Purity of the sacred lotus, or escape from contamination in biological

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Planta (1997) 202: 1–8
Purity of the sacred lotus,
or escape from contamination in biological surfaces
W. Barthlott, C. Neinhuis
Botanisches Institut und Botanischer Garten der Universität Bonn, Meckenheimer Allee 170, D-53115 Bonn, Germany
Received: 19 August 1996 / Accepted: 12 November 1996
Abstract. The microrelief of plant surfaces, mainly
caused by epicuticular wax crystalloids, serves different
purposes and often causes effective water repellency.
Furthermore, the adhesion of contaminating particles is
reduced. Based on experimental data carried out on
microscopically smooth (Fagus sylvatica L., Gnetum
gnemon L., Heliconia densiflora Verlot, Magnolia grandiflora L.) and rough water-repellent plants (Brassica
oleracea L., Colocasia esculenta (L.) Schott., Mutisia
decurrens Cav., Nelumbo nucifera Gaertn.), it is shown
here for the first time that the interdependence between
surface roughness, reduced particle adhesion and water
repellency is the keystone in the self-cleaning mechanism
of many biological surfaces. The plants were artificially
contaminated with various particles and subsequently
subjected to artificial rinsing by sprinkler or fog generator. In the case of water-repellent leaves, the particles
were removed completely by water droplets that rolled
off the surfaces independent of their chemical nature or
size. The leaves of N. nucifera afford an impressive
demonstration of this effect, which is, therefore, called
the ‘‘Lotus-Effect’’ and which may be of great biological
and technological importance.
Key words: Contamination (plant surface) – Cuticle –
Epicuticular wax – Lotus-Effect – Nelumbo – Wettability
(plant surface)
Introduction
All primary parts of plants (except roots) are covered by
a cuticle that is the interface between plants and their
Dedicated to Professor Andreas Sievers on the occasion of his
retirement
Abbreviations: CA ˆ contact angle; SC ˆ silicon carbide; SEM ˆ
scanning electron microscopy
Correspondence to: W. Barthlott; FAX: 49(228) 73 3120
environment. The cuticle is composed of soluble lipids
embedded in a polyester matrix (Holloway 1994). Due to
its chemical composition, the cuticle in most cases forms
a hydrophobic surface.
In the past 25 years, scanning electron microscope
studies of biological surfaces have revealed an incredible
microstructural diversity of the outer surfaces of plants.
Microstructures such as trichomes, cuticular folds, and
wax crystalloids serve different purposes and often
provide a water-repellent surface, which is not rare in
terrestrial plants. Water repellency is mainly caused by
epicuticular wax crystalloids which cover the cuticular
surface in a regular microrelief of about 1–5 lm in height
(Baker 1982; Jeffree 1986).
The principle connections between surface roughness
and water repellency were worked out by Cassie and
Baxter (1944). Later, the wetting properties of surfaces
were the subject of intensive studies in physics as well as
in biology and reviewed several times (e.g. Fowkes 1964;
Holloway 1970; de Gennes 1985; Adamson 1990). In
addition, the measurement and characterization of
different kinds of particles and their impact on vegetation has been studied thoroughly (e.g. Belot and
Gauthier 1975; Little 1979; Chamberlain and Little
1981; Coe and Lindberg 1987; Farmer 1993).
The relationship between surface roughness and
wettability or particle deposition, respectively, is well
known. Surprisingly few reports exist – most of which
lack experimental data – concerning the correlation
between surface roughness, water repellency and the
removal of particles (Engel 1939; Davies 1961;
Rentschler 1971; Barthlott 1990). However, there has
been a vague knowledge of the correlation between
water repellency and reduced contamination for more
than a century (Lundström 1884).
During the routine interpretation with respect to
systematics of scanning electron microscopy (SEM)
micrographs of the leaf surfaces of some 10000 plant
species (Barthlott 1990, 1993), we observed a peculiar
effect. Independently of the degree of pollution at the
collection site, species with smooth leaf surfaces always
had to be cleaned before examination, while those with
2
W. Barthlott and C. Neinhuis: Self-cleaning of biological surfaces
epicuticular wax crystals were almost completely free of
contamination.
Later, we validated these observations by performing
simple qualitative experiments. As one example, microscope slides were affixed to water-repellent leaves of
Indian cress (Tropaeolum majus) and examined by SEM
six weeks later. While the rough leaf surface was
virtually clean, the smooth glass slides had accumulated
particulate contaminations. Based on a number of
experiments, it was proven that water repellency causes
an almost complete surface purification (self-cleaning
effect): contaminating particles are picked up by water
droplets or they adhere to the surface of the droplets and
are then removed with the droplets as they roll off the
leaves.
Contaminants. Several different particles of various grain sizes
(range of the diameters is given) were used for contamination: dried
soil, barium sulphate (5–30 lm), siliconcarbide (SC) dust 360 (5–
25 lm) and 1200 (0.5–3.5 lm, both Guilleaume, Bonn, Germany),
titanium dioxide (1–20 lm; Merck, Darmstadt, Germany), toner of
a Xerox photocopier (5 lm), Sudan-III pigment powder (1–20 lm,
Merck), silanized (Silbond 600 MST) and non-silanized (Silbond
600 AST) quartz dusts (6–25 lm; Quarzwerke, Frechen, Germany),
spores of the tree fern Cibotium schiedei (20 lm), and conidia of the
grey moulds Botrytis cinerea (20–30 lm) and Tiletia caries
(20 lm).
Materials and methods
Plant material. Leaves from approx. 340 plant species, cultivated at
the Botanical Garden in Bonn, were investigated by contact-angle
measurements and high-resolution SEM. A selection of these species
was used for quantitative contamination experiments. Smooth
surfaces of differing wettability (Table 1) were represented by the
leaves of two evergreen trees (Gnetum gnemon L., Magnolia
denudata L.), the rainforest herb Heliconia densiflora Verlot, and
beech (Fagus sylvatica L.). Water-repellent, rough surfaces were
represented by leaves of the sacred lotus (Nelumbo nucifera Gaertn.),
kohlrabi (Brassica oleracea L.), taro [Colocasia esculenta (L.)
Schott] and the petals of a composite (Mutisia decurrens Cav.).
Contact-angle (CA) measurement. Measurement of CA were
carried out on the adaxial surfaces of young, fully developed
leaves. Samples of 1 cm2 cut from the central area of the leaf lamina
were affixed to glass slides by double-sided adhesive tape (TesaFix;
Beiersdorf, Hamburg, Germany) to ensure an even surface.
Droplets (10 ll) of distilled water were applied to the surface and
the static CA was measured with a horizontal microscope equipped
with the Goniometer G1 (Erma Optical, Tokyo, Japan). In Table 1,
the mean values and standard deviation of 20 CA measurements
are noted.
Scanning electron microscopy (SEM). For examination of the
surface relief, samples of about 1 cm2 cut from the middle of the
leaf lamina of young, fully developed leaves were prepared by
liquid substitution according to Ensikat and Barthlott (1993). For
high-resolution SEM of epicuticular waxes, fresh leaf samples were
affixed to aluminium stubs by double-sided adhesive tape (TesaFix)
and air-dried. All specimens were sputter-coated (Balzers Union
SCD 034; Balzers, Wiesbaden, Germany) and examined in a
Cambridge Stereoscan 200 (Leica, Bensheim, Germany) equipped
with a Lanthan-Hexaboride cathode.
Table 1. Mean values (± SD) of 20 measurements of the static CA
(°) on the adaxial leaf surfaces of the species used for contamination experiments
Plant species
CA
Heliconia densiflora
Gnetum gnemon
Magnolia denudata
Fagus sylvatica
Nelumbo nucifera
Colocasia esculenta
Brassica oleracea
Mutisia decurrens
28.4
55.4
88.9
71.7
160.4
159.7
160.3
128.4
±
±
±
±
±
±
±
±
4.3
2.7
6.9
8.8
0.7
1.4
0.8
3.6
Artificial contamination. Whole plants or individual leaves were
placed in a contamination chamber consisting of a frame measuring
60 cm × 60 cm × 100 cm and covered by plastic foil. The chamber
was divided by a removable wooden plate 40 cm above the ground
covering the specimens. The contaminants were blown into the
upper part of the contamination chamber by pressurised air. After
15 s, when the largest particles and particle aggregates had
sedimented onto the plate, the latter was removed and the particles
were deposited onto the specimens evenly. Particle density could be
varied by the time of exposure to the dust. After each contamination, the chamber was cleaned with water. The number of particles
was determined by SEM in combination with a digital image
analysis system (TCL-Image; Multihouse TSI, Amsterdam, The
Netherlands) before and after rinsing.
Artificial rinsing. Following contamination, the specimens were
subjected to natural and artificial rain of various droplet sizes.
Artificial rain was simulated by a sprinkler producing water
droplets of 0.5–3 mm diameter. Fog treatment was performed in
a chamber equipped with a high-pressure fog system (Osberma,
Engelskirchen, Germany) producing very fine fog droplets (1–
20 lm diameter). Fog treatment was performed in order to obtain
an experimental set-up which avoided the high kinetic energy of
larger water droplets.
Results
Surface characteristics and wettability of microscopically
rough and smooth leaves. The majority of the wettable
leaves (CA < 110°) investigated were more or less
smooth, without any prominent surface sculpturing. In
particular, epicuticular wax crystals were absent
(Fig. 1a–d). Some leaves were covered by trichomes
during leaf expansion and several species showed an
ornamentation due to slightly convex epidermal cells, as
well as sunken or raised nerves. The CAs ranged from
110° in young leaves to less than 10° in old, naturally
contaminated leaves. In contrast, water-repellent leaves
exhibited various surface sculptures, mainly epicuticular
wax crystals in combination with papillose epidermal
c
Fig. 1a–h. Scanning electron micrographs of the adaxial leaf surface
of smooth, wettable (a–d) and rough, water-repellent (e–h) leaf
surfaces. The smooth leaves of Gnetum gnemon (a) and Heliconia
densiflora (b) are almost completely lacking microstructures while
those of Fagus sylvatica (c) and Magnolia denudata (d) are
characterized by sunken and raised nervature, respectively. The rough
surfaces of Nelumbo nucifera (e) and Colocasia esculenta (f) are
characterized by papillose epidermal cells and an additional layer of
epicuticular waxes. Brassica oleracea leaves (g) are densely covered by
wax crystalloids without being papillose, and the petal surfaces of
Mutisia decurrens (h) are characterized by cuticular folds.
Bars ˆ 100 lm (a–d) and 20 lm (e–h)
W. Barthlott and C. Neinhuis: Self-cleaning of biological surfaces
3
4
cells (Fig. 1e–g). Their CAs always exceeded 150°. The
petals of Mutisia decurrens were characterized by
cuticular folds (Fig. 1h). They were not as water
repellent as leaves with epicuticular wax crystalloids,
but they had higher mean CAs than smooth leaves.
Depending on the wettability, applied water droplets
(40 ll) displayed distinct characteristics when rolling off
the leaves. On water-repellent surfaces, water contracted
to form spherical droplets. It ran off the leaf very
quickly, even at slight angles of inclination (< 5°),
without leaving any residue. In smooth leaves with
CAs above 70°, water contracted to form more or less
hemispherical droplets that ran off the leaves comparatively slowly and at higher angles of inclination
(10–30°). This was true also for the petals. In smooth
leaves with low CAs, water spread quickly and partially
ran off the leaves at inclination angles of > 40°.
W. Barthlott and C. Neinhuis: Self-cleaning of biological surfaces
Fig. 3. Particles remaining on smooth and rough leaf surfaces after
artificial contamination with silicon carbide (SC ) of two different
grain sizes and exposure to a natural rainstorm. While rough surfaces
are completely cleaned, smooth surfaces retain 5–50% of the particles,
depending on the particle size
The self-cleaning properties of microscopically rough and
smooth surfaces. In general, particles of any kind were
always removed entirely from water-repellent leaves
when subjected to natural or artificial rain, independent
of their size and chemical nature, as long as the surface
waxes were not destroyed. Figure 2 summarizes four
series of experiments carried out with Sudan III, barium
sulfate, spores of Cibotium schiedei, and conidia of
Botrytis cinerea. After contamination, the leaves were
subjected to artificial rain for 2 min at an inclination
angle of 15°. While the smooth surfaces retained 40–80%
of their particles after the treatment, the sculptured
surfaces were completely cleaned. Although the CAs
were considerably lower in M. decurrens petals, they also
displayed a high self-cleaning ability.
Generally, the results were not influenced by particle
chemistry and size, or by procedure and duration of
rinsing. Wettable plant surfaces always retained a
considerable number of the contaminating particles
after rinsing and drying of the leaves. Larger numbers of
particles were removed from smooth leaves only when
subjected to heavy natural rain. Droplets of rainstorms
are especially large and have a high kinetic energy which
facilitates particle removal. Figure 3 presents the percentage of particles remaining after contamination with
SC 1200 and 360 and exposure to a natural rainstorm
during which total precipitation amounted to 5 mm.
When subjected to very fine fog having droplets of
almost no kinetic energy, the results were different. The
rough surfaces of N. nucifera and C. esculenta retained a
certain amount of extremely small particles (e.g. SC
1200) on the leaf within the troughs between the
epidermal papillae (Fig. 4). However, these particles
were easily removed from the surfaces when subjected to
Fig. 2. Results summarizing four series of contamination experiments
carried out with Sudan III, barium sulfate, Cibotium schiedei spores
and Botrytis cinerea conidia. The columns represent the mean values
of the percentage of particles remaining on smooth and rough leaves
after artificial rinsing; initial number set as 100%
Fig. 4. Particles remaining after artificial contamination with silicon
carbide (SC ) 360 and 1200, subjected to 1 mm artificial fog at 15°
inclination angle. Among species with water repellent surfaces the
ones with epidermal papillae retain a small amount of very fine
particles
W. Barthlott and C. Neinhuis: Self-cleaning of biological surfaces
gentle rain or to single droplets that were allowed to fall
onto the leaves from a height of about 5 cm.
The effect could be demonstrated on the microscopic
level using mercury as an analogous liquid. The roughness of the papillose leaves led to a reduced contact area
between particles and surface (Fig. 5), as well as between
droplets and surface (Fig. 6). Droplets rested only on the
tips of epicuticular wax crystals on the top of the
papillose epidermal cells. Contaminating particles were
picked up by the liquid and carried away when the
droplet rolled off the leaf (Fig. 7).
Fig. 5. Contaminating particle on a regularly sculptured wing surface
of Cicada orni, demonstrating the decreased contact area between a
particle and a rough surface. Bar ˆ 1 lm
Fig. 6. Mercury droplet on the papillose adaxial epidermal surface of
Colocasia esculenta demonstrating the effect of roughness on
wettability. Due to the decreased contact area between liquid and
surface, air is enclosed between the droplet and the leaf, resulting in a
particularly strong water-repellent surface. Bar ˆ 20 lm
Fig. 7. Mercury droplet on the adaxial leaf surface of Colocasia
esculenta, demonstrating the Lotus-Effect. Contaminating particles
adhere to the surface of the droplet and are removed from the leaf
when the droplet rolls off. Bar ˆ 50 lm
5
Discussion
The results presented above document an almost
complete self-cleaning ability by water-repellent plant
surfaces. This can be demonstrated most impressively
with the large peltate leaves of the sacred lotus (Nelumbo
nucifera). According to tradition in Asian religions, the
sacred lotus is a symbol for purity, ensuing from the
same observations we have made. This knowledge is
already documented in Sanskrit writings, which fact has
led us to call this phenomenon the ‘‘Lotus-Effect’’.
Physical background of the Lotus-Effect. The surface
physics behind the Lotus-Effect can be derived from the
behavior of liquids applied to solid surfaces. Until now
there have been only a few investigations dealing with
the interaction between rough biological surfaces, particles and water. However, since the wettability of solid
surfaces is well investigated in surface science (e.g.
Dettre and Johnson 1964; de Gennes 1985; Adamson
1990; Myers 1991), it is possible to draw conclusions
about the conditions on leaf surfaces.
The wetting of a solid with water, with air as the
surrounding medium, is dependent on the relation
between the interfacial tensions (c) water/air (cwa),
water/solid (cws) and solid/air (csa). The ratio between
these tensions determines the CA h of a water droplet on
a given surface and is described by Young’s equation
csa ) cws ˆ cwa cosh. A CA of 0° means complete
wetting, and a CA of 180° corresponds to complete
non-wetting. Neither case is apparent in plant cuticles.
Solids with large csa are more easily wetted than those
with low csa (e.g. Teflon). In the latter, water tends to
form hemispherical droplets with a high CA.
If a droplet is applied to a solid surface, it will wet the
surface to a certain degree. The amount of wetting
depends on the ratio between the energy necessary for
the enlargement of the surface and the gain of energy
due to adsorption, which compensates for the former. At
equilibrium, the energy of the system is minimized
(Adamson 1990; Myers 1991).
Surfaces with only few or completely lacking polar
groups exhibit a very low interfacial tension (de Gennes
1985). This applies also to many components of
epicuticular waxes (e.g. hydrocarbons). In the case of
water-repellent rough surfaces, air is enclosed between
the epicuticular wax crystalloids, forming a composite
surface (Fig. 6). This enlarges the water/air interface
while the solid/water interface is minimized (Dettre and
Johnson 1964; Holloway 1970). On such a rough ‘‘low
energy’’ surface, the water gains very little energy
through adsorption to compensate for any enlargement
of its surface. In this situation, spreading does not occur,
the water forms a spherical droplet, and the CA of the
droplet depends almost entirely on the surface tension of
the water.
Particles deposited on a waxy surface consist, in most
cases, of material which is more readily wetted than
hydrophobic wax components. In addition, they are in
general larger than the surface microstructures and rest
only on the very tips of the latter (Fig. 5). As a result, the
6
W. Barthlott and C. Neinhuis: Self-cleaning of biological surfaces
interfacial area between both is minimized. In the case of
a water droplet rolling over a particle, the surface area of
the droplet exposed to air is reduced and energy through
adsorption is gained. The particle is removed from the
surface of the droplet only if a stronger force overcomes
the adhesion between particle and water droplet
(Adamson 1990). On a given surface, this is the case if
the adhesion between particle and surface is greater than
the adhesion between particle and water droplet. Due to
the very small interfacial area between particle and
rough surface, adhesion is minimized. Therefore the
particle is ‘‘captured’’ by the water droplet and removed
from the leaf surface (Fig. 7).
The effectiveness of the self-cleaning ability decreased
in the case of fog and dew, in contrast to rain. Rain
droplets have a high kinetic energy. Elastic deformation
allows them to penetrate between epidermal papillae and
remove particles within the troughs. This does not
happen with fog, and especially not with dew. This
explains the fact that in the case of the papillose leaves of
N. nucifera and C. esculenta, a certain number of very
small particles is retained after fog treatment, while no
difference could be observed in the non-papillose leaves
of B. oleracea.
The quantity of particles removed from a smooth
surface depends mainly on its wettability. In surfaces
with high CAs, spreading is very limited, and the
velocity of droplets running off a surface is relatively
low. Therefore, particles are mainly displaced to the
sides of the droplet and re-deposited behind the droplet,
but not removed. Especially hydrophobic particles tend
to remain on such surfaces. This result, which was
observed also by Davies (1961), may be explained by the
similar interfacial tensions between the particles and the
surface. In surfaces with a low CA, droplets spread very
quickly and the water runs off the leaves with considerable velocity. It is very likely that particles are carried
along with the moving liquid front, a mechanism that
was also presumed responsible for the removal of
microorganisms from leaf surfaces (Lips and Jessup
1979). This explains the comparatively effective cleaning
effect in the leaves of Heliconia, in contrast to Magnolia
and Gnetum. After several weeks, however, Heliconia
leaves also accumulate particles and are easily colonized
by bacteria, fungi, and algae, which was not observed in
water-repellent leaves. The latter always exhibited a very
low degree of contamination. In intact leaves, colonization by bacteria or algae could not be observed.
The disparate results obtained from smooth and
rough surfaces with respect to wettability and particle
removal are summarized in Fig. 8a,b.
The biological implications of the Lotus-Effect. The
cuticle is the outermost barrier of plants towards their
environment and is, therefore, the first protective layer
(Dickinson 1960; Martin 1964; Campbell et al. 1980;
Juniper 1991). Because the air contains many kinds of
particles, leaf surfaces are continuously contaminated.
Many deposits are more or less neutral, but various
kinds of contamination may cause considerable damage
to the plants, depending on size and chemical nature. It
was shown that in polluted areas where plants are
heavily contaminated with dust, leaf surface temperatures increased under insolation (Eller 1977). In addition, particles within a certain size range may occlude
stomata and influence stomatal diffusive resistance
(Flückiger et al. 1979). These and other interactions
between dust particles and plants have been reviewed
extensively by Farmer (1993). Water-repellent plants
escape from those harmful effects through the LotusEffect. Although it was shown that particles are captured
more effectively by rough leaf surfaces (Chamberlain
1967; Belot and Gauthier 1975), this disadvantage is
compensated for by a very effective self-cleaning capability.
The Lotus-Effect plays another important role in the
defense against pathogens. Spores and conidia of
pathogenic microorganisms, as well as inorganic particles, are deposited on the leaf surfaces. Again, wettability is important for the adhesion of microorganisms to
leaf surfaces (Rogers 1979). In addition, on waterrepellent surfaces, spores and conidia are deprived of the
Fig. 8a,b. Diagram summarizing the
connection between roughening and
self-cleaning. While on smooth surfaces the particles are mainly redistributed
by water (a), they adhere to the
droplets surfaces on rough surfaces
and are removed from the leaves when
the droplets roll off (b)
W. Barthlott and C. Neinhuis: Self-cleaning of biological surfaces
7
water necessary for germination (Campbell et al. 1980;
Allen et al. 1991; Juniper 1991). Therefore, the epicuticular wax crystalloids and their physical properties
may be regarded as the first line of defense against
pathogens. Our results indicate that the Lotus-Effect
may be the most important function of epicuticular
waxes and the reason for pervasive microsculpturing of
many leaf surfaces. There are but a few pathogens that
are able to overcome this barrier. Powdery mildews, for
example, contain a small amount of water within their
conidia which enables them to germinate on virtually dry
surfaces. A dry surface seems to be beneficial to them,
while there is some indication that a wet surface may
impede germination (Wheeler 1981).
As shown before, epicuticular wax crystalloids provide a highly effective self-cleaning surface to many
plants. On the other hand, they are very fragile structures and may be easily altered, especially by mechanic
abrasion (van Gardingen et al. 1991; BermadingerStabentheiner 1994). This also influences the waterrepellent function: within altered areas, particles may be
retained permanently. If the damage is not too grievous,
it can be compensated for by the regeneration of the wax
crystalloids (e.g. Hallam 1970). Apart from naturally
occurring wax alterations, some anthropogenic influences can be very serious. This is especially true for
surfactants. They are an important component in allwater-based pesticides, since they enable the uptake of
an active ingredient through the cuticle (Stevens and
Bukovac 1985; Lownds et al. 1987; Knoche and
Bukovac 1993). However, the surfactants cause considerable damage to the wax ultrastructure (Noga et al.
1987; Wolter et al. 1988). Due to the alterations in the
wax ultrastructure, the wettability of the leaves is
increased for at least several days and water is retained
within the altered areas. As a result, contaminating
particles, including spores and conidia of pathogens, are
also found within the areas of altered waxes (Neinhuis
et al. 1992). Under unfavourable conditions, the probability of an infection in a plant may be enhanced, which
is in contrast to the aim of a pesticide application.
The Lotus-Effect is not restricted to plants; indeed, it
has an overall biological importance, e.g. for insects. In
particular, those insects with large wings, which cannot
be cleaned by legs, have water-repellent wing surfaces
that exhibit the self-cleaning ability (Wagner et al. 1996).
In this case, not only the removal of particles is of
interest, but also the maintenance of flight capability,
which may be lost due to an unequal load on the wings.
The present paper is based on research that was supported by
several organizations and persons. For funding we are indebted
to: Bundesministerium für Forschung und Technologie (Bonn),
Deutsche Forschungsgemeinschaft (Bonn), Akademie der Wissenschaften und Literatur (Mainz, Germany). For helpful comments
and discussions we are indebted to H. Erhard and co-workers
(Fachbereich Physik, Universität Kaiserslautern, Germany), Z.
Hejnowicz (Department of Biophysics and Cell Biology, Silesian
University, Katowice, Poland), M. Markus (Max-Planck-Institut
für Molekulare Physiologie, Dortmund, Germany) and A. Sievers
(Botanisches Institut, Universität Bonn).
Conclusion. Many terrestrial plants and animals are
water-repellent due to hydrophobic surface components
in connection with a microscopic roughness. It was
shown that these surfaces provide a very effective antiadhesive property against particulate contamination.
This self-cleaning mechanism, called the Lotus-Effect,
may be the most important function of many microstructured biological surfaces. We assume that this effect
can be transferred to artificial surfaces (e.g. cars, facades,
foils) and thus find innumerable technical applications.
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