Evaporation kinetics of surfactant solution droplets on rice (Oryza sativa) leaves
Evaporation kinetics of surfactant solution droplets on rice (Oryza sativa) leaves
Zhao-Lu Zhou☯ 0 1 2
Chong Cao☯ 0 1 2
Li-Dong Cao 0 1 2
Li Zheng 0 1 2
Jun Xu 0 1 2
Feng-Min Li 0 1 2
Qi- Liang Huang 0 1 2
0 Key Laboratory of Integrated Pest Management in Crops, Ministry of Agriculture, Institute of Plant Protection, Chinese Academy of Agricultural Sciences , Beijing , China
1 Funding: This study was supported by the National Natural Science Foundation of China (NSFC) , no. 31471805, Prof. Qi-Liang Huang , and the National Natural Science Foundation of China (NSFC) , no. 31601673, Dr. Chong Cao
2 Editor: Scott W. McCue, Queensland University of Technology , AUSTRALIA
The dynamics of evaporating sessile droplets on hydrophilic or hydrophobic surfaces is widely studied, and many models for these processes have been developed based on experimental evidence. However, few research has been explored on the evaporation of sessile droplets of surfactant or pesticide solutions on target crop leaves. Thus, in this paper the impact of surfactant concentrations on contact angle, contact diameter, droplet height, and evolution of the droplets' evaporative volume on rice leaf surfaces have been investigated. The results indicate that the evaporation kinetics of surfactant droplets on rice leaves were influenced by both the surfactant concentrations and the hydrophobicity of rice leaf surfaces. When the surfactant concentration is lower than the surfactant CMC (critical micelle concentration), the droplet evaporation time is much longer than that of the high surfactant concentration. This is due to the longer existence time of a narrow wedge region under the lower surfactant concentration, and such narrow wedge region further restricts the droplet evaporation. Besides, our experimental data are shown to roughly collapse onto theoretical curves based on the model presented by Popov. This study could supply theoretical data on the evaporation of the adjuvant or pesticide droplets for practical applications in agriculture.
Data Availability Statement; All relevant data are within the paper
Rice is one of the most widely grown crops in the world [
], and severely affected by plant
diseases, insect pests, and weeds, all of which are mainly controlled by foliar spraying of pesticide
solutions. Spray application is a complex dynamic process that involves many interdependent
components. Transportation of an active ingredient is a complicated process, which starts
with the preparation of the spray solution followed by atomization, translocation, and impact
between the solution and the leaf surface [
]. The leaf surface characteristics, spray solution
properties, and environmental conditions affect the spray deposition of pesticide solutions
onto the target crop leaves. Thereby, the evaporation behavior of droplets significantly affects
the deposition formation, drying process, penetration and translocation within the target crop
tissue, and bio-efficiency. The high temperatures of rice paddies cause the rapid evaporation of
pesticide droplets after spray, especially the rice leave surfaces which are hydrophobic [
highly water repellent, making it easy for the pesticide droplets to bounce and roll off. All of
these factors could reduce the efficacy of pesticides and even have an influence on food quality,
eco-environmental security, and human health [
]. Thus, the evaporation of pesticide droplets
and their retention on rice leaf surfaces play important roles in effective control of pesticides.
For example, the evaporation time is crucial for the efficiency of systemic pesticides, since they
would be effective only after being absorbed by the plant. Longer evaporation times could
endow plants more chance to contact with the active ingredient that helps control the disease.
The evaporation of sessile droplets on a solid substrate has been investigated both
theoretically and experimentally [5±10]. Many studies have been reported in different research areas
including surface patterning [
], inkjet printing [
], colloidal photonic crystal fabrication
]. The evaporation of droplets is influenced by many factors, such as the chemical
] and physical properties (e.g., the roughness of the substrate [
]), and the properties
of the liquid droplet [
] of the substrate. Picknett and Bexon [
] studied the evaporation of
sessile droplets in an open atmosphere and have developed two modes for droplets
evaporation that act on droplets on a smooth substrate: the constant contact radius (CCR) mode and
the constant contact angle (CCA) mode. Stauber et al. [
] reported a complete description of
the relationship between the lifetime of a droplet on a solid substrate in a stick-slide mode and
that of initially identical droplets in the extreme modes (CR and CA modes). They found that
generally, the lifetime of a droplet is not constrained by the lifetimes of extreme modes. Also, if
droplets evaporate in an idealized stick-slide mode the dependence of the lifetime on the initial
contact angle is qualitatively different from that when the relationship between the initial and
the receding contact angles is not taken into account [
]. The evaporation flux on the surface
of droplets was assumed to be constant in early models [
6, 8, 9, 20
]. However, Deegan and
] argued that the evaporation flux along the droplet surface is nonuniform. Popov
] reported an analytical solution to describe the rate of mass loss in terms of the entire
range of contact angles. Gelderblom et al. [
] verified experimentally the validity of Popov's
ªdiffusion-limitedº model [
] for droplet evaporation on a superhydrophobic surface with a
fixed contact line. The ªdiffusion-limitedº model is widely used among experiments for sessile
droplets with small contact angles (< 90Ê) when it is assumed that the evaporation of droplets
is quasi-steady and limited by the diffusion of vapor in the quiescent atmosphere above the
droplet. To date, relatively few research has been done for hydrophobic [6, 24±26] or
22, 23, 25, 27, 28
] surfaces. The extreme CCA and CCR evaporation modes
become indistinguishable on strongly hydrophobic substrates [
]. It is appropriate to use the
so-called ª2/3 power lawº to extrapolate the lifetime of droplets that evaporate from strongly
hydrophobic substrates for both CCR and CCA modes. The ªdiffusion-limitedº model
provides the good agreement with a smooth hydrophobic surface (contact angle ~120Ê), while
the structured super-hydrophobic surface (contact angle ~160Ê) demonstrates a significant
deviation from the diffusion-limited model [
]. Experimental investigations of the
evaporation kinetics of sessile water droplets on micropillared super-hydrophobic surfaces  have
shown an initial large contact angle that provides a narrow wedge region. Within this region,
the liquid−vapor diffusion is significantly restricted. Even fewer experiments have been
performed for evaporation from disordered super-hydrophobic surfaces, such as natural real
leaves. The wetting of natural leaf surfaces is different from that of artificial ones since the leaf
roughness has an effect on the retention of water droplets on leaves [
]. The leaf surface
roughness, related to the wettability [
], was effectively quantified by a fractal dimension
analysis of cryo-scanning electron microscopy (cryo-SEM) [
]. Leaf surfaces vary a lot among
different species [
]Ðfor example, from the smooth surfaces of amorphous waxes to rough
surfaces with fine epicuticular wax crystals. Moreover, the composition of the wax layer is
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closely related to the leave wettability, which varies among leaf development stages and leaves
In agriculture, the evaporation process of a pesticide droplet consists of evaporation during
droplet transport and on the leaf surface, without considering atmospheric factors, such as
temperature, wind, and humidity. The former process is mainly influenced by the droplet
properties, which can be changed if a surfactant is added. Surfactants are widely used to
facilitate the wetting of surfaces and spreading of water-based formulations of agrichemicals [
]. Adding surfactants to the aqueous droplet can considerably suppress evaporation,
especially for insoluble monolayers in the condensed state . But some surfactants can also
facilitate the water evaporation, which decreases the contact angle and thus increases the contact
line radius [16, 41±43]. While the latter process is closely related to the droplet properties,
surface roughness, surface strain, and so on.
Motivated by these previous studies, herein, the impact of the surfactant concentration on
contact angle, contact diameter, droplet height, and evolution of the evaporative droplet volume
on rice leaf surfaces was explored in this research. The experimental results were compared to
Popov's model [
]. This study should provide theoretical data concerning the evaporation of
the adjuvant and support practical application of pesticide droplets in the future.
Materials and methods
Plants and sample preparation
The seeds of the rice variety used in this study are called Dongjin (Oryza sativa ssp. japonica). It
is commonly cultivated in South China and provided by the Institute of Plant Protection,
Chinese Academy of Agricultural Sciences. After seeding on a water bed, the rice plants were
transplanted into small plastic pots containing soil. And after three leaf stages, the seedlings were
transplanted into oblong plastic pots (50 cm × 30 cm × 17 cm) inundated with water. Three
seedlings were sown in one plant pot in the glasshouse under the same controlled
environmental conditions: photoperiod, 14 h; relative humidity, 65±80%; and day and night temperatures of
30 and 26ÊC, respectively. A rice plant with seven leaves was chosen for this experiment.
The fresh rice leaves were fixed to glass slides using a double-sided adhesive tape. The fresh
leaves, with the middle vein removed leaving only the side leaf, were adhered to the glass slide.
Touching the leaves and placing them in contact with other surfaces were avoided during the
experiment to maintain the leaf structure.
Surfactant was provided by the Dauni Research Center of Advanced Science and Technology
Co., Ltd, which consisted of hydrophilic polyoxyethylene moieties, hydrophobic alkyl chains,
and a main-chain with positive and negative segments. The chemical structure of the
surfactant is poly(acrylic acid/dimethyldiallylammonium chloride/octadecyl methyl-acrylate). The
molecular weight of the surfactant is 300000±400000.
Five surfactant solution concentrations (wt.% = 0.001%, 0.005%, 0.01%, 0.05%, and 0.10%)
were prepared and diluted with deionized water. For comparison, droplets of pure water were
also prepared in these experiments.
Measurements of the contact angle of droplet and surface tension of surfactant
Measurements of contact angles (CA) were performed with a high-speed optical CA
measuring device OCAH200 (precision: ±0.01, Data Physics Instruments GmbH, Filderstadt,
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Germany) equipped with a high-speed CCD video system and the built-in software SCAT,
which could automatically measure static and dynamic CA values.
The droplets were observed during their whole evaporation time and photographed at 1-s
time intervals. The high-speed CCD video system computed contact angle, contact diameter,
droplet volume (mass), and droplet height at every instant. The droplets were allowed to
evaporate in a chamber with a small hole at the top, which was controlled at 27±1ÊC (same as the
temperature in laboratory environment) and a humidity of 26.1%. A droplet with an initial
volume of 4 μL was dispensed using a carefully calibrated microsyringe Gastight-1750 Trace
syringe (Hamilton Switzerland) through the hole and deposited onto the rice leaf surfaces. It is
much smaller than the capillary length (which is 2.7 mm for a water droplet [
]), so the
influence of gravity could be neglected. Five concentrated of surfactant solutions and pure water
were deposited onto rice leaf surfaces. The experiment was repeated three times to ensure the
Surface tension of surfactant was measured by OCAH200 (precision: ±0.01, Data Physics
Instruments GmbH, Filderstadt, Germany) and DCAT21 (Data Physics Instruments GmbH,
Results and discussions
The surface tension of the surfactant
Surface tension of the surfactant solution was measured using the normal Pt-plate and the
pendant-drop method. As shown in Fig 1A, the critical micelle concentration (CMC) is 0.01%. Fig
1B shows the concentration dependency effect on dynamic surface tension of the surfactant in
the long-time regime. When the concentrations are lower than CMC (0.001%, 0.005%), more
than 2000 seconds is needed for the dynamic surface tension curves to reach the equilibrium,
and such long time will lower the measurement precision on account of the water evaporation.
Conversely, when the concentrations were higher than CMC (0.05%, 0.10%), the surface
tension takes a short time to reach the equilibrium, and the value is near 37 mN m-1 at the
concentration of 0.10%. Obviously, the surface tension decreases with the surfactant concentration
When the concentrations become lower than CMC, the surface tension decreases slowly by
a slow adsorption of the molecules at the liquid-vapor interface; while the concentration is
higher than CMC, the interfacial concentration becomes higher as the time continues, thus
leading to a decrease in the surface tension. A fast absorption of molecules in the liquid-vapor
interface occurs with the increasing concentration.
Fig 1. The surface tension for different concentrations of surfactant solution was measured by the normal
Pt-plate (a) and the pendant-drop method (b).
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Typical evolution of droplet contact angle and contact diameter on rice leaf surfaces
Fig 2 shows the developments in the droplet shapes during evaporation under different the
concentrations varying from 0% to 0.001%, 0.005%, 0.01%, 0.05%, and 0.10%, and various
evaporation times to achieve the same normalized volume is listed under each image. Compared to
droplet of pure water (0%), the shapes of droplets containing lower concentrations of surfactant
change a little over the whole evaporation period. With the concentration increase from 0.01%
to 0.05%, the leaf wetting by the droplets is improved and a CCR mode is nearly observed,
which is primarily influenced by the surfactant and the hydrophobicity of the leaf surfaces.
Droplet evaporation kinetics on rice leaf surfaces
Fig 3 shows the evolution of the contact angle and contact diameter of a sessile droplet under
different concentrations of surfactant solutions during evaporation on rice leaf surfaces. The
evaporation of droplets containing 0.001% (Fig 3B), 0.005% (Fig 3C), and 0.10% (Fig 3F) are
dominated by a mixed mode of evaporation (decreasing contact angle and contact diameter).
The distinct evaporation periods (in the mixed mode) are indicated by vertical dotted lines. A
more rapid decrease in contact angle and a quicker evaporation of the droplet could be
observed for a concentration of 0.1%, which is the main difference between 0.001%, 0.005%,
and 0.10%. In contrast, the droplets of other surfactant concentrations undergo three
sequential evaporation periods (start steady stage ! CCR mode ! mixed mode), as shown in Fig 3A
(pure water), Fig 3D (0.01%), and Fig 3E (0.05%), respectively. In addition, the distinct
evaporation periods are indicated by vertical dotted lines.
Notably, the mechanism of aqueous surfactant solutions spreading over hydrophobic
substrates have not yet been completely understood [
], since the spreading dynamic of
surfactant solutions is affected by the following: (i) a time-dependent adsorption/desorption of
surfactant molecules at all interfaces (i.e., liquid/vapor, solid/liquid, and solid/vapor) is
Fig 2. The typical changes in contact angle and contact diameter of pure water droplets (0%),
relatively low concentrations (0.001%, 0.005%), and high concentrations (0.01%, 0.05%). Furthermore,
various evaporation times to achieve the same normalized volume is listed under each image.
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Fig 3. Evolution of the contact angles (blue squares) and contact diameters (red triangles) of a sessile
droplet of (a) pure water droplets and (b±f) droplets containing different concentrations of surfactant over the
evaporation period on rice leaf surfaces. The distinct evaporation periods (the steady start stage, CCR, and mixed
mode) are indicated by vertical dotted lines. The vertical lines are determined by the significant change in the slope of
the contact diameter shown by black lines in the picture.
involved, which can drastically change the interfacial tension and the energy balance at the
moving three phase contact line; (ii) resulting interfacial tension gradients and Marangoni
flow as a consequence; and a (iii) disjoining/conjoining (Derjaguin's) pressure gradient. At the
concentrations of 0.001% and 0.005% (C<CMC), droplets show a slower decrease in contact
diameter and contact angle than others. As reflected in Fig 1B, molecules transported to the
three-phase contact line is delayed by a slow absorption at the liquid-vapor interface.
Therefore, a worsened wetting state occurs on the hydrophobic rice leaf surfaces, which keep the
droplet in the Cassie-Baxter state. In this case, the contact between the liquid with the leaf
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surface is minimal; therefore, air is contained among the three-phase contact line which can
facilitate the evaporation of the droplet and result in the existence of the narrow wedge region.
Within this region, the diffusion of liquid vapor is highly restricted during evaporation [
Besides, the evaporation of the mixed mode results in a little change of the droplet shape,
which prolongs the presence time of the narrow wedge region. It is assumed that the narrow
wedge region disappears at a contact angle of ~ 95Ê.
On the other hand, better wetting of the rice leaf surfaces occurs with a decrease of surface
tension for the solutions containing 0.01% and 0.05% surfactant (Fig 3D and 3E), and then
results in a lower air content at the three-phase contact line, consequently suppressing the
evaporation of droplet at the three-phase contact line. The trend of a transition from the
Cassie-Baxter to the Wenzel wetting state is characterized by a sudden decrease in contact angle
and increase in contact diameter at the beginning steady stage. In this case, the evaporation
kinetics shows an almost constant contact diameter and a decreasing contact angle (CCR
mode). In addition, the unchanged contact diameter indicates strong contact line pinning [
throughout the evaporation process. It is proposed that the strong contact line pinning is
induced by the absorption of surfactant. This kinetic evaporation progress causes a rapid
change to the shape of the droplet, resulting in a quicker disappearance of the narrow wedge
region and a reduction in the evaporation time. The pinning of the droplet boundary is related
to the intermolecular interactions at the three-phase contact line [
] and is affected by the
surface morphology, chemical heterogeneity, and interfacial wetting states [47±49].
As shown in Fig 3F, corresponding to 0.10% droplet, the highest concentrations of
surfactant in this experiment underwent evaporation via the mixed mode, which results in a sharp
decrease in contact angle, thus leading to a significant reduction of the narrow wedge region.
Aside from the effect of the narrow wedge region, the molecules of the high concentrations of
adjuvant may occupy too much space. Water in the droplet is squeezed out to the surface,
resulting in an increase in the rate of evaporation. Furthermore, a sharp decrease of contact
angle and contact diameter occurs under all concentrations at the end of the evaporation when
less water and higher concentrations of surfactant are present.
These evaporation periods depend on the surfactant concentrations and the hydrophobicity
of the rice leaf surface. Scanning electron micrograph (SEM) of the rice leaf surface is shown in
Fig 4. Apparently, it is hard for droplets with lower concentrations to make a smooth wetting
state on this disordered superhydrophobic leaf surface.
To further clarify the evaporation behavior, the evaporation trends of droplets under
different concentrations of surfactant are shown in Fig 5A and 5B (low concentrations of 0.001%
and 0.005%) and in Fig 5C and 5D (high concentrations of 0.01% and 0.05%). As shown in
Fig 5A for the concentrations of 0.001% and 0.005%, the poor wetting state results in a large
Fig 4. The scanning electron micrograph of the rice leaf surface used in the experiment.
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Fig 5. Sketches of two main droplet evaporation mode for droplets containing low concentrations of
(a, b) 0.001% to 0.005% and high concentrations of (c, d) 0.01% to 0.05%. Figs (b) and (d) show
enlarged sections of (a) and (c), respectively. The color changes are used to represent the evaporation of
the droplets. The blue dots respect the vapor evaporated from the droplet surface. Also, the density in Fig (a)
with a worse wetting state is higher than that of Fig (c), which has a better wetting state. The higher density of
vapor within the small narrow region also restricts the evaporation rate of the droplet.
amount of air content at the three-phase contact line, facilitating the evaporation of water and
contributing to a decrease in contact angle and contact diameter. This evaporation does not
change the profile of the droplet, but may result in a longer evaporation duration of the very
narrow wedge region magnified in Fig 5B, where the diffusion of liquid vapor is restricted
during evaporation [
]. In contrast, for the concentrations of 0.01% and 0.05%, the air content is
lower at the three-phase contact line, which results in a better wetting state on the surface of
the rice leaves, as is shown in Fig 5D. Such behavior is consistent with the CCR mode (i.e.,
constant contact diameter and decreasing contact angle) during the majority of the evaporation
phase, followed by a mixed mode (i.e., decrease in both contact angle and contact diameter)
near the end. This evaporation type results in a rapid change to the shape of the droplet and a
reduction in the evaporation time during which a narrow wedge region appears.
As shown in Fig 6, the contact angle is divided by the contact diameter. After the start of the
steady stage, the ratio exhibits two different trends. A decreasing ratio signifies a more rapid
change in contact angle than in contact diameter. However, the increasing ratio indicates a
more rapid change in contact diameter than contact angle. Besides, the increasing ratio for
droplets with concentrations of 0.001% and 0.005% is beneficial in maintaining the droplet
profile, which prolongs the presence of the narrow wedge region. Moreover, a decrease in the
ratio indicates a faster changing contact angle, leading to a more rapid disappearance of the
narrow wedge region, which is consistent with the conclusions from the data in Fig 3.
Droplet volume and droplet height on rice leaf surfaces
Fig 7A shows the evolution of the droplet volume with evaporation time (v/v0 vs. t). The plot is
initially linear, and then deviates from linearity at the end of the droplet lifetime. In addition,
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Fig 6. Evolution of the ratio of contact angle and contact diameter (contact angle/contact diameter vs.
time) for pure water droplets and droplets containing different concentrations of surfactant over the
the evaporation time of the droplet volume is related to the surfactant concentration: (1) when
the surfactant concentrations are 0.001% and 0.005%, the evaporation time is longer than that
of the water droplet; (2) similar evaporation times are observed for droplets containing 0.01%
surfactant concentrations and pure water; (3) when the surfactant concentrations of droplets
are 0.05% and 0.10%, the evaporation time is reduced, and such trend is more significant at
higher concentration levels. The deviation from linearity in Fig 7A is assumed to be due to the
existence of narrow wedge regions in water, droplets containing 0.001% and 0.005% surfactant
concentrations, as well as the better wetting state of droplets with concentrations of 0.01%,
0.05%, and 0.10%. But a stronger linear relationship is obtained by using the power-law model
[(v/v0)2/3 vs. t)] as shown in Fig 7B, and this situation allows a more accurate prediction of the
volume transfer rate than the initial model (v/v0 vs. t). Furthermore, the gradients of fitted lines
Fig 7. (a, b) Evolution of the volume of a pure water droplet and droplets containing different concentrations of
surfactant over the whole evaporation time, (v/v0) vs. t and (v/v0)2/3 vs. t, respectively.
PLOS ONE | https://doi.org/10.1371/journal.pone.0176870
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are -1.99, -1.86, -2.05, -2.26, and -2.68 (10−4/s) for surfactant concentrations from 0.001% to
0.10%, respectively, whereas that of a pure water droplet is only -2.07 (10−4/s). The more rapid
evaporation rate indicates the more rapid evaporation of the droplet, which is consistent with
the data shown in Fig 7A. Moreover, the evolution of the droplet height was also investigated as
shown in Fig 8. The evaporation rate can be reflected by the change of droplet height [
the droplet heights for all droplets decrease with increasing evaporation time. Although the
rates changed in a different way, it has a similar trend to that obtained for volume changes.
Different concentrated droplets have nearly the same height. It is obvious that the droplet height
changed slower than that of water under the concentrations of 0.001% and 0.005%, while it
changed faster than that of water with increasing concentrations from 0.01% to 0.05%.
In addition, the evaporation time required for the first 90% droplet volume (*4 μL)
(avoiding the measurement errors when the contact angle is too small to be calculated accurately)
of water and different concentrated surfactant on rice leaf surfaces is shown in Fig 9. The
evaporation time gradually increased with the increase in surfactant concentration, i.e., from
water to the concentration level of 0.005%. Furthermore, the evaporation time is significantly
reduced, even lower than that of water containing relatively high concentrations from 0.01%
to 0.1%. That is, relatively the low surfactant concentration can prolong the droplet
evaporation time, while higher surfactant concentrations correspond to the quicker droplet
evaporation. As with to the volume change, this behavior can be attributed to the existence of a narrow
wedge region at relatively low surfactant concentrations and a better wetting state at higher
concentrations, i.e., 0.01% to 0.10%.
Comparison between theory and experiment
Based on the Popov's model [
], Hanneke Gelderblom et al. [
] investigated the evaporation
of water droplets on a superhydrophobic substrate. To describe a universal behavior that is
Fig 8. Evolution of the height for water-only droplet and droplets of different concentrations of
surfactant with an initial volume of 4 μL on the surface of a rice leaf.
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Fig 9. Average time required to evaporate 90% of the volume of a pure water droplet and those
containing different concentrations of adjuvant (initial volume 4 μL) on natural rice leaf surfaces.
independent of drop size and other parameters cs, H, ρ, and D, they introduce the
nondimensional mass and time as
In our experiment, we used the following conditions: temperature of 27±1ÊC, D = 22.5×10 −6
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where M is the mass of the droplet, t is the evaporation time, ρ is the density of the liquid
(approximately to the density of water for the low concentrations of surfactant and the
evaporation of water vapor), R is the contact radius of the droplet, D is the diffusion coefficient, cs
and c1 are the saturated vapor concentration at the droplet surface and far from it respectively.
Then the relations that only rely on the contact angle can be obtained:
In these formulas, θ is the contact angle and f(θ) is the functional variation of contact angle
evaluated using a numerical integration scheme in MATLAB[
Z 1 1 cosh 2yt
0 sinh 2pt
Fig 10. The dimensionless droplet mass plotted against the dimensionless time (a). The rate of mass loss
of the droplet vs the contact angle (b). The color lines represent the experimental data, which are derived from
the measured droplet volume. The black solid lines represent the theoretical prediction according to Popov's model.
The experimental data are scaled according to (6). The time is set to 0 at the end of the droplet life.
m 2 /s, ρ* 996.5 kg/m3, c s = 2.60 × 10 −2 kg/m3, and c1 = H c s (all obtained from ) by
To make a comparison between theory and experiment, the experimental data is rescaled
according to (1). The time is set to 0 in the end of the droplet life. Meanwhile, the droplet
volume, contact angle, and contact radius can be obtained independently. Then, relation (3) is
used to derive the droplet mass theoretically according to the change of contact angle.
Furthermore, the rate of the mass loss given the contact angle can be obtained by Eqs (2) and (4) to
make a comparison between the experiment and theory. Fig 10A shows the dimensionless
droplet mass plotted against the dimensionless time. The color lines represent the
experimental data, which are derived from the measured droplet volume. The black solid lines represent
the theoretical prediction according to Popov's model [
]. Clearly, the experimental data is in
excellent agreement with the theoretical prediction (3). Fig 10B exhibits the rate of mass loss of
the droplet vs. the contact angle. Basically, the experimental date can roughly collapse onto the
theoretical curves for the superhydrophobic rice leaf surface according to the
ªdiffusion-limitedº Popov model. The disordered microstructure structure is shown in Fig 4, and the
chemical heterogeneity of leaves and the presence of the narrow wedge region can be seen in Fig 3.
Fig 10A shows the dimensionless droplet mass plotted against the dimensionless time. Fig
10B shows the rate of mass loss of the droplet plotted with the contact angle. The color lines
represent the experimental data, which are derived from the measured droplet volume. The
black solid lines represent the theoretical prediction according to the Popov model. The
experimental data are scaled according to (6). The time is set to 0 at the end of the droplet life.
Evaporation of the water droplets containing different concentrated surfactants on fresh rice
leaf surfaces are shown to occur by a mixed mode for droplets with concentrations of 0.001%
and 0.005%, whereas both a CCR and a mixed mode occur in water droplets and those with
concentrations of 0.01%, 0.05%, and 0.10%. The experimental results and analysis reveal that
the assumptions of the ªdiffusion-limitedº model are approximately applicable in the case of
droplets of water and different concentrated surfactant solutions on rice leaf surfaces. The
evaporation kinetics of the droplet is closely related to the surfactant concentrations and the
characteristics of rice leaf surfaces. It is found that when the concentrations of droplets are
0.001% and 0.005%, the adsorption of the molecules at the liquid-vapor interface is too slow to
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make a good wetting state for the droplet. The evaporation of the droplet is mainly in a mixed
mode, which results in the long existence of a narrow wedge region due to the slow change in
the droplet profile. Furthermore, the presence of the narrow wedge region restricts the
diffusion of liquid vapor, which contributes to the longer evaporation time compared to water
without any surfactant. However, due to the improved wetting state in higher levels of
concentration such as 0.01% and 0.05%, the mainly decrease of contact angle in the CCR mode results
in a quicker disappearance of the narrow wedge, which then reduced the evaporation time.
Furthermore, the evaporation time is significantly reduced in droplets containing 0.10%
surfactant, partly because a large proportion of the droplet volume is occupied by the surfactant
molecules. This result is further confirmed by the time required for the loss of the first 90%
droplet volume. The same trends are observed for the evolution of droplet volumes and droplet
heights. The results proved to a roughly collapse to the theoretical curves based on the model
presented by Popov [
In the field of agriculture, the addition of a surfactant could effectively enhance the wetting,
retention, and retention of pesticide droplets on target crops [
]. Consequently, the
evaporation of droplets containing surfactant is of great significance for the effective utilization of
surfactants and pesticide [
] retention. In this work, the evaporation of droplets containing
relatively high surfactant concentrations of 0.01% and 0.05% were dominated by the CCR
mode, which shows a decreasing contact angle and almost constant diameter. It is beneficial
for the droplet to obtain a steady state on rice leaf surfaces and to further prevent the droplet
from rolling off from the leaf surface. In addition, the improved wetting and a reduced
evaporation time gives longer retention times of the surfactant and helps to reduce droplet drift.
Therefore, our study of the evaporation of surfactant solutions on rice leaf surfaces is
important to understand the effect of surfactant addition in water and guide the utilization of
surfactants and pesticides in agriculture.
Conceptualization: Q-LH Z-LZ CC.
Data curation: Z-LZ CC LZ L-DC JX F-ML.
Formal analysis: Z-LZ CC.
Funding acquisition: Q-LH.
Investigation: Z-LZ CC LZ L-DC.
Visualization: Z-LZ CC.
Writing ± original draft: Z-LZ CC Q-LH.
Writing ± review & editing: Z-LZ CC LZ L-DC JX F-ML Q-LH.
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