# Counter-intuitive evaporation in nanofluids droplets due to stick-slip
nature

Hari Govindha A  Department of Mechanical and Aerospace Engineering, Indian
Institute of Technology Hyderabad, Kandi - 502284, Telangana, India  Pallavi
Katre  Department of Chemical Engineering, Indian Institute of Technology
Hyderabad, Kandi - 502284, Telangana, India  Saravanan Balusamy  Department of
Mechanical and Aerospace Engineering, Indian Institute of Technology
Hyderabad, Kandi - 502284, Telangana, India<EMAIL_ADDRESS>Sayak
Banerjee  Department of Mechanical and Aerospace Engineering, Indian Institute
of Technology Hyderabad, Kandi - 502284, Telangana, India
<EMAIL_ADDRESS>Kirti Chandra Sahu  Department of Chemical Engineering,
Indian Institute of Technology Hyderabad, Kandi - 502284, Telangana, India
<EMAIL_ADDRESS>
###### Abstract

We experimentally investigate the evaporation characteristics of a sessile
ethanol droplet containing Al2O3 and Cu nanoparticles of sizes 25 nm and 75 nm
on a heated substrate using shadowgraphy and infrared imaging techniques. Our
results demonstrate that the droplet contact line dynamics resulting from the
presence of various nanoparticles plays a dominant role in the evaporation
process. This is in contrast to the widely-held assumption that the enhanced
evaporation rate observed in sessile nanofluid droplets is due to the higher
thermal conductivity of the added nanoparticles. We observe that even though
the thermal conductivity of Al2O3 is an order of magnitude lower than that of
Cu, droplets containing 25 nm-sized Al2O3 exhibit pinned contact line dynamics
and evaporate much more rapidly than droplets containing Cu nanoparticles of
both sizes and 75 nm Al2O3 nanoparticles that exhibit stick-slip behaviour. We
also found that the droplets with different nanoparticles display distinct
thermal patterns due to the difference in contact line behaviour, which alters
the heat transfer inside the droplets. We establish this counter-intuitive
observation by analysing the temporal variations of the perimeter, free
surface area, and deposition patterns on the substrate.

Keywords: Wetting dynamics, sessile droplet, nano-fluid, thermal conductivity,
thermal Imaging, machine learning

##  1 Introduction

Evaporation of sessile droplets laden with nanoparticles is relevant in a wide
range of practical applications, such as inkjet printing 1, 2, 3, 4,
fabrication of DNA microarrays 5, 6, estimating the lifetime of saliva
droplets 7, coating technology 8, 9, spray and hotspot cooling 10, 11, 12,
microfluidics 13, to name a few. Additionally, this subject attracted the
attention of researchers due to the profound scientific curiosity to
understand the underlying mechanism of the resulting deposition patterns,
including the commonly observed “coffee-stain” or “coffee-ring” effect 13, 14,
15. It is a prevalent belief that increasing the thermal conductivity of a
liquid increases the heat transfer rate 16, 17, 18. Thus, the addition of
nanoparticles in working liquids to enhance their thermal conductivity is a
common strategy that has been employed for a long time in various applications
19, 20, 21.

Many researchers theoretically and experimentally studied the evaporation
dynamics of sessile droplets in the presence of nanoparticles at ambient and
elevated temperatures. Orejon et al. 22 investigated the three-phase contact
line dynamics for pure water and ethanol on different substrates of varying
hydrophobicities and showed that more hydrophobic surfaces favour the
depinning of the contact line. They performed experiments with TiO2 -water
nanofluids and showed that the stick-slip behaviour depends on the
nanoparticle concentration. Moffat et al. 23 reported the enhancement of the
stick-slip behaviour with increasing nanoparticle concentration in
TiO2-ethanol nanofluid on a silicon wafer coated with Polytetrafluoroethylene
(PTFE). Yunker et al. 24 eliminated the coffee ring effect to obtain uniform
deposition using ellipsoidal particles. These particles, with their attractive
long-range forces, form structures near the contact line that prevents further
deposition near the contact line. Dugyala and Basavaraj 25 studied the effect
of particle shape using colloidal ellipsoids and reported that the patterns do
not depend on particle shape but are rather influenced by the interactions
between particle and substrate. Nguyen et al. 26 generated inner coffee ring
deposits with dendritic architectures using silica nanoparticles owing to the
secondary pinning of the contact line when the forces acting on the particles
are balanced. Kovalchuk et al. 27 experimentally investigated the effect of
nanoparticle concentration on the evaporation dynamics and found an increase
in the overall rate of diffusive evaporation with an increase in nanoparticle
concentration. The type and concentration of nanoparticles can also
significantly impact the evaporation rate 28. Vafaei et al. 29 observed that
the contact angle of the drop increases with increasing nanoparticle
concentration and particle size. In pendant droplets laden with aluminium
nanoparticles, it was found that the evaporation rate decreases with an
increase in the particle concentration from 0 to 3 wt.% Gerken et al. 30,
while the surface tension is independent of the particle concentration 31.
Jung et al. 32 analysed the forces acting on the nanoparticles during the
evaporation of a droplet on a hydrophilic substrate and found that the
particles mostly experienced drag and surface tension forces. Chen et al. 33
used clay, silver, and iron oxide nanoparticles during the evaporation of a
pendant water drop and found that the evaporation rate can be increased or
decreased depending on the concentration and the type of nanoparticle. All
these studies considered the evaporation dynamics of nanofluid droplets at
room temperature.

A few researchers have performed molecular dynamics simulations to study
droplet evaporation. The effect of electric fields and surface temperature on
the evaporation of ionic droplets was investigated by Chatterjee et al. 34.
They found a critical value of the electric field beyond which the hydration
effect due to the ions was suppressed. Caleman and van der Spoel 35 obtained a
relationship between the type of ion and water droplet evaporation. They also
observed that the presence of the sodium and chlorine ions reduces the
evaporation, while the hydrogen ions do not alter the evaporation. Chen et al.
36 adopted molecular dynamic simulation to study the bubble nucleation on non-
uniform wettability substrates. They observed that the nucleation position
migrated towards the hydrophilic region with increased substrate temperature.

A few researchers have also investigated the evaporation dynamics of nanofluid
droplets at elevated substrate temperatures 37, 38, 39, 40, 41. Patil et al.
40 studied the effect of substrate temperature, colloidal particle
concentration, and wettability on evaporation dynamics and deposition patterns
in sessile droplets. They observed a ring-type deposition pattern in the inner
region at elevated temperatures. Zhong et al. 41 found that increasing the
substrate temperature from 10∘C to 50∘C for a graphite nanofluid droplet on a
silicon wafer changes the deposition pattern from a uniform disk profile to a
dual ring structure. By varying the substrate temperature from 25∘C to 99∘C,
Parsa et al. 42 obtained uniform, dual ring, and stick-slip deposition
patterns in a sessile water droplet containing copper-oxide nanoparticles. The
changes in the substrate temperatures affect the interplay between the
capillary and Marangoni flows, which alters the deposition patterns. Sefiane
and Bennacer 37 experimentally investigated the evaporation and wetting
dynamics of a sessile ethanol droplet laden with aluminium nanoparticles on a
PTFE substrate. They found that although the surface tension remains
unaffected by the presence of nanoparticles, the contact angle increases due
to the modification of the solid-liquid interfacial tension. Brutin et al. 38
used an infrared (IR) camera to visualize the thermal patterns during the
evaporation of sessile droplets of different semi-transparent liquids and
observed that the surface instability depends on the fluid considered. Zhong
and Duan 43 reported that the increasing substrate temperature enhances the
thermocapillary instabilities and the temperature heterogeneity of
hydrothermal waves. Using IR thermography, Sefiane et al. 44 showed that the
hydrothermal waves extend across the entire droplet volume, and the thermal
patterns affect the overall heat flux distribution inside the droplet.

As discussed above, apart from the various factors that affect the evaporation
rates and deposition patterns, the thermal conductivity of the substrate and
nanoparticles are important for evaporation since it expedites heat transfer
45. In this context, Sobac and Brutin 46 experimentally investigated the
effect of temperature and thermal properties of the substrate on the
evaporation of a pinned water droplet. Ristenpart et al. 47 correlated the
relative thermal conductivity of the substrate and liquid to the direction of
the thermal-Marangoni flow, which alters the resulting deposition patterns.
The higher evaporation rates were observed on substrates with high thermal
conductivity 48. It was found that the thermal conductivity of the liquid
increases with the addition of nanoparticles 49, 50, 51. This enhancement in
the thermal conductivity of the nanofluids has been attributed to the
dispersion and Brownian motion of the nanoparticles. Warrier and Teja 52
investigated the effect of the size of silver nanoparticles in ethylene glycol
on the resultant thermal conductivity and found that the thermal conductivity
of the nanofluid increases with an increase in particle size. Beck et al. 53
also observed similar behaviour for alumina nanoparticles. Patel et al. 54
reported that the thermal conductivity of nanofluids with metallic
nanoparticles is significantly higher than that with oxide nanoparticles. The
theoretical studies 19, 55 also reveal that the presence of metallic
nanoparticles enhances the thermal conductivity of the base fluids.

As the abovementioned literature review suggests, adding nanoparticles
increases the thermal conductivity of a base fluid, which in turn accelerates
evaporation. However, the universality of this result has been questioned by
some researchers 16. Thus, it is important to understand the mechanism
underlying improved heat transfer in the presence of different nanoparticles.
In the present work, we investigate the evaporation dynamics of sessile
ethanol droplets with and without nanoparticle loading using shadowgraphy and
infrared (IR) imaging techniques. Four different nanoparticles, Al2O3 (25 nm),
Cu (25 nm), Al2O3 (75 nm) and Cu (75 nm) of various sizes with varying
concentrations have been considered. The captured images are post-processed
using the Matlab® and a machine learning technique in the framework of a
Convolutional Neural Network (CNN) based on the U-Net architecture. It is
found that the lifetime of the droplets is not significantly affected by the
increase in nanoparticle concentration. The droplet laden with Al2O3 (25 nm)
nanoparticles shows pinned behaviour, whereas droplets laden with Cu (25 nm),
Al2O3 (75 nm) and Cu (75 nm) show stick-slip behaviour. Our results reveal
that a droplet containing Al2O3 (25 nm) nanoparticles evaporates significantly
faster than droplets containing Cu nanoparticles (25 nm and 75 nm) and Al2O3
(75 nm) nanoparticles. This counter-intuitive behaviour is dedicated to the
droplet contact line dynamics due to the presence of different nanoparticles.
Additionally, the droplets with different nanoparticles exhibit distinct
thermal patterns, altering the heat transfer inside the droplets.

##  2 Experimental Methodology

###  2.1 Experimental Setup

We experimentally investigated the evaporation dynamics of a sessile ethanol
droplet laden with different nanoparticles using shadowgraphy and infrared
imaging techniques. The schematic diagram of the experimental setup is shown
in Fig.1. The goniometer unit is customized for our requirements (Make:
Holmarc Opto-Mechatronics Pvt. Ltd.). It consists of a multilayered metal
block, a motor-driven pump for dispensing the droplets on the substrate, a
proportional-integral-derivative (PID) controller for regulating the substrate
temperature, a complementary-metal-oxide-semiconductor (CMOS) camera (Make:
Do3Think, Model: DS-CBY501E-H), an infrared camera (Make: FLIR, Model:
X6540sc), and an LED light source with a diffuser to distribute the light to
the CMOS camera uniformly. The side and top views of the evaporating droplet
were captured with the help of the CMOS and IR cameras, respectively. The
entire assembly was placed inside the goniometer box to minimize external
environmental disturbances. The goniometer box was maintained at an ambient
temperature of $22\pm 2^{\circ}$C and relative humidity of $45\pm 5$%. The
relative humidity was measured using a hygrometer (Make: HTC, Model: 288-ATH)
fitted inside the goniometer box.

Figure 1: Schematic diagram of the experimental setup (customized goniometer)
to study the evaporation of sessile droplets laden with nanoparticles.

The multilayered metal block consists of (i) a stainless steel base fitted
with two electrical heaters operated by the Proportional–Integral–Derivative
(PID) controller and (ii) an aluminum plate of size 100 mm $\times$ 80 mm
$\times$ 15 mm coated with black paint to minimize the reflection in the IR
images. A CMOS camera with a spatial resolution of $1280\times 960$ pixels
recorded the side view of the droplet at 10 frames per second (fps), which
were used to extract various droplet parameters, such as the wetted diameter
($D$), height ($h$), contact angle ($\theta$) and volume ($V$). The IR camera
captured the temperature distribution on the droplet surface from the top view
with a resolution of $640\times 512$ pixels at 50 fps in the spectral range of
$3$ $\mu$m – $5$ $\mu$m. A polytetrafluoroethylene (PTFE) tape of thickness
100 $\mu$m is pasted on the aluminum plate, which is used as the substrate.
The roughness and thermal stability of the PTFE tape were verified for the
temperature range considered in this study 56. The required substrate
temperature was obtained for each experiment by setting the PID controller and
turning on the heater. A K-type thermocouple (Make: OMEGA Engineering
Singapore) was used to check whether the substrate attained the steady state
temperature before mounting the droplet. Before performing each experiment, it
is ensured that the PTFE substrate is thoroughly cleaned with isopropanol,
dried with compressed air, and then pasted onto the aluminum plate. The
nanofluid solutions were prepared by dispersing the nanoparticles in absolute
ethanol (99.9% purity) on a weight percentage (wt.%) basis. Then the mixture
was ultrasonically shaken using an ultrasonic unit (Make: BRANSON, Model:
CPX1800H-E) for about an hour, ensuring uniform nanoparticle distribution.
Al2O3 and Cu nanoparticles with an average particle size of 25 nm and 75 nm
were purchased from Sisco Research Laboratories Pvt. Ltd. and Intelligent
Materials Pvt. Ltd., respectively. A 100 $\mu$L U-tek (Make: Unitek Scientific
Corporation) chromatography syringe (with a piston size of 1.59 mm and fitted
with a 21G needle with an inner orifice diameter of 0.514 mm) was connected to
the motorised pump to control the volume flow rate, which in turn dispensed
droplets of a constant size. A droplet of volume ($3.5\pm 0.3$ $\mu$L) created
using this mechanism was placed on the substrate, and its evaporation dynamics
were recorded using the CMOS and IR cameras. In our experiments, time, $t=0$,
is the instant when the droplet touches the substrate. After each experiment,
the PTFE tape was replaced, and the syringe was cleaned with acetone. We have
performed a minimum of three repetitions for each set of the experimental
condition. A digital microscope (Make: Keyence, Model: VHX-6000) was used to
examine the dried deposition pattern once evaporation was completed.

###  2.2 Post-processing

To extract the droplet side view profiles, the post-processing of the side
view images recorded by the CMOS camera was performed using an in-house
program in the framework of Matlab®. It was accomplished using a median
filtering technique to eliminate random noise and an unsharp masking technique
to sharpen the image, improving the gradients. The filtered image was then
converted to a binary image using a suitable threshold that differentiates the
background from the droplet boundary. Finally, the holes were filled inside
the droplet boundary, and the reflection of the droplet was removed. A Matlab®
function was used to trace the droplet contour from which the droplet
parameters were measured. Figure S1(a-e) shows the steps followed in the image
processing of the side-view images of the droplets. The detailed description
of the post-processing procedure is similar to that of Gurrala et al. 57. In
order to analyze infrared images, the intensity data of the image was
converted to a temperature field 58. The Convolution Neural Network based on
U-net architecture was used for the boundary extraction59. The U-net design
uses data augmentation by elastically deforming the annotated input photos,
enabling the network to use the available annotated images more. The network
was trained using 40 manually annotated grey-scale infrared images. A computer
equipped with a GPU (NVIDIA Quadro P1000) was used for the training of the
images. The network was then used to extract the binary masks and droplet
boundaries from the infrared images, as shown in Figure S2. Finally, a Matlab®
code was used to remove the background, and the temperature profiles of the
evaporating droplets at different instants were analysed.

##  3 Results and Discussion

###  3.1 Droplet lifetime ($t_{e}$)

We investigate the evaporation dynamics of sessile ethanol droplets on heated
substrates with and without Al2O3 and Cu nanoparticle loadings. The substrate
temperature is kept at $T_{s}=50^{\circ}$C. The particle size and the particle
loading concentration are varied, and the impact of particle type, particle
size and concentration on droplet evaporation dynamics have been investigated.
We consider two different mean diameter sizes for both the Al2O3, and Cu
nanoparticles, viz. 25 nm and 75 nm. Four different particle loading
concentrations, 0 wt.%, 0.3 wt.%, 0.6 wt.% and 0.9 wt.% are considered for
each particle types and diameters. Table 1 shows the lifetime of the droplets
for all the loading cases.

Table 1: Lifetime of an ethanol droplet (in seconds) laden with Al2O3 and Cu
nanoparticles of different sizes and concentrations at $T_{s}=50^{\circ}$C.
Size Concentration | 0.3 wt.% | 0.6 wt.% | 0.9 wt.%
---|---|---|---
Al2O3 | Cu | Al2O3 | Cu | Al2O3 | Cu
25 nm | 43$\pm 1$ | 65$\pm 2$ | 43$\pm 1$ | 64$\pm 2$ | 44$\pm 1$ | 63$\pm 3$
75 nm | 66$\pm 2$ | 60$\pm 3$ | 69$\pm 4$ | 62$\pm 1$ | 64$\pm 6$ | 63$\pm 3$

We observe that the lifetime of a pure ethanol droplet is $74\pm 3$ seconds. A
comparison of the pure ethanol droplet lifetime with the lifetimes of the
nanoparticle-laden droplets given in Table 1 reveals that the lifetime of the
droplets is reduced by the addition of nanoparticles irrespective of particle
type, particle diameter or extent of loading wt.%. However, the extent of
reduction in droplet lifetime varies significantly for the different cases.
For Cu nanoparticles of both 25 nm and 75 nm mean diameters, the decrease in
the lifetime is modest, with the total lifetimes varying between 87% to 81% of
the pure droplet lifetime. The impact of increasing the particle concentration
is also relatively small. The same statement holds for Al2O3 laden droplets
where the mean particle size is at 75 nm, with the droplet lifetimes being
about 86% to 92% of the pure droplet lifetime with no significant impact
observed for increased particle concentrations. However, the state of affairs
is markedly different when 25 nm sized Al2O3 nanoparticle-laden droplets are
considered. For these cases and all concentrations, the droplet lifetime shows
a marked decrease, reducing to 58% of the lifetime of the pure ethanol
droplet. Thus the Al2O3 laden nanoparticle droplets show a significant impact
of particle size on the droplet evaporation time, which is not seen in the Cu
nanoparticle case. Remarkably, the 25 nm sized Al2O3 nanoparticle case shows
anomalously faster evaporation rates than all the other conditions. This
finding appears counter-intuitive since the thermal conductivity of Cu
nanoparticles are more than 10 times higher than that of Al2O3 nanoparticles
(Table 2). Further investigations presented in this manuscript attempt to
elucidate the reasons for this behavior. Since different particle loadings do
not show any significant impact, the results discussed in the subsequent
sections of this work deal with 0.6 wt.% nanoparticle loading cases only.

Table 2: The properties of nanoparticles at 27∘C 60.
Nanoparticle | Density | Thermal conductivity | Molar mass | Specific heat
---|---|---|---|---
(kg/m3) | (W/mK) | (kg/kmol) | (J/kgK)
Al2O3 | 3.9 | 36 | 101.96 | 765
Cu | 8.9 | 401 | 63.55 | 385

###  3.2 Evaporation dynamics: Side view profiles

This section presents the temporal evolution of the side contour profile of an
ethanol droplet with and without nanoparticles at 0.6 wt.% loading. The
experimental section has already discussed details of extracting contour
profiles from CMOS camera data. The side-view droplet images for the various
cases are shown in Figure S3. Figure 2 shows the superimposed droplet contour
profiles at different dimensionless time $(t/t_{e})$, wherein $t_{e}$ is the
lifetime for the given case. The $x$ axis provides a measure of the droplet
spread, while the $y$ axis provides a measure of droplet height. The contours
are provided from the initial time ($t/t_{e}=0$) to 80% of the droplet
lifetime ($t/t_{e}=0.8$). Figure 2a depicts the side contour profiles of a
pure ethanol droplet. It can be seen that as $t/t_{e}$ increases, the droplet
wetting diameter decreases monotonically and in a symmetrical fashion for an
ethanol droplet without nanoparticle loading. This observation is consistent
with the Constant Contact Angle (CCA) mode of evaporation, where a sessile
droplet maintains a constant contact angle with respect to the substrate
throughout its evaporation lifetime, which leads to a monotonic decrease in
its wetting diameter.

(a)

(b) (c)

(d) (e)

Figure 2: Temporal evolution of ethanol droplet contours (a) without
nanoparticle loading, (b) 0.6 wt.% loading of 25 nm Al2O3, (c) 0.6 wt.%
loading of 25 nm Cu, (d) 0.6 wt.% loading of 75 nm Al2O3 and (e) 0.6 wt.%
loading of 75 nm Cu nanoparticles at $T_{s}=50^{\circ}$C.

Figure 2b gives the side contour profile for the droplets laden with 25 nm
sized Al2O3 nanoparticles with 0.6 wt.% loading. It can be observed that the
evolution of the droplet side profile is dramatically different, with the
droplet spread remaining more or less constant up to 80% of the droplet
lifetime and the droplet contact angle decreasing monotonically with time. The
droplet evaporation behavior is therefore consistent with the Constant Contact
Radius (CCR) mode of evaporation, where the droplet spread diameter remains
constant throughout its lifetime. Hence, it can be concluded that the presence
of 25 nm sized Al2O3 nanoparticles has resulted in a droplet pinning effect
where the contact line cannot retract from its initial position despite
progressive evaporation.

Figures 2(c-e) show the droplet side profile evolutions for 25 nm Cu, 75 nm
Al2O3 and 75 nm Cu loaded nanoparticle cases respectively, all at 0.6 wt.%
loading and at substrate temperature of $50^{\circ}$C. In all these cases, the
contour evolution is irregular and asymmetric. The spread diameter and the
contact angle show an irregular decrease with time. The rate of decrease is
also different between the left and right sides, and thus, at several time
points, the center of the droplet shifts leftward or rightward, depending on
which edge has contracted the most. Such behaviour is characteristic of the
stick-slip mode of droplet evaporation61.

Figure 3: Variations of the height ($h$ in mm), wetted diameter ($D$ in mm)
and contact angle ($\theta$ in degree) of ethanol droplets at
$T_{s}=50^{\circ}$C. The first row (a, b, c) and second row (d, e, f)
represent the droplets containing nanoparticles of size 25 nm and 75 nm,
respectively.

The variations in the height ($h$ in mm), wetted diameter ($D$ in mm), and
contact angle ($\theta$ in degree) of the droplet with and without
nanoparticle loading are plotted with respect to normalized evaporation time
in Figure 3. The first row of figures, Fig. 3(a-c), compares the no-loading
condition with droplets having 25 nm Al2O3 and Cu nanoparticle loading cases.
The second row of figures, Fig. 3(d-f), compares the no-loading condition with
droplets having 75 nm Al2O3 and Cu nanoparticle loading cases. It is seen that
the wetted diameter of the pure ethanol droplet decreases monotonically while
the contact angle remains constant. This is consistent with the CCA mode of
evaporation, as noted earlier. For droplets with 25 nm Al2O3 loading, the
wetted diameter is observed to be constant while the contact angle is observed
to decrease monotonically, as expected for the CCR mode of evaporation. In
contrast, the Cu (25 nm) droplet includes regimes of pinning, i.e. CCR mode
evaporation, where the droplet diameter stays constant, and the droplet
contact line decreases monotonically, that are followed by regions of de-
pinning and droplet contraction, where the diameter of the droplet shows a
steep decrease in a very short period and the contact angle shows a rapid
increase. The de-pinning process ends within a short period, and the droplet
stabilizes into a new pinned evaporation phase with a lower wetted diameter.
The duration of the pinned phase is highly uneven, with some pinned phases
lasting over significant fractions of the droplet lifetime followed by a de-
pinning phase with abrupt and marked contraction ‘jump’. At other instances,
the pinned-depinned regimes occur in rapid succession in micro-steps or
‘jerks’ that almost replicate the CCA mode of droplet diameter evolution.
Overall the 25 nm Cu nanoparticle-laden droplet exhibits a stick-slip mode.

Now, considering the droplet containing Al2O3 (75) nm and Cu (75 nm)
nanoparticles in Figure 3(d-f), it can be seen that both these droplets
exhibit stick-slip behaviour. For the cases shown, the Al2O3 laden droplet
evaporates through a series of micro-pinning and de-pinning processes that
follow each other in rapid succession. Thus, its diameter and height evolution
are close to the CCA mode exhibited by the pure droplet. In contrast, the Cu
nanoparticle droplet passes through a few large and stable pinned phases,
followed by rapid large contractions in droplet diameter accompanied by
increases in droplet height and droplet contact angle. It is to be noted,
however, that the stick-slip behavior can shift from micro pinning and de-
pinning mode to long-duration pinned regimes for different runs of the same
case, as is shown in Figure S4. The number of stick slips and the time at
which each stick-slip occurs are not the same for different individual runs of
the droplets containing Cu (25 nm), Al2O3 (75 nm), and Cu (75 nm)
nanoparticles. The variations in the wetted diameter of Al2O3 and Cu of
different sizes are compared in Figure S5, which clearly shows that the 25 nm
Al2O3 nanoparticle case has the distinct pinned mode evaporation, whereas the
rest have stick-slip mode evaporation. The thermal patterns and instabilities
seen during droplet evaporation are analyzed in the next section.

###  3.3 Evaporation dynamics: Top view profiles

In this section, the temperature distribution on the droplet surface with and
without nanoparticle loading is investigated using the IR camera mounted above
the droplet in a plane perpendicular to the substrate. The top view of the
ethanol droplets with and without nanoparticle loading is shown in Figure 4.

Figure 4: Temporal evolution of the temperature contours on the surface of the
droplet in the no loading and 0.6 wt.% loading conditions at
$T_{s}=50^{\circ}$C. The compositions of droplet containing different
nanoparticles are presented as: First row (no loading), second row (Al2O3 of
25nm), third row (Cu of 25nm), fourth row (Al2O3 of 75 nm) and fifth row (Cu
of 75nm). The videos showing thermal profiles of the droplet for no loading,
Al2O3 (25nm), Cu (25nm), Al2O3 (75nm) and Cu (75nm) are included as Videos
S1-S5, respectively.

In Figure 4, it is evident that the droplet without loading shows a continuous
decrease in the wetted diameter while the droplet with Al2O3 (25 nm) shows
pinned behaviour. The other droplets with Cu (25 nm), Al2O3 (75 nm), and Cu
(75 nm) display stick-slip behaviour and because of uneven pinning, deviate
from a spherical cap profile in the later stages of their lifetimes. The
hydrothermal waves, which originate from the droplet periphery, are observed
in all the droplets as quasi-regular undulations in the iso-temperature
profiles as viewed from the top. For the droplet with Al2O3 (25 nm)
nanoparticles, the height decreases at constant wetting diameter due to
pinning, which results in the propagation of hydrothermal waves towards the
centre of the droplet. This promotes mixing inside the droplet, enhancing heat
transfer and thereby decreasing the lifetime. This can be visualized by
observing the central region of the droplet, which clearly shows a higher
temperature compared to the central regions of the other droplets. Now,
comparing the temperature profiles of droplets with Cu (25 nm), Al2O3 (75 nm),
and Cu (75 nm), we can observe that the central regions of droplets with Cu
(25 nm) and (75 nm) have a higher temperature than that of Al2O3 (75 nm). This
slight increase could be attributed to the increased thermal conductivity of
the Cu nanoparticles, which still could not significantly alter the lifetime
of these droplets. From this, it can be realised that the evaporation dynamics
are majorly affected by the contact line dynamics, due to which the pinned
Al2O3 (25 nm) droplet has a lower lifetime, even though it has a lower
conductivity compared to that of copper. A few repetitions of the thermal
profiles showing stick-slip in different directions for the ethanol droplet
with Cu (25 nm) and Cu (75 nm) are shown in Figures S6 and S7, respectively.

###  3.4 Perimeter and free surface area

Additional insight into the evaporation dynamics of the nanofluid droplets is
obtained by plotting the temporal variations of its contact line perimeter and
free surface area in the presence and absence of nanoparticle loading at
$T_{s}=50^{\circ}$C. Figure 5(a-b) and 5(c-d) show the variations in the
perimeter and free surface area of the pure ethanol droplet and droplets
containing nanoparticles of size 25 nm and 75 nm, respectively. Many studies
have shown that the evaporation of droplets primarily occurs at the triple
contact line 62. Moreover, for a heated droplet, due to natural convection,
the evaporation flux depends on the surface area of the droplet 57. The pure
ethanol droplet exhibits the CCA mode of evaporation; hence, its perimeter and
surface area decrease nearly monotonically with time. Hence the droplet
evaporation rates also decrease along with the decrease in the droplet surface
area and the triple contact line perimeter. In contrast, the droplet with 25
nm Al2O3 nanoparticles shows a pinning effect as they evaporate in the CCR
mode, and hence the perimeter and the free surface area remain unchanged
throughout its lifetime. Thus, during its lifetime, the Al2O3 (25 nm) droplets
have a higher contact line perimeter and free surface area than all other
droplets. Hence it is expected to have the highest evaporation rates and the
shortest droplet lifetime. Due to the stick-slip nature of Cu (25 nm), Cu (75
nm) and Al2O3 (75 nm) droplets, the perimeter and free surface area decline at
rates slightly lower than the pure ethanol case, and hence they have a
slightly higher evaporation rate compared to that of a pure ethanol droplet.
These observations explain why the Al2O3 (25 nm) laden droplets have the
smallest droplet lifetimes, the pure ethanol droplets have the largest
lifetimes, and the Al2O3 (75 nm) and 25 nm and 75 nm Cu nanoparticle droplets
have lifetimes slightly shorter than the pure ethanol case as was shown in
Table 1. The preceding discussion clarifies that, at least for low loading
concentrations (up to 0.9 wt.% nanoparticles), the thermal conductivity of
nanoparticles does not play a significant role in determining the heat
transfer and evaporation rates of sessile droplets from a heated substrate.
Instead, the droplet evaporation rates and lifetimes are determined by how the
nanoparticle loading affects the contact line dynamics of the evaporating
droplet.

Figure 5: Temporal variation of the perimeter ($P$ in mm) and surface area
($a$ in mm2) of the droplets at $T_{s}=50^{\circ}$C. The first row (panels a,
b) and second row (panels c, d) are associated with the droplets laden with
nanoparticles of size 25 nm and 75 nm, respectively.

###  3.5 Deposition pattern and roughness profile

After a nanofluid droplet evaporates, the deposited nanoparticles form
different patterns on the substrate depending on the evaporation and contact
angle dynamics experienced by the droplet. The deposition patterns on the
substrates after the droplets laden with Al2O3 and Cu nanoparticles of 25 nm
and 75 nm are fully evaporated have been depicted in Figure 6. The
corresponding roughness profiles obtained with the help of a digital
microscope are shown in Figure 7. It is seen that for the droplet with Al2O3
(25 nm) nanoparticles, the deposits are concentrated mainly near the triple
contact line. As the droplet evaporates, it experiences maximum evaporation at
the triple line, which sets up a radial capillary flow from the droplet centre
to the droplet periphery. The nanoparticles are displaced and brought to the
triple contact line by this flow, where they pin the droplet. The Marangoni
flow, which emerges as a consequence of the gradients in surface tension, also
occurs in combination with the radial capillary flow. As a result, some of the
nanoparticles are moved away from the triple contact line. As the evaporation
continues, more particles are carried to the triple line by these radial
flows, which gives a distinct pinned pattern, also known as the coffee ring
13, 14, 15. The droplets with Cu (25 nm), Al2O3 (75 nm), and Cu (75 nm) show
stick-slip patterns. Even in these droplets, the radial and Marangoni flows
prevail, but the stick-slip nature prevents most of the nanoparticles from
depositing near the initial triple contact line. When the depinning occurs,
the contact line gets displaced, where further deposits are found. Here the
stick-slips pattern does not occur concentrically. Thus, we can observe a few
locations around the initial contact line where the depositions are more, as
in Figure 6(c) (at the top-most portion of the droplet) and Figure 6(d) (at
two portions just above and below the heavily concentrated final deposition
region). These correspond to the contact line portions that were shared by two
or more droplet parts that experienced stick-slip. When comparing the droplet
with Al2O3 (75 nm) and Cu (75 nm) nanoparticles, the droplet with Cu (25 nm)
does not show an apparent stick-slip behaviour. The reason behind this
behaviour is not known, and further investigation is required to address this
issue.

The stick-slip behaviour could be explained with the help of a theoretical
model developed by Shanahan 63. It was suggested that the triple contact line
has a potential energy barrier because of the mechanical (roughness) or
chemical heterogeneity of the solid substrate. For an ideal substrate, Young’s
equation gives the equilibrium contact angle of the droplet. As the droplet
evaporates, in order to minimise the surface free energy at any given moment,
it would prefer to maintain the equilibrium contact angle, thus evaporating in
a CCA mode. However, roughness and chemical heterogeneities provide an
anchoring effect for the triple contact line. This anchoring could be
associated with the potential energy barrier along the triple contact line.
This anchoring prevents the droplet from attaining a state of minimum energy,
and the excess energy is stored as the excess free energy in the droplet. As
the droplet evaporates further, more excess energy is stored until it
overcomes the potential energy barrier, where it slips to another equilibrium
position. Thus, the droplet sticks until the excess energy in the droplet
overcome the potential energy barrier and slips once it is equal to it, hence
the occurrence of stick-slip dynamics. It can be said that during evaporation,
the anchoring effect disturbs the capillary equilibrium, which in turn is
responsible for the excess energy in the droplet. Lin et al. 64 observed an
increase in the potential energy barrier of polymeric substrates with an
increase in roughness due to which the droplet is pinned to rough substrates.

(a) (b)

(c) (d)

Figure 6: Deposition pattern of ethanol droplets laden with nanoparticles of
Al2O3 (a,c) and Cu (b,d) at $T_{s}=50^{\circ}$C. Panels (a,b) and (c,d)
correspond to the nanoparticles size of 25 nm and 75 nm, respectively.

Considering the deposition of nanoparticles along the triple contact line as a
source of roughness, we can now compare the pinned and stick-slip behaviour of
the droplets. For the Al2O3 (25 nm) droplet, the nanoparticles are deposited
near the triple contact line, which increases the local roughness at that
point. This increases the potential energy barrier along the triple contact
line, which prevents the slipping of the droplet. The Al2O3 (25 nm)
nanoparticles are lighter compared to other nanoparticles of Cu (25 nm), Al2O3
(75 nm), and Cu (75 nm) due to its smaller diameter and lower density as given
in Table 2. Due to this, the radial capillary forces can deposit more Al2O3
(25 nm) nanoparticles at the triple line. Thus the rate of increase of the
potential energy barrier is faster than the rate of excess energy stored in
the droplet, and thereby, the droplet cannot overcome the potential energy
barrier and remains pinned throughout its lifetime. As for the case of Cu (25
nm), Al2O3 (75 nm), and Cu (75 nm), owing to the heaviness of these particles,
the potential energy barrier could not be increased at a faster rate. Thus
there are times when the excess energy in the droplet overcomes the barrier
and slips to a new location with a contact angle less than or equal to the
equilibrium contact angle. This process continues, which gives rise to the
stick-slip pattern.

Figure 7: Average roughness profile along a horizontal strip for the
deposition pattern of ethanol droplets containing (a) 25 nm Al2O3, (b) 25 nm
Cu, (c) 75 nm Al2O3, and (d) 75 nm Cu nanoparticles.

The roughness profiles obtained by considering a small horizontal strip along
the centre of the droplet are plotted and shown in Figure 7. The dried
deposition pattern of an ethanol droplet containing the nanoparticles was
scanned using a digital microscope, and the corresponding images were
processed using ImageJ software to obtain the roughness profile. It is seen
that peaks from the roughness plots are in accordance with the deposition
patterns in Figure 6. The highest roughness at the triple contact line is
given by the pinned droplet Al2O3 (25 nm), which relates to an increased
deposition near the triple contact line compared with the other stick-slip
droplets. The droplets with Cu (25 nm), Al2O3 (75 nm), and Cu (75 nm) have
individual peaks which relate to the stick-slip patterns. In the droplets with
Al2O3 (75 nm) and Cu (75 nm), after the complete evaporation of the droplet,
the nanoparticles are deposited in a small region due to which they show areas
of increased roughness ( rightmost portion of the drop). In the case of the
droplet with Cu (25 nm), individual peaks along with a uniform deposition are
present. The 3D images of the deposition pattern are shown in Figure S8.

##  4 Conclusions

It is a dogma that increasing the thermal conductivity of a liquid by adding a
small amount of nanoparticles increases the heat transfer rate 16, 17, 18.
Thus, it has been used as a common strategy to enhance heat transfer in many
applications, such as inkjet printing, fabrication of DNA microarrays, coating
technology, spray and hotspot cooling and microfluidics. However, the
universality of this result has been questioned by some researchers16.
Moreover, it is important to understand the mechanism underlying the
improvement of heat transfer in nanofluid droplets. Thus, in the present
study, the evaporation of sessile ethanol droplets laden with and without
nanoparticles on a heated substrate is investigated using shadowgraphy and
infrared (IR) imaging techniques considering Al2O3 and Cu nanoparticles of
sizes 25 nm and 75 nm. The captured images are post-processed using Matlab®
and a machine learning technique. We found that the lifetime of a droplet is
reduced by the addition of nanoparticles irrespective of particle type and
size. However, the extent of loading has an insignificant effect on the
evaporation time of the droplets. We observe that although the thermal
conductivity of Al2O3 is an order of magnitude lower than that of Cu, droplets
laden with 25 nm sized Al2O3 evaporate much faster than other droplets
(droplets with 25 nm and 75 nm sized Cu nanoparticles, droplets with 75 nm
sized Al2O3 nanoparticles). As the droplets with 25 nm Al2O3 nanoparticles
exhibit pinned contact line dynamics while other droplets show stick-slip
behaviour during the evaporation process, the counter-intuitive enhanced
evaporation in the case of droplets with 25 nm Al2O3 can be attributed to the
droplet contact line dynamics due to the presence of different nanoparticles.
Additionally, the droplets with different nanoparticles exhibit distinct
thermal patterns due to the difference in contact line behaviour, which alters
the heat transfer inside the droplets. The temporal variations of the
perimeter and free surface area, and the deposition patterns on the substrate
for different loading conditions support our claim that the pinned contact
line dynamics plays the dominant role in the enhanced heat transfer process
rather than the increase in thermal conductivity of the nanoparticles. We
believe that the light-weight 25 nm Al2O3 nanoparticles are more effectively
transported to the triple contact line by radial thermo-capillary forces,
resulting in more efficient pinned behaviour for these nanofluid droplets
compared to the droplets with other type of nanofluid droplets considered in
our study. Thus, the present study answers a fundamental prevalent question
and provides a guideline for choosing the type and size of nanoparticles to
increase the evaporation rate.

Credit authorship contribution statement

Hari Govindha and Pallavi Katre performed the experiments. All the authors
contributed to the analysis of the results and to the preparation of
manuscript. The project was coordinated by Kirti Chandra Sahu.

Declaration of Competing Interest

The authors declare that there is no conflict of interest.

Supporting Information: Additional experimental details, Image processing
steps and repeatability of experiments. Temporal evolution of the shape of the
droplet and its wetted diameter for different conditions. Digital microscope
images of the deposited nanoparticles.

Acknowledgement: The financial support from Science & Engineering Research
Board, India through the grant number: CRG/2020/000507 is gratefully
acknowledged.

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##  Appendix A Simulation Table

Table 5: Cosmological (magneto-)hydrodynamical simulations of massive clusters
of galaxies adopted in this work. Here we include only cosmological models,
i.e. simulations that start from cosmologically-motivated initial conditions
on large spatial scales, which are run to $z\sim 0$. These simulations differ
in that they adopt not only different codes (Smooth-Particle-Hydrodynamics,
Adaptive-Mesh-Refinement, meshless or moving mesh) but also different
underlying galaxy formation models. All simulations include feedback from
Super-Massive Black Holes, but with varying choices and implementations.
IllustrisTNG includes MHD. Magneticum includes thermal conduction.

Simulation project | Hydrangea | Horizon-AGN | Magneticum | IllustrisTNG
---|---|---|---|---
Run(s) | Hydrangea Zooms | AGN | Box4, Box2b | TNG100
Code | GADGET-3 | RAMSES | GADGET-3 | AREPO
Lowest available redshift | $z=0$ | $z=0$ | $z=0.2$ | $z=0$
Box Size [com Mpc] |  3200a | 142 | 68, 909 | 111
Star-particle Mass Resolution [$10^{6}M_{\odot}$] | 1.8 | 2.0 | 2.6, 50 | 1.4
# clusters with $M_{\mathrm{200c}}\geq 10^{14}\,M_{\odot}$ | 24 | 14 | 3, 4268 | 14
# clusters analyzed in this paperb | 27 | 14 | 1, 13 | 11
$\Lambda$CDM Cosmology | Planck2014 | WMAP7 | WMAP7 | Planck2015
| Planck Collaboration et al. (2014) | Komatsu et al. (2011) | Komatsu et al. (2011) | Planck Collaboration et al. (2016)
Star formation | density threshold | density-threshold | density-threshold | density-threshold
Stellar feedback: method | direct ISM heating | direct (momentum and energy) | direct energy, temporary | temporary hydro decoupling
|  |  | decoupled momentum |
Stellar feedback: timing |  stochastic, $\Delta T=10^{7.5}K$ |  continuous (winds + SNII + SNIa)† | (continuous thermal, probabilistic |  continuous probabilistic, $\propto$ SFR
|  |  |  winds) $\propto$ SNII, |
|  |  |  continuous thermal $\propto$ SNIa |
Stellar feedback: feedback | thermal | kinetic + thermal | kinetic + thermal | kinetic + thermal (warm)
Stellar feedback: orientation | random | isotropic | isotropic | isotropic
SMBH: seed mass [$10^{6}M_{\odot}$] |  | 0.1 | 0.12, 0.45 | 1.2
SMBH: accretion |  | Eddington/Bondi-Hoyle-Lyttleton | Eddington/Bondi-Hoyle-Lyttleton | Bondi–Hoyle
SMBH feedback: mode(s) | thermal | thermal (high), kinetic (low) |  dual: radio/quasar mode∗ | dual:high-state/ low-state
SMBH feedback: timing |  stochastic, $\Delta T=10^{9}K$ | continuous | contineous | continuous/pulsated
SMBH feedback: energy | thermal | thermal/kinetic | thermal | thermal/kinetic
SMBH feedback: orientation | random | isotropic (high) / bipolar (low) | isotropic | isotropic
Simulation/Method References | Schaye et al. (2015) | Dubois et al. (2014) | Hirschmann et al. (2014) | $\clubsuit$
| Bahé et al. (2017) |  | Teklu et al. (2015) |

a Here the box size denotes the size of the parent box: Hydrangea comprises a
number of so-called zoom-in simulations, with haloes identified and
resimulated out of a large parent box.
b For this paper, we focus on clusters in a narrow mass range, namely:
$\log_{10}\,(M_{\mathrm{200c}}\,/M_{\odot}{})=[14.0,14.5]$. Additionally, in
the case of the Magneticum run Box2b, we apply additional selection criteria
based on relaxedness (see text for details).
${\dagger}$ SNII: (Girardi et al., 2000), winds: (Leitherer et al., 1992),
SNIa: (Matteucci & Greggio, 1986)
∗ Fabjan et al. (2010)
$\clubsuit$ Pillepich et al. (2018b); Nelson et al. (2018); Springel et al.
(2018); Marinacci et al. (2018); Naiman et al. (2018); Nelson et al. (2019)

Table 5 gives a summary of the main parameters of the different cosmological
simulations used in this work.

##  Appendix B Fractions per Cluster

Fig. 13 shows the average of all the observed BCG+ICL (left) and ICL (right)
fractions per cluster, as a function of cluster mass. The measurements are
colour-coded by the number of individual observer measurements per cluster.
This shows that the average fractions do not depend on the number of
measurements included in the average.

Figure 13: The mean BCG+ICL (left panel) and ICL (right panel) fractions
averaged over all measures as a function of cluster mass. The colours indicate
the number of measurements made for each cluster. The error bars indicate the
minimum and maximum fraction measured for each cluster.