Static and dynamic behaviour of aqueous drops on thin lubricatingfluid-coated slippery (LCS) surfaces

M SHARMA, B BHATT, S GUPTA, R PANT and K KHARE*

Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016, India

*Author for correspondence (kcharya@iitk.ac.in)

MS received 17 October 2019; accepted 14 January 2020

Abstract. Inspired by Nepenthes pitcher plants, lubricating fluid infused slippery (LIS) surfaces have recently gained

tremendous attention from various research groups. We, alternatively, present lubricating fluid-coated slippery (LCS)

surfaces based on smooth solid surfaces. The biggest advantage of LCS surfaces over LIS surfaces is that solid surfaces

need not be rough or porous. We discuss that the surface energy of the underlying solid surfaces plays the most important

role in preparing the LCS surfaces. Lubricating fluid-coated hydrophilic surfaces result in sinking aqueous drops due to

the instability of the thin lubricating film. Additionally, stable and floating aqueous drops are observed on similar

hydrophobic surfaces. We also observed that the presence of surface roughness enhances the stability and performance of

LCS surfaces. Later we discuss various characteristics of LCS surfaces and its effects on the static and dynamic behaviour

of aqueous drops on LCS surfaces.

Keywords. Wetting; liquid–liquid interface; sinking; slipping; lubricant.

1. Introduction

Inspired by Nepenthes pitcher plants [1], lubricating fluid

infused slippery surfaces (LIS) have recently shown

prominence in micro and nanotechnology due to their

excellent performance of shedding the droplets and main-

taining non-wetting characteristics for a variety of test liq-

uids. Non-wetting performance is attributed to the fact that

the micro/nano textures of the surface are filled with a

suitable lubricating fluid forming a smooth lubricant inter-

face for the motion of drops of test liquids and hence cre-

ating a fluid–fluid interface between a lubricant and the test

liquid to be repelled [2–8]. The presence of a lubricating

fluid beneath the test drop minimizes the contact line pin-

ning by providing a smooth motion of the three-phase

contact line of the drop resulting in very low contact angle

hysteresis [5,8]. On a rigid solid surface, the equilibrium

wetting behaviour is defined by the Young’s contact angle

(hY), which is obtained by balancing the three interfacial

tensions cst, csg and ctg where s, t and g represent solid, test

liquid and surrounding gas phase, respectively, as shown in

figure 1a [9]. Whereas on thin lubricating fluid-coated solid

surface, due to vertical deformation of the three-phase

contact line, the three-phase contact point does not lie on

the same plane as the solid surface. The vertical component

of test liquid–gas interfacial tension (ctg) pulls the three-

phase contact point upward which results in the formation

of a wetting ridge around a test liquid drop. Therefore, the

simple Young’s contact angle cannot be defined in this case.

At the three-phase contact point, one can construct a Neu-

mann’s triangle and define the Neumann’s contact angle

(hN) [10] between ctg and ctl interfacial tensions (cf. fig-

ure 1b). Equation (1) shows the analytical expressions of

Young’s and Neumann’s contact angles

cos hY ¼csg � cst

ctgand cos hN ¼

c2lg � c2tg � c2tl2ctgctl

: ð1Þ

In 2011, Aizenberg and co-workers first designed slip-

pery lubricant-infused porous surfaces (SLIPS) by infusing

functionalized porous Teflon membrane with a low surface

energy liquid with the capability to repel various simple and

complex fluids [8]. For this four-phase system (solid,

lubricating liquid, test liquid and gas), Varanasi and co-

workers determined all possible thermodynamic states of a

static water droplet on such slippery surfaces [6]. Out of all

possible wetting states, only stable states are beneficial to

enhance the drop mobility. They also demonstrated that on

LIS, test drops could be cloaked by an ultrathin layer (*25

nm) of the lubricating fluid depending upon the interfacial

energies of test liquid and lubricating fluid [4,6]. Since then,

the LIS has been explored to understand various unan-

swered fundamental issues related to slippery surfaces.

With such distinctive features, LIS acts as a promising

candidate in numeral applications, including drag reduc-

tion [7,11,12], self-cleaning [2,13], anti-icing [14–16],

antifouling [17,18], fog harvesting [19], enhancing con-

densation [20], anti-corrosion [21,22], optical transparency

[23,24] and commercial food packaging [25].

Bull Mater Sci (2020) 43:191 � Indian Academy of Scienceshttps://doi.org/10.1007/s12034-020-02161-z Sadhana(0123456789().,-volV)FT3](0123456789().,-volV)

While designing LIS, it is important to understand the

role of physical properties of the underlying substrate, drop

and lubricating fluid on the slippery performance. Previous

studies have reported that the drop mobility is affected by

the surface tension and viscosity of the lubricating fluid by

ensuring the full coverage of microstructures by a lubri-

cating fluid and hence avoiding direct contact between the

drop and the substrate [26–29]. Chakraborty and co-workers

[30] recently fabricated oleoplaned rose petal replica-based

slippery surfaces and investigated their wetting states and

slippery behaviour. Also most importantly, wettability of

the underlying solid surface plays a vital role to determine

the stability of slippery surfaces. An essential condition to

get stable slippery behaviour is that underlying solid surface

should be hydrophobic, failing which the drop would sink

into the lubricating fluid and will not slip upon tilting

[2,8,31]. Lafuma and Quere [2] derived condition for the

sinking or floating of test drops on slippery surfaces

depending upon the interfacial energies of solid and the

liquid. Carlson et al [32] studied the short and long time

drop dynamics on thin oil-coated surfaces and also studied

the stability of the underneath oil film. Recently, Daniel

et al [33] investigated static and dynamic states of the

lubricating film using thin-film interference and reported

various lubrication states originating from the combined

effect of van der Waals interaction and interfacial effects.

Most of these studies have been reported on structured or

porous solid surfaces to infuse the lubricating fluid. Alter-

natively we used smooth solid surfaces over structured or

porous surfaces to get lubricant-coated surfaces (LCS). The

biggest advantage of having rough surfaces over smooth

surfaces is to enhance the drop mobility.

Here in this paper, we have studied the stable and

unstable behaviour of aqueous drops on silicone oil-coated

surfaces resulting in sinking or slipping of aqueous drops

depending upon the wettability of the underlying solid

surface and the viscosity of the lubricating fluid. Hydro-

philic substrates coated with lubricating fluid result in

sinking of the aqueous drops, and the dynamics of sinking

depend upon the oil viscosity and substrate hydrophilicity.

However, the equilibrium configuration is independent of

the oil viscosity. However, on hydrophobic oil-coated sur-

faces, aqueous drops are stable and easily move down the

surface and leave the surface clean upon tilting by few

degrees, and the performance of the slippery surface is

characterized in terms of their slip velocity. Later, we also

show that introducing a small amount of surface roughness

enhances the slippery behaviour and also reduces the

deterioration of the lubricating oil during the slipping of

water drops.

2. Experimental

Transparent microscopy glass slides and single-side pol-

ished silicon wafer were used as solid substrates. The sub-

strates were cleaned in an ultrasonic bath of ethanol,

acetone and toluene, respectively, for 10 min to remove any

organic contamination and subsequently dried with N2.

Hydrophilic surfaces were prepared by exposing the cleaned

samples to O2 plasma (Harrick Plasma, USA) for 1 min. A

self-assembled monolayer of octadecyltrichlorosilane

(OTS) molecules was grafted on the cleaned samples to

prepare hydrophobic surfaces. Water contact angles on

hydrophobic and hydrophilic surfaces were found about 109

(±2)� and 5 (±2)�, respectively. Surfaces with intermediate

contact angles between about 110 and 5� were prepared by

exposing the OTS-grafted samples in O2 plasma for

Figure 1. Schematics of a test liquid drop sitting on (a) a dry and (b) thin lubricating fluid-coated solid surface showing Young’s (hY)and Neumann’s (hN) contact angles, respectively, obtained by balancing various interfacial tensions (c). An apparent contact angle (happ)on the lubricated surface is shown in panel (b). (c) and (d) show binary images of water drops on dry and lubricated surfaces generated

using Python codes.

191 Page 2 of 7 Bull Mater Sci (2020) 43:191

different time intervals [34]. This resulted in samples with

water contact angles of 76 and 42�. All prepared surfaces

were coated with thin film of lubricating fluid, silicone oil

(Gelest Inc., USA), by spin coating. Silicone oil with

kinematic viscosity varying from 100 to 100,000 cSt was

used to study the effect of viscous drag on sinking and

slippery behaviour. A volume of 2 ll de-ionized (DI) water

drops were used as test liquid drops to investigate the

sinking/floating and slippery behaviour of the prepared

lubricating oil-coated slippery surfaces. Wetting behaviour

of dry and lubricating oil-coated surfaces was investigated

by a contact angle goniometer (OCA-35, DataPhysics,

Germany) using sessile drop method. Since the three-phase

contact point is not visible in images captured by the

goniometer, a Python-based image analysis program was

developed to accurately measure the apparent contact angle

on LCS surfaces. In this program, first a drop image is

converted into a binary, and then the base line is drawn by

identifying two extreme points by horizontal scanning.

Subsequently, a circle is fitted to the curved part of the

binary image of the drop and the apparent contact angle is

measured at the intersection of the base line and circle. All

measurements were performed at least three times on three

similar samples to estimate errors. Rough surfaces were

prepared by etching polished silicon wafers using aqueous

solution of NaBF4 and AgNO3 followed by immersing in

aqueous solution of HCl and HNO3 [35].

3. Results

Figure 1a and b shows the schematics of water drops on dry

and thin lubricating fluid-coated solid surfaces. During

contact angle measurement experimentally, it is not very

straightforward to identify the three-phase contact point,

hence it is more convenient to define an apparent contact

angle (happ) [36] as also shown in figure 1b. Figure 1c and d

shows corresponding binary images of water drops on dry

and LCS surface used for the Python-based image analysis

program to extract the Young’s and apparent contact angles.

Surface energy or wettability of solid substrates affects the

drop behaviour on lubricated substrates. Figure 2 shows the

behaviour of water drops, in terms of its apparent contact

angles, on lubricated surfaces prepared using hydrophilic

and hydrophobic solid substrates. On a hydrophilic surface,

with water contact hws = 5�, water drops are not found to

be stable upon lubricating fluid coating as they sink inside

the lubricating film with final apparent contact angle

happ = 36�. The sinking of water drops on such hydrophilic

surfaces coated with thin lubricating film is associated with

the stability of the oil film underneath the drop which will

be discussed later. Besides, in a similar study on

hydrophobic solid surfaces with water contact angle

hws = 110�, water drops are found to be very stable with

happ = 109�. Therefore, the wettability or surface energy of

the underlying solid surface plays the most crucial role in

the preparation of such slippery surfaces. Lafuma and Quere

[2] calculated the condition for sinking/floating in terms of

the interfacial tensions of both the liquids and contact

angles on the solid surface. The condition for floating was

calculated as Dc ¼ cl cos hls � ct cos hts � clt [ 0: For the

present case with lubricating fluid as silicone oil

(cl ¼ 21 mJ m-2) and test liquid as water (ct ¼72 mJ m-2), Dc = -90.6 and 2.5 mJ m-2 for hydrophilic

and hydrophobic substrates, respectively. Therefore,

hydrophilic surfaces result in sinking water drops whereas

hydrophobic ones show stable and floating water drops.

Subsequently, to understand the reason behind the sink-

ing of water drops, controlled experiments were performed

Figure 2. Optical images of water drops on dry and lubricating oil-coated hydrophilic (hws = 5�) and hydrophobic (hws = 110�)surfaces. Due to the negative value of Dc (= -90.6 mJ m-2) water drops on hydrophilic oil-coated surfaces sink hence show very low

value (happ = 36�) apparent contact angle. Whereas on hydrophobic oil-coated surfaces, Dc is positive (= ?2.5 mJ m-2), hence water

drops float on them showing large (happ = 109�) apparent contact angle.

Bull Mater Sci (2020) 43:191 Page 3 of 7 191

where a lubricating oil drop and thin uniform oil film were

investigated in air and under water. Figure 3 shows a

stable oil drop in air with contact angle 7�. Upon immersing

this oil drop under water, the drop dewets and its contact

angle increases to 129� due to the increased interfacial

tension. Therefore, an oil drop under water forms smaller

oil–solid interfacial area compared to in air. Similarly when

a uniform oil film, with almost 0� contact angle, is

immersed under water, it breaks into multiple drops to

minimize its surface energy. This is the main reason for

unstable or sinking water drops on thin oil film coated on

hydrophilic surfaces. The sandwiched oil film between a

water drop and hydrophilic solid substrate dewets and

breaks into multiple drops, which brings the water drop into

direct contact with the hydrophilic solid surface, and the

apparent contact angle goes down to 36� as shown in fig-

ure 2. Whereas for a hydrophobic solid substrate, an oil film

sandwiched between a water drop and solid surface remains

stable, and the water drop floats on the thin oil film with

almost no change in the apparent contact angle. Therefore,

the substrate wettability is the most important criterion

while fabricating lubricating fluid-coated slippery surfaces.

We further investigated the dynamics of the sinking of

water drops on thin lubricating fluid-coated hydrophilic

substrates. We also studied the effect of substrate

hydrophilicity and lubricating fluid viscosity on the sink

dynamics. Substrates with different hydrophilicity (water

contact angles 5, 42, 76 and 109�) were coated with thin

layer of silicone oil and the apparent contact angle of water

drops deposited on them was measured as a function of time

which is shown in figure 4a. It is clear from the figure that

for hws = 110� (hydrophobic substrate), the apparent con-

tact angle does not change at all as the water drop floats on

the lubricating oil film. Whereas for hws = 76, 42 and 5�,water drops sink as their apparent contact angle decreases

with time. Here, the important point to note is that the

extent of sinking depends upon the hydrophilicity of the

solid substrates. For the substrate with hws = 5� water dropssink rapidly leading to the equilibrium apparent contact

angle happ of 36� whereas for hws = 42 and 76�, sinking is

relatively slow and the equilibrium apparent contact angle

values are 68 and 92�, respectively. This tells that the extentof sinking is lower for substrates with smaller

hydrophilicity. Figure 4b shows the effect of viscosity of

Figure 3. Schematics and optical images of an oil drop and oil film in air and under water on a hydrophilic solid substrate. An oil drop

in air shows the contact angle of 7� which increases to 129� when immersed under water. Completely spreading oil film in air breaks into

multiple oil drops under water.

Figure 4. Effect of (a) substrate wettability and (b) viscosity of

lubricating fluid on sink dynamics of water drops on thin

lubricating fluid-coated solid surfaces.

191 Page 4 of 7 Bull Mater Sci (2020) 43:191

the lubricating silicone oil on the sink dynamics. It is clear

from the figure that sink dynamics becomes slower with

increasing viscosity of silicone oil or in other words,

dynamic apparent contact angle decreases slowly with

increasing viscosity. This is due to the increasing retarding

viscous drag during sinking of water drops with increasing

viscosity. However, the equilibrium apparent contact angle

is independent of the oil viscosity as it should only depend

upon various interfacial tensions. Therefore, at longer time

scale water drops show the same apparent contact angle for

all different viscosities. Hence, the equilibrium apparent

contact angle depends only on the substrate wettability and

not on the viscosity of the lubricating oil. Figure 5 shows

optical images of sinking water drops on a completely

hydrophilic solid substrate coated with silicone oil of vis-

cosities 100, 1000 and 5000 cSt at different time interval. It

is clear from the image the water drops on different vis-

cosity samples take different time to reach the same

apparent contact angle. Also, all the samples show the same

equilibrium apparent contact angle of 35� upon complete

sinking. Hence, it is clear that the extent of sinking depends

only upon the substrate wettability and the viscosity of

lubricating fluid only controls the time to reach the

equilibrium.

We subsequently investigated the slippery behaviour of

water drops on hydrophobic (hws = 110�) solid surface

coated with thin lubricating silicone oil of different vis-

cosities. The samples were tilted by 10� and the velocity of

moving water drops was measured. Figure 6a shows the

position of water drops on tilted slippery surfaces at dif-

ferent time intervals for two different silicone oil viscosi-

ties. It is clear from the image that drops move faster on

lower viscosity surfaces due to smaller viscous drag.

Figure 6b shows the plot of slip velocity of water drops as a

function of the viscosity of silicone oil. Varanasi and co-

workers [6] theoretically calculated a scaling model to

calculate the slip velocity (m) of slipping water drops which

is given as

m� qgðsin a� sin a�Þgl

R2b ð2Þ

where q is the density of water, g is the acceleration due to

gravity, a and a* are tilt and critical tilt angles, Rb is the

base radius of a slipping water drop and gl is the viscosity ofthe lubricating oil. It is clear from equation (2) that the slip

velocity depends on the square of the base radius of water

drops and is inversely proportional to the viscosity of

lubricating oil. This model is fitted to the experimental data

in figure 6b which is shown as the solid red line. The

thickness of the lubricating film also affects the slip velocity

of aqueous drops. With increasing film thickness, slip

velocity initially increases (until all surface heterogeneities

are covered by the lubricating film). Increasing film thick-

ness after this value (within lubrication approximation, i.e.,

Figure 5. Sinking of water drops on hydrophilic solid surfaces coated with lubricating oil of different viscosities showing the same

equilibrium apparent contact angle at long time.

Figure 6. (a) Optical images of slipping water drops at different

time intervals on 100 and 5000 cSt viscosity silicone oil-coated

slippery surfaces. (b) Variation of slip velocity of water drops with

the viscosity of silicone oil (black data point showing experimental

data and solid red line corresponds to the theoretical model).

Bull Mater Sci (2020) 43:191 Page 5 of 7 191

film thickness\\ lateral dimension) does not affect the slip

velocity. The effect of thickness on slip velocity becomes

less pronounced with increasing viscosity of the lubricating

fluid. Zhang et al [37] observed similar behaviour for

slipping water and n-decane drops on their LIS surfaces. For

the static case, we measured the apparent contact angle of

water drops on LCS surfaces for different thicknesses of

lubricating fluids. It was observed that larger portion of

water drops is submerged with increasing lubricant film

thickness, which results in decreasing values of the apparent

contact angles. Figure 7 summarizes the variation in the

apparent contact angle (left Y-axis) and slip velocity (right

Y-axis) with thickness of the lubricating film.

Further, we also investigated the slippery behaviour on

rough surfaces and tried to understand the effect of surface

roughness on the final slippery behaviour. A small amount

of surface roughness is found helpful in the slippery beha-

viour as it increases the stability of lubricating oil on solid

surfaces. We prepared two rough surfaces with rmsroughness 25 and 140 nm and investigated their slippery

behaviour and the stability of lubricating oil on them

compared to a smooth surface. As water drops slip on a

lubricating fluid-coated surface, they also remove little bit

of the lubricating oil with them. Hence, we investigated the

slippery behaviour by measuring the slip velocity and

contact angle hysteresis on them as a function of the total

dispensed volume of slipping water drops for smooth and

rough surfaces. Figure 8 shows the deterioration in slippery

behaviour in terms of slip velocity (figure 8a) and contact

angle hysteresis (figure 8b) as a function of total dispensed

water volume. The slip velocity of water drops decreases

with increasing dispensed liquid volume and the resulting

contact angle hysteresis increases. Therefore, the small

roughness samples show lesser deterioration compared to

smooth and large roughness samples. This improvement can

be attributed to the better stability of the lubricating oil due

to increased surface area on small roughness samples

compared to the smooth samples. Additionally, for large

roughness, slipping water drops feel pinning force hence

show smaller slip velocity and large contact angle hysteresis

with increasing dispensed liquid volume.

4. Conclusion

We conclude that solid surfaces, coated with thin film of

lubricating fluid, can be used as slippery surfaces for suit-

able test liquid drops. The performance of the slippery

behaviour of water drops on thin silicone lubricating oil-

coated surfaces depends strongly on the wettability or sur-

face energy of the solid surface. For hydrophobic solid

surfaces, water drops float on the thin lubricating film

whereas, for hydrophilic surfaces, they sink into the oil film.

This is because the sandwiched oil film between water

drops and hydrophilic solid surface undergoes instability

and dewets into smaller drops resulting in bringing the

water drops into contact with the hydrophilic solid surface.

The dynamics of the sinking behaviour also depends on the

hydrophilicity of the solid surface and the viscosity of the

Figure 7. Variation in apparent contact angle (black data points

corresponding to left Y-axis) and slip velocity (red data points

corresponding to right Y-axis) of water drops on LCS surfaces

with increasing thickness of the lubricating film.

Figure 8. Degradation study of slippery surfaces in terms of

(a) slip velocity and (b) contact angle hysteresis of water drops onsmooth and rough surfaces with dispensed liquid volume.

191 Page 6 of 7 Bull Mater Sci (2020) 43:191

lubricating oil. On hydrophobic substrates-based slippery

surfaces, water drops slip as the surfaces are tilted by few

degrees, and the slip velocity of water drops is found to be

inversely proportional to the viscosity of the lubricating oil.

Also, introducing a small amount of surface roughness not

only enhances the slippery behaviour, but also reduces the

deterioration of slippery behaviour.

Acknowledgements

This research study was supported by Hindustan Unilever

Limited, India and DST, New Delhi through its Unit of

Excellence on Soft Nanofabrication at IIT Kanpur.

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