forces. The porous texture is generally func-
tionalized with a coating to enhance the sta-
bility of the lubricant. The lubricant is also
chosen such that it is immiscible with any
contacting liquid. Liquid droplets can display
exceptionally lowDqand sliding angles on such
surfaces as the contacting liquid never comes
in contact with the solid surface. TheDqmea-
sured on these surfaces is related to the viscous
forces between the contacting and lubricating
liquids, instead of the adhesion forces between
the contacting liquid and solid, as is common
for nonlubricated surfaces. LowDqvalues on
lubricated surfaces are possible even with rela-
tively low values ofq(Fig. 1B). The values
for the apparent contact angle clearly distin-
guish between the properties of air-infused
and lubricant-infused liquid-repellent surfaces
(Fig. 1B), even though both types of surfaces
can display lowDqwith a variety of contact-
ing liquids. Note that it can be difficult to
accurately measure values ofq>> 150°, and
consequentlyDqfor air-infused surfaces.
A related approach, one that also minimizes
any liquid-solid interaction, is the chemical
grafting of mobile polymer chains to the under-
lying substrate ( 38 , 39 ). The grafted chains are
chosen such that the operating or testing tem-
peratures are far above their glass transition
temperature, and thus they display high inter-
facial mobility with any contacting liquid or
solid. Consequently, they can display lowDq
and sliding angles with a variety of contact-
ing liquids. Such surfaces can overcome some
of the challenges associated with lubricant-
infused surfaces, as noncovalently bonded lu-
bricants can be depleted due to evaporation or
because of removal by moving droplets ( 40 ).
However, depending on the underlying sub-
strate coverage, in many cases the liquid-like
polymer chain–coated surfaces display higher
Dqthan lubricant-infused coatings (Fig. 1B)
( 38 , 39 ).Applications of surfaces that control
liquid accretion
Current state-of-the-art boiling and conden-
sation systems used in power generation, dis-
tillation, air-conditioning, and refrigeration
all suffer from considerable energy inefficiency
inherent in liquid-vapor phase change pro-
cesses. This inefficiency can be manifested as
poor thermodynamic efficiency at low heat
fluxes and violent instability at higher heat
fluxes ( 41 , 42 ). For example, the heat transfer
coefficient (HTC) associated with boiling is
determined by two factors–how quickly bub-
bles nucleate on the heating surface during
boiling, and how quickly the bubbles depart
( 41 , 42 ). When the heat flux is low, lowgSVsur-
faces, or those with texture, facilitate bubble
nucleation and enhance HTC values ( 41 , 42 ).
However, as the heat flux increases to reach
the so-called critical heat flux (CHF), the rate
of nucleation of bubbles increases to the ex-
tent that the overcrowded bubbles coalesce
and form a continuous film of vapor between
the heating surface and the liquid. This film
causes an abrupt thermal glitch within the sys-
tem, typically leading to its failure. To enhance
the overall energy efficiency for these systems,
it is important to simultaneously increase the
HTC and the CHF. HighgSVsurfaces, such as
hydrophilic or superhydrophilic surfaces, tendto increase CHF but suffer from low HTC,
whereas lowgSVsurfaces can increase the HTC
but suffer from low values of CHF. Surfaces
with patterned wettability, i.e., nonwettable
domains on a wettable background, have now
been developed to simultaneously increase
HTC and CHF during boiling ( 41 , 42 ).
Hydrophilic surfaces can enhance the HTC
during the condensation of water vapor. This
can be rationalized through the classical nu-
cleation theory, which shows that the Gibbs
free energy for nucleation on a smooth sur-
face,DG¼ ^43 prc^3 DGvðÞ 2 3cosqþcos^3 q=8,
whereqis the contact angle of the liquid on
the surface andrcis the critical radius of a
stable liquid drop formed on the surface ( 43 ).
This critical radius is given byrc¼ D^2 GgLVv, where
DGvis the Gibbs free energy difference between
liquid and vapor phases per unit volume ( 44 ).
Thus, a surface with lowqwould favor drop-
let nucleation, leading to higher values for
HTC. However, if one tries to increase the con-
densation rate by lowering the temperature,
beyond the CHF, multiple water drops merge
with one another, forming a thin, continuous,
insulating layer of water, drastically lowering
the condensation efficiency ( 45 ). Wettable do-
mains on a nonwettable background have
been utilized to simultaneously increase HTC
and CHF during condensation by promoting
dropwise condensation (Fig. 3B) instead of
filmwise condensation (Fig. 3A) ( 41 , 42 ). Various
other physical and chemical surface design
strategies have been developed to enhance con-
densation heat transport with water and lower
surface tension organic liquids ( 41 , 42 , 46 ).
Water droplet removal from the condensingDhyaniet al.,Science 373 , eaba5010 (2021) 16 July 2021 4 of 13
Fig. 3. Engineering surfaces to control liquid
accretion.(A) Filmwise condensation on a
smooth hydrophilic Cu tube (HTC ~ 19 kW/m^2 K).
(B) Dropwise condensation on a silane coated
smooth Cu tube. The inset shows a nanostructured,
superhydrophobic CuO surface that enhances
dropwise condensation via the jumping-droplet
phenomena (HTC ~ 92 kW/m^2 K). Reprinted with
permission from ( 45 ), copyright the American
Chemical Society (2012). (C) A steel grid
(square pores with 1-mm spacing) coated with
electrospun fibers containing 9.1 wt % fluorodecyl
POSS used for oil-water separation. Octane
droplets (red) easily pass through the membrane,
whereas water droplets (blue) bead up on the
surface. Figure from ( 23 ). Reproduced with
permission from AAAS. (DandE) Droplets of
water (dyed blue) and rapeseed oil (dyed red) on
dip-coated stainless-steel mesh (top) and
polyester fabric (bottom). Insets show the surface
texture of the developed membranes ( 5 ). (F) An
optical image showing the continuous separation
of a water-in-hexadecane emulsion using a
superhydrophilic and oleophobic membrane at the
bottom, and a superhydrophobic and oleophilic membrane at the side of the apparatus ( 5 ). Reproduced with permission from Springer Nature.
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