surfaces can be obtained

combining surface roughness and low surface energy

materials or coatings.

• SH surfaces can have apparent contact angles greater

than 150° and contact angle hysteresis near to 0°.


Superhydrophobicity

Hydrophilic surfaces: Θeq < 90°

Hydrophobic surfaces: Θeq > 90°

Superhydrophobic surfaces: Θeq > 150°

To promote high droplet mobility the surfaces must present a

Cassie-Bexter wetting regime, with very low hysteresis.

High hysteresis means high adhesion of the drop on the

substrate, which decreases the effective superhydrophobic

properties even with very high Θeq

During pure steam condensation on superhydrophobic nano-

structured surfaces vapor could condense between the

surface textures, leading to Wenzel wetting regime of the

droplets. In this case, droplet mobility can be favored by

vapor velocity.

Superhydrophobicity can be obtained combining:

• micro-/nano- superficial roughness

• low surface energy



• During condensation, droplet nucleation can initiate within

the surface roughness and the droplet can undergo a non-

equilibrium wetting process where Wenzel and Cassie-

Baxter equations for which equilibrium is assumed, may

not apply.

• Studies on structured superhydrophobic surfaces have

demonstrated that, during condensation, highly adhered

Wenzel droplets form that are distinct from the mobile

Cassie droplets formed upon fluid deposition with a

syringe.



• Miljkovic et al., 2013 have shown

that three different droplet

morphologies exist during

condensation:

• Wenzel (W), partially wetting (PW)

and suspended (S).

• Both S and PW droplets are highly

mobile relative to W droplets and, as

such, are favorable due to their

increased ability to depart form the

surface.


Superhydrophobic surfaces• Both PW and S droplets are highly mobile compared to W

droplets.

• However, growth prior to departure also affects heat transfer. In

fact, in certain cases, surface structuring can degrade heat

transfer performance.

• A recent study demonstrated for a specific geometry that the

growth rate and individual droplet heat transfer of PW droplets

are higher than those of S droplets.

• This difference is due to the composite vapor–solid interface

beneath S droplets, where the vapor provides a significant

thermal resistance to droplet growth.

• Structure design needs to be considered for maintaining easy

droplet removal while simultaneously avoiding the thermal

resistance of vapor beneath droplets.


Superhydrophobic surfaces:

jumping droplets• Superhydrophobic surfaces have potential to enhance

condensation performance by reducing droplet departure size

and enabling faster clearing of the surface for re-nucleation.

• This is possible due to the low contact angle hysteresis, which

allows less pinning force to hold the droplet in place against the

body force due to gravity.

• Smaller droplet departure sizes than those observed during

DWC on a flat surface are expected.

• When a structured surface is suitably designed, coalescence-

induced jumping condensation occurs and departure radii are

orders of magnitude smaller.


Superhydrophobic surfaces:

jumping droplets• Jumping occurs due to a release of surface energy upon

coalescence of two droplets, some of which is converted to

kinetic energy manifested as the motion of the merged droplet

perpendicular to the condensing surface.

• Jumping condensation offers an alternative method for

transportation of condensate in phase-change systems.

• The key limitation for jumping condensation occurs when the

nucleation density becomes too high and the spacing between

droplets is reduced, at which point the surface is “flooded” and

droplet jumping cannot be sustained.

• In this case, discrete droplets form which are highly adhered to

the surface, and heat transfer performance is worse than for

DWC.


Surface treatmentsIn the recent years several methods have been proposed to obtained a

desired superficial roughness, such as micromachining, micro

contact printing, deep radiative ion etching and chemical etching.

The chemical etching is probably the most common procedure and

consists in a controlled corrosion process of the substrate, immersing

it into an appropriate solution (NaOH, HCl, FeCl3, …).

To decrease the surface energy usually the substrate is coated with a

very thin layer of a proper material, such as organic substances,

polymers and noble metals. These can be deposited over the surface

either by physical or chemical deposition processes.

The literature demonstrates that properly combining surface etching and

functionalization it is possible to obtain surfaces having static

contact angles > 160° and contact angles hysteresis < 5°.


Superhydrophobic sample preparation

(copper surface)TWO MAIN STEPS

Initially the copper substrate is mechanically polished and finely

cleaned

• 1. CHEMICAL ETCHING. Dipping the sample in a mixture solution

of 2.5 M L-1 NaOH and 0.1 M L-1 (NH4)S2O4 for 12 min. → WIRE-LIKE

NANOSTRUCTURES ON THE SURFACE

• At this stage, the surface is superhydrophilic. the sample is rinsed

with DI water and dried in a N2 stream

• 2. SURFACE FUNCTIONALISATION. Immersing the sample, at

room temperature, in an ethanol solution of 1 mM L-1 1H,1H,2H,2H-

persluorodecanethiol for 30 minutes followed by immersing it in

ethanol for 1 hour. → SURFACE ENERGY CHANGE


Superhydrophobic sample

UNTREATED SAMPLES: Θeq = 86 ± 2° (HYDROPHILIC)

TREATED SAMPLES: Θeq = 159 ± 2° (SUPERHYDROPHOBIC)


Experimental

apparatus

• Thermosyphon test rig

• Filled with DI water

• NCGs presence is avoided

• Overpressure during the night

• p = 1.43 bar (Tsat = 110°C)


Test section

• Rectangular Teflon

minichannel (Dh = 3.6 mm)

• Front glass (heated)

• Cylindrical copper specimens

(D = 20 mm)

• Water cooling system on the

back side (finned copper plate)

Water

inlet

Water

outlet


Data reduction

Specimens are fitted with

5 T-type thermocouples.

Twall is evaluated from the

acquired temperature profile

.

q = -k dT/dz

h = q / (Tsat – Twall)


Experimental results: effect of vapor velocity

• Heat flux increases when increasing temperature difference and vapor velocity

• Heat transfer coefficient depends only on vapor velocity

• Increasing vvapor leads to a reduction of droplet departing size, thus leading to high

mobility and high rate of thermal transport

0

100

200

300

400

500

600

700

0 5 10 15

q [k

W m

-2]

Tsat - Twall [K]

6 m s^-1

12 m s^-1

18 m s^-1

0

10

20

30

40

50

60

70

0 5 10 15

h [k

W m

-2K

-1]

Tsat - Twall [K]

6 m s^-1

12 m s^-1

18 m s^-1


Flow visualization

ΔT = 3.5 K vsteam = 18 m s-1

ΔT = 3.5 K

Increasing the vapor velocity the size of departing droplets decreases and

the frequency increases.

Reducing the droplets departing diameter leads to thermal performance

enhancement, due to the lower thermal resistance of the smaller drops.


Experimental results: Lifetime test

• For the first five days no sign

of degradation was found

• At the same subcooling, heat

flux is reduced by 35% after six

working days

• After six days steam

condenses over the specimen

no more in dropwise mode, but

changes to filmwise0

100

200

300

400

500

600

700

0 5 10 15 20

q [k

W m

-2]

Tsat - Twall [K]

Day-1

Day-2

Day-3

Day-4

Day-5

Day-6

vvapor = 12 m s-1


Lifetime test

• Performances decrease is due to the deterioration of the

hydrophobic monolayer and of the surface morphology.

Day 1 Day 6


Experimental results: Comparison

against non-treated surface• On the naturally oxidized polished

copper sample FWC occurs

• While the superhydrophobicity is

sustained, the treated surface

performs clearly better than the

untreated one for ΔT > 5 K

• After 6 consecutive working days,

thermal performance of the

naturally oxidized surface

becomes higher0

100

200

300

400

500

600

0 5 10 15 20

q [k

W m

-2]

Tsat - Twall [K]

DWC Superhydrophobic Day-1

FWC Superhydrophobic Day-6

FWC Oxidized

vvapor = 12 m s-1


Concluding remarks

• DWC enhances heat transfer performance as compared

to FWC, because of absence of liquid film and droplet

mobility.

• DWC mode is promoted by using hydrophobic or

superhydrophobic surfaces.

• The challenge is to realize robust surface treatments that

are able to promote DWC.

• The performance of superhydrophobic surfaces can be

limited by flooding.


References DWC• Abu-Orabi M., Modeling of heat transfer in dropwise condensation, Int. J. Heat Mass

Transf., Vol. 41, pp. 81–87, 1998.

• Bisetto A., Bortolin S., Del Col D., Experimental analysis of steam condensation over

conventional and superhydrophilic vertical surfaces, Experimental Thermal and Fluid

Science, Vol. 68, pp. 216–227, 2015.

• Bisetto A., Bortolin S., Martucci A., Del Col D., Condensation of steam over nano-

engineered surfaces, 9th International Conference on Boiling and Condensation Heat

Transfer, Boulder, Colorado, April 26-30, 2015.

• Del Col D., Parin R., Bisetto A., Bortolin S., Martucci A., Film condensation of steam

flowing on a hydrophobic surface, Int. J. Heat Mass Transf., Vol. 107, pp. 307–318, 2017.

• Khandekar S., Muralidhar K., Dropwise Condensation on Inclined Textured Surfaces,

Springer, 2014.

• Kim S., Kim K.J., Dropwise Condensation Modeling Suitable for Superhydrophobic

Surfaces, J. Heat Transfer., Vol. 133, 81502, 2011.

• Miljkovic N., Enright R., Nam Y., Lopez K., Dou N., Sack J., Wang E.N., Jumping-droplet-

enhanced condensation on scalable superhydrophobicnanostructured surfaces, Nano

Lett., Vol. 13(1), pp. 179–187, 2013.

• Miljkovic N., Enright R., Wang E.N., Modeling and optimization of superhydrophobic

condensation, J. Heat Transfer, 135(11), 111004, 2013.

• Miljkovic, N., Preston, D.J., Enright, R., Adera, S., Nam, Y. and Wang, E.N., Jumping

droplet dynamics on scalable nanostructured superhydrophobic surfaces, J. Heat

Transfer, Vol. 135(8), 080907, 2013.


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Thanks

for

your attention!

Davide Del Col

University of Padova

Department of Industrial Engineering

E-mail: [email protected]

http://stet.dii.unipd.it/

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