Journal of Colloid and Interface Science 470 (2016) 22–30

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Journal of Colloid and Interface Science

journal homepage: www.elsevier .com/locate / jc is

The dynamic spreading of nanofluids on solid surfaces – Role of thenanofilm structural disjoining pressure

http://dx.doi.org/10.1016/j.jcis.2016.02.0440021-9797/� 2016 Elsevier Inc. All rights reserved.

⇑ Corresponding author.E-mail address: wasan@iit.edu (D. Wasan).

Sangwook Lim, Hua Zhang, Pingkeng Wu, Alex Nikolov, Darsh Wasan ⇑Department of Chemical and Biological Engineering, Illinois Institute of Technology, Chicago, IL 60616, United States

g r a p h i c a l a b s t r a c t

Top view depicting the movement of th

e outer and inner contact lines with time in the pre-equilibrated oil/polymeric nanofluid on the glass substrate.

a r t i c l e i n f o

Article history:Received 6 January 2016Revised 16 February 2016Accepted 17 February 2016Available online 18 February 2016

Keywords:Polymeric nanoparticlesStructural disjoining pressureContact angleOil detachmentEnhanced oil recovery

a b s t r a c t

Nanofluids comprising nanoparticle suspensions in liquids have significant industrial applications. Priorwork performed in our laboratory on the spreading of an aqueous film containing nanoparticles displac-ing an oil droplet has clearly revealed that the structural disjoining pressure arises due to the layering ofthe nanoparticles normal to the confining plane of the film with the wedge profile. The pressure drivesthe nanofluid in the wedge film and the nanofluid spreads. We observed two distinct contact lines: theinner contact line, where the structural disjoining pressure dominates the Laplace capillary pressure,and the outer contact line, given by the Laplace equation prediction extrapolated to the solid substratewhere the structural disjoining pressure contribution is negligible. We report here our results of theeffects of several parameters, such as the nanoparticle concentration, liquid salinity, temperature, andthe substrate contact angle, on the motion of the two contact lines and their effects on the detachmentof the oil droplet. We also studied the equilibrated and non-equilibrated oil/nanofluid phases, the time ofadhesion of the oil droplet on the solid substrate and the drying time of the substrate. We employed thefrictional model to predict the outer contact line velocity and our previous theoretical model (based onthe structural disjoining pressure) to predict the inner contact line velocity. The theoretical predictionsagreed quite well with the experimentally measured values of the velocities.Our experimental results showed that the motion of the inner contact line was accelerated by the

increase in the nanoparticle concentration, temperature, and hydrophilicity of the substrate for thepre-equilibrated oil/nanofluid phases, which resulted in the faster detachment of the oil droplet.

Fig. 1. (a) A sketch illustrates the dynamic spreadingwith the Laplace and microscopic (MI) contact anglethickness (layers) [25].

S. Lim et al. / Journal of Colloid and Interface Science 470 (2016) 22–30 23

The speed of the two contact lines decreased upon the increase in the drying time of the substrate and theoil adhesion time on the substrate.The present results provide new insights into the complex spreading behavior of nanofluids on solid

substrates.� 2016 Elsevier Inc. All rights reserved.

1. Introduction

Nanofluids, which are composed of liquid suspensions of nano-sized particles, have significant technological applications in areasas diverse as enhanced oil recovery [1–3], soil remediation [4], heattransfer [5,6], lubrication [7], and drug delivery [8]. Recent investi-gations of the spreading and wetting of nanofluids have demon-strated the inadequacy of the well-known concepts of thespreading and adhesion of pure liquids on solid surfaces [9–24].

Recent experiments and modeling [3,9,18,19,25–28] conductedin our laboratory have clearly demonstrated that the spreading ofnanofluids on solids is enhanced by the nanoparticle self-structuring in the confined three-phase oil/nanofluid/solid contactregion (Fig. 1). A layering phenomenon for a pure liquid wasreported by Cazabat and de Gennes [29]. We analyzed the equilib-rium profile of an oil drop on a smooth solid substrate with consid-eration to the Laplace equation and structural disjoining pressure.The drop profile extrapolated to the solid gives the macroscopicthree-phase contact angle and has to satisfy the Young equation’sprediction of the three-phase contact angle. However, when con-sidering the contribution of the structural disjoining pressure oper-ating at a distance less than three nanoparticle diameters from thesubstrate, the oil drop profile deviates from the Laplace prediction;the drop shape at the three-phase contact region becomes step-wise (like a wedge shape), and the film and meniscus form themicroscopic (MI) contact angle (see Fig. 1a).

The nanoparticle structuring phenomenon gives rise to thestructural disjoining pressure (a force normal to the interface) inthe wedge film (see Fig. 1b): it can be related to the spreading coef-ficient S of nanofluids by the following equation: [25,28]

S ¼ PcðheqÞheq þZ 1

heq

PðhÞdh ð1Þ

of the nanofluid in a wedge-shapeds [28]. (b) The nanoparticle layeri

where PcðheqÞ represents the sum of the capillary pressures at theequilibrium film thickness, heq. PðhÞ is the disjoining pressure,including the structural pressure of the nanoparticles in the wedgefilm region. The second term on the right side of the equation (theintegral of the disjoining pressure over the thickness of the wedge)represents the film tension. As the film thickness decreases (towardthe vertex of the wedge), the film tension increases, and this filmtension gradient arising from the nanoparticle structural pressurein the wedge drives the enhancement of the nanofluid spreadingon a solid substrate. Therefore, the film tension gradient vs. nano-film thickness (number of layers) drives the nanofluid in the wedgefilm to spread and displace oil from the substrate (Fig. 1) [9,25].

Fig. 2 shows that the spreading coefficient increases with adecrease in the film thickness, that is, the spreading of a nanofluidtoward the vertex of the wedge occurs due to the structural dis-joining pressure of the nanoparticles [9].

The magnitude of the structural disjoining pressure depends onthe nanoparticle volume fraction, particle size, polydispersity, andthree-phase contact angle. In the wedge film region, the structuraldisjoining pressure dominates the Laplace capillary pressure,resulting in the appearance of two distinct contact lines: an outerline, the Laplace prediction extrapolated to the substrate, and aninner line, the nanofilm extrapolated to the substrate (Fig. 1a).

The first experimental study on the dynamic spreading ofnanofluids (micellar solutions) on a solid surface was conductedby Kao et al. [30]. Using a differential interference microscope, theyobserved two distinct contact lines during the separation of crudeoil droplets from a solid silica surface in the presence of a micellarsolution: an outer one (between the oil, solid, and water film) andan inner one (a nanofluidic film between the oil, solid, and mixedoil/water film) (see Fig. 3). The spreading of the nanofluidic filmwas later understood to be driven by the structural disjoining pres-sure gradient arising from the ordering of the micelles in the

film driven by the structural disjoining pressure gradient between the oil and solidng in the wedge film leads to the structural disjoining pressure gradient vs. film

Fig. 2. Spreading coefficient arising due to the particle disjoining pressure [9].

24 S. Lim et al. / Journal of Colloid and Interface Science 470 (2016) 22–30

wedge-film region. Wasan and Nikolov [9], Nikolov and their co-workers [25–28,31] further noted that the dynamics of the innercontact line are dependent on the combination of the nanoparticleformulation, contact angle, and the capillary pressure. A suitablecombination of these factors accelerates the spreading of the nano-fluid on the solid surface, thereby detaching the oil from thesubstrate.

In our previous experimental studies on the motion of contactlines and the dynamic spreading of nanofluids on solid substrates,we used a colloidal suspension of silicon oxide (with a nominaldiameter of 19 nm) in an alkali aqueous solution (pH = 9.0) andcommercial canola oil. The alkali solution of the nanofluid withthe canola oil induced saponification at the nanofluid-oil interface,producing surface active materials during the experiment. In thepresent study, we used a simple model IIT nanofluid system(patent applied) containing polymeric nanoparticles of polyethy-lene glycol (with a nominal diameter of 9.5 nm) dispersed indeionized water (DI) as a polymeric nanofluid (PNF). We pre-equilibrated the Cargille oil with the nanofluid to avoid the effectsof any surface active impurities during the experiment.

We also investigated the effects on the motion of the contactlines of several parameters such as the nanofluid concentration,oil adhesion time, drying time of the substrate, substrates with dif-ferent hydrophilicities, salinity of the nanofluid, and temperature.Many of these factors can significantly affect the dynamics of nano-fluid spreading and the time of the detachment of the oil dropletfrom the solid substrate.

Fig. 3. Photomicrograph taken using reflected-light interfero

We also employed theoretical models to rationalize the motionof the two contact lines and compared the theoretical predictionswith the experimental measurements.

2. Experimental

2.1. Materials

Cargille immersion oil (density = 0.854 g/cm3, viscos-ity = 0.0181 Pa s, surface tension = 29.4 mN/m, refractiveindex = 1.474 at 25 �C, Cargille Laboratories, USA) was used inexperiments as a sessile drop of oil on a solid surface surroundedby a nanofluid. A small amount (<100 ppm) of Oil Red EGN dye(Aldrich Chemical Co., USA) was added to the oil sample to increasethe contrast in order to better visually monitor the oil displace-ment process from the side view. Polyethylene glycol (PEG) 8000and sodium chloride (NaCl) were purchased from Fisher Scientific(USA). Sodium dodecyl sulfate (SDS) was obtained from VWR Sci-entific (USA).

Four solid substrates were used in this study: a premium coverglass (Fisher Scientific, USA), muscovite mica (grade V, Ted Pella,USA), a gold-coated microscope slide (Platypus, USA), and a stain-less steel plate (McMaster-Carr, USA). The oil was deposited on thesolid substrate with a Hamilton micro-syringe with a B-D needle(25G 5/8).

2.2. Methods

2.2.1. Nanofluid preparationPolyethylene glycol was used as the polymeric nanoparticle

(PNP) and dispersed in DI water to prepare the PNF. For the salinityexperiments, the PNP was dissolved in 0.25 wt% NaCl solution(brine) to prepare the PNF in brine. We optimized the wettingcharacteristics of the solid surface by using an appropriate amountof a wetting agent (3 mM SDS, less than the critical micelle concen-tration in water) in the PNF in order to reduce the oil/nanofluid/-solid three-phase contact angle and maximize the structuralforce resulting from the confinement of the nanoparticles in thewedge film. The size and polydispersity of the PNFs in DI waterwere characterized by the dynamic light scattering method (Mal-vern Instruments, UK). The average diameter was found to be9.5 ± 0.5 nm, with a polydispersity of around 8% at 25 �C. The samesize and polydispersity were found for the PNF in brine.

metry depicting the inner and outer contact lines [26].

S. Lim et al. / Journal of Colloid and Interface Science 470 (2016) 22–30 25

The volume fraction of the PNP in the PNF, /, was calculatedbased on the molar concentration of the polymer, c, and the diam-eter of the PNP, d.

By multiplying the number of the PNP in the PNF with the vol-ume of one PNP, we derived the following relation to calculate thevolume fraction of the PNP in the PNF.

/ ¼ cNA16pd3

� �ð2Þ

where c is the polymer molar concentration (mol/L), NA is the Avo-gadro constant and d is the diameter of the PNP.

We conducted experiments on the spreading of the PNF com-posed of the 0.15, 0.20, and 0.25 volume fractions of the PNP.

We pre-equilibrated the PNF with the oil by stirring the vialcontaining the PNF and the oil before the experiments in order tominimize the partitioning effect of the impurities in the oil. Duringpre-equilibration, the oil phase was dispersed into the aqueousnanofluid solution as drops and left overnight for a phase separa-tion in a glass container. We used the suction repeatedly to sepa-rate the pre-equilibrated oil from the top of the container.

2.2.2. Interfacial tension measurementThe classical method of drop-shape analysis fitted to the

Laplace equation was used to calculate the oil/nanofluid interfacialtension (IFT). The drop-shape profile was obtained from the side-view method during the oil detachment. This profile was analyzedto determine the IFT with different volume fractions of the PNP at25, 35, and 50 �C. The measured value of the IFT showed goodagreement with the value from the analysis of the drop profilefrom the goniometric technique (Kernco Instruments Co.). Thedetailed procedure is described in our previous work [18].

Table 1 lists the IFT of the oil and different volume fractions of thePNP at 25 �C for non-equilibrated and pre-equilibrated systems.Wefound that the pre-equilibrated system had a 4–5 mN/m greaterreduction in the IFT than that which occurred in the non-equilibrated one. Table 1 shows that for the non-equilibrated sys-tem, we expected the partitioning effect of the impurities in theoil and the PNF during the oil detachment which may affect theoil detachment from the substrate. In order to minimize theseeffects, we chose the pre-equilibrated oil/nanofluid system for thisstudy.

2.2.3. Contact angle measurementWe characterized the wettability of the solid substrates by mea-

suring the oil/nanofluid/substrate three-phase contact angle withthe goniometer. An oil drop was deposited on the solid substrate.The solid substrate was then turned upside-down and placed ontwo supports inside a transparent glass cuvette. The PNF was intro-duced into the cuvette with a microsyringe. The image of the oildrop on the solid was captured with a digital camera (CanonA720 IS) after the drop-shape profile stopped changing. Eachexperiment was conducted at room temperature (25 ± 1 �C). Theoil/nanofluid/substrate three-phase contact angle was calculatedby image analysis (Image Pro, version 6).

Table 1Oil and nanofluid IFT vs. volume fraction of the PNP for non-equilibrated and pre-equilibrated systems.

PNP volume fraction IFT (mN/m)

Non-equilibrated system Pre-equilibrated system

0.15 24 ± 1.5 19 ± 1.40.20 22.9 ± 1.0 17 ± 1.70.25 21.4 ± 1.0 16 ± 1.0

2.2.4. Solid substrate preparationThe premium cover glass slides and all of the glassware were

precleaned by immersing them in a mixture of sulfuric acid andchromic acid at 40 �C overnight; they were then rinsed and washedwith DI water and immersed in it for 1 day. We separately driedthe cleaned glass slides for 12 h and 24 h at 25 �C in order to checkthe effects of the drying time on the oil separation from the glassslides.

The fresh micas were cleaned with DI water and immersed in itfor 1 day.

The gold plates were cleaned by immersion in a sequence oftoluene for 6 h, acetone for 6 h, and DI water for 1 day.

The stainless steel plates were cleaned by immersing them in asequence of xylene for 6 h, acetone for 6 h, and DI water for 1 day.

All the substrates (mica, gold, and stainless steel) were dried inair for 12 h at 25 �C before being used in the experiments.

2.3. Microscopy to study the contact line motion

We used a recently-developed advanced microscope technique[25] to directly observe the spontaneous spreading of the PNF on asolid substrate. The spreading dynamics of the PNF that led to theoil displacement were monitored using the digital optical appara-tus shown in Fig. 4.

An oil drop of 1.2 ± 0.2 lL was placed on the lower surface of asolid substrate using a micro-syringe. Different oil adhesion times(such as 1, 24, and 72 h) were selected to test the adhesion time’seffect on the oil detachment. The slide with the oil drop was thenimmersed in the nanofluid in a transparent experimental box in acontrolled environment to form a sessile drop. Two square sup-ports were used to lift the glass slide in order to provide for goodvisual observation. A sessile oil drop was formed when the airwas displaced by the nanofluid around the oil drop on the glasssurface. The buoyancy in this configuration presses the droptoward the supporting glass surface. The dynamics of the nanofluidspreading on the solid surface were simultaneously monitored andrecorded by two sets of digital CCD video cameras from the top andside views at 30 frames per second. This optical set-up is uniquebecause it enables the simultaneous monitoring of the oil dropfrom both the top and side views. The positions of the nanofluidcontact lines were monitored in the top view via a vertical micro-scope in reflected light mode with a long focus objective. Fig. 5shows the observation of the nanofluid contact line’s movementon the glass substrate from the top view with a 0.15 volume frac-tion of the PNF. As shown in Fig. 5, the oil/water/solid contact lineinitially shrank after the PNF was introduced. During the shrinkingof the contact line, the dynamic contact angle decreased. When theangle became small enough, the oil/water/solid contact linestopped moving and the inner contact line started to appear, indi-cating the nanofluid film formation due to the nanoparticle struc-turing between the two distinct lines (outer and inner contactlines). The inner contact line moved at a constant velocity untilthe oil was detached from the substrate while the outer contactline was pinned, as we observed in our previous study [26,27].

The oil droplet’s side view was captured by a horizontal micro-scope in transmitted light mode with a high magnification lens.The side-view objective was adjusted so that the droplet’s reflec-tion on the glass and the position of the outer contact line werealways observed. The position of the outer contact line from theside view was used for measuring the contact angle and interfacialtension.

Digital images were obtained from the recorded video usingAdobe Premiere 6.5. These images were then analyzed with imageanalysis software (Image Pro, version 6). The changes in the posi-tion of the contact line were obtained. Pixel/length calibrationwas done using a known length. The change in the position of

Fig. 4. Apparatus and experimental set-up for monitoring nanofluid spreading dynamics and micrographs depicting the top and side views of the oil drop.

Fig. 5. Top view depicting the position of the contact line with time in the pre-equilibrated oil/PNF for the 0.15 volume fraction of the PNF on the glass substrate (dryingtime = 12 h and oil adhesion time = 1 h).

26 S. Lim et al. / Journal of Colloid and Interface Science 470 (2016) 22–30

the contact line with respect to time was plotted. Each experimentwas repeated at least three times.

A transparent polystyrene box (50 mm � 50 mm � 20 mm)with two glass supports was used for the experiments on theeffects of the temperature. An oil drop of 1.2 ± 0.2 lL was attachedto the lower surface of the glass substrate for 3 days. Then, the sub-strate was relocated to the experimental box with the two sup-ports. The box and the 0.20 volume fraction of the PNP were firstpre-heated using a hot plate with a water bath until they reachedthe desired temperature. We then slowly introduced the pre-heated nanofluid into the pre-heated box in the temperature-controlled water bath and measured the oil detachment time.

The experiment was conducted at 25, 35, and 50 �C; the tempera-ture was kept constant. The accuracy of the temperature measure-ment was ±0.1 �C.

3. Results and discussion

3.1. The effect of the PNP volume fraction on contact line movement

Fig. 6 shows the three-phase contact radius changes with timefor the 0.15, 0.20, and 0.25 volume fractions of the PNP on the glasssubstrate (the drying time was 12 h and the oil adhesion time was1 h). The contact radius shrinks quickly to establish its equilibrium

Time (min)0.0 0.5 1.0 1.5 2.0

Con

tact

rad

ius (

mm

)

0.0

0.1

0.2

0.3

0.4

0.50.15 PNF outer line0.15 PNF inner line0.20 PNF outer line0.20 PNF inner line0.25 PNF outer line0.25 PNF inner line

mm/min11.020.0

=−PNPdt

dr

mm/min0. 25015.0

=−PNPdt

dr

mm/min14.025.0

=−PNPdt

dr

Fig. 6. Graph depicting the position of the three-phase contact line on the glasssubstrate (the drying time was 12 h and oil adhesion time was 1 h) afterintroducing the different volume fractions of the PNF at 25 ± 1 �C.

Time (min)0 1 2 3 4

Con

tact

rad

ius (

mm

)

0.0

0.2

0.4

0.6Drying 12 hours/adhesion 12 hours (outer)Drying 12 hours/adhesion 12 hours (inner)Drying 24 hours/adhesion 12 hours (outer)

Fig. 7. Graph depicting the effect of the glass substrate’s drying time on the positionof the three-phase contact line after introducing the 0.15 volume fraction of PNF at25 ± 1 �C.

Table 2Oil detachment time, inner contact line velocity, and oil/nanofluid/glass three-phasecontact angle at different drying times and oil–glass adhesion times using the 0.15volume fraction of PNF at 25 ± 1 �C.

Scenarios Oil detachmenttime (min)

Inner contact linevelocity (mm/min)

Contactangle (�)

Drying 12 h/adhesion 1 h 2–3 0.052 ± 0.011 4–7Drying 12 h/adhesion 12 h 3–4 0.047 ± 0.015 5–8Drying 24 h/adhesion 12 h N/A N/A 18–22Drying 12 h/adhesion 24 h 4–7 0.041 ± 0.020 7–10Drying 12 h/adhesion 72 h 80–110 �0.011 12–14

Table 3Oil/nanofluid/solid three-phase contact angle and oil detachment time from the solidvs. solid substrate type using the 0.25 volume fraction of the PNP at 25 ± 1 �C.

Substrate type Contact angle (�) Separation time (min)

Premium cover glass 3 ± 1 �1Mica 10 ± 2 1–3Gold plate 130 ± 3 N/A

S. Lim et al. / Journal of Colloid and Interface Science 470 (2016) 22–30 27

state where the interfacial forces are balanced. We observed thatthe movement of the outer contact line was almost independentof the volume fraction of the PNP. For the inner contact line move-ment, however, the inner contact line velocity increased from0.052 mm/min to 0.14 mm/min when the volume fraction of thePNP increased from 0.15 to 0.25, resulting in a faster oil dropdetachment (note the constant slope of the inner contact line inFig. 6).

We demonstrated that the structuring effect due to the confine-ment in the wedge region is stronger when the aqueous phase con-tains more nanoparticles [32]. Trokhymchuk et al. [33]theoretically derived the structural disjoining pressure for a fluid/-suspension confined in a film and found that its amplitudeincreases with the increasing nanoparticle volume fraction. Thus,we can expect a higher driving force for the inner contact linemovement with a higher nanoparticle volume fraction during thesame period of time. The detailed calculation of the structural dis-joining pressure with the volume fraction of nanoparticles will bediscussed in Section 3.6.2.

Stainless steel plate 144 ± 2 N/A

3.2. The effect of substrate drying and oil adhesion time on contact linemovement

Fig. 7 shows the effect of the drying time of the glass substrateon the movement of the three-phase contact line. Fig. 7 shows thatwhen the drying time for the glass substrate is 12 h, the outer con-tact line shrinks quickly after introducing the 0.15 volume fractionof the PNF and stops moving at around 1 min; then, the inner con-tact line appears. The oil drop is detached from the glass substrateafter around 3–4 min. However, when the drying time is increasedto 24 h, the outer contact line initially shrinks quickly and thenadvances very slowly; no detachment of the oil drop from the sub-strate is observed for 2 days. When we increased the drying time ofthe glass substrate from 12 h to 24 h, we found that the oil/-nanofluid/glass three-phase contact angle increases from 5–8� to18–21� as described in Table 2. That is, we do not expect thenanoparticle structuring between the oil and glass substrate withthe sample that was dried for 24 h resulting in no detachment ofthe oil from the glass substrate [25].

Table 2 summarizes the effect of the glass substrate’s dryingtime and oil adhesion time on the glass substrate. Table 2 indicatesthat as we increase the glass drying time and oil adhesion time, thethree-phase contact angle increases and it takes much longer forthe oil drop to detach from the substrate with the slower inner

contact line velocity. This can be explained by the fact that thenanoparticle structuring becomes less pronounced with increasesin the contact angle. Therefore, we can expect less spreading ofthe PNF on the glass as the drying time and oil adhesion timeincrease.

3.3. The effect of solid substrates’s wettability on oil detachment

Kondiparty et al. [25] theoretically predicted that more hydro-philic surfaces aid in spreading the nanofluid on the solid surface;they noted that there exists a critical oil/nanofluid/solid three-phase contact angle beyond which the structural disjoining pres-sure is balanced by the capillary pressure without establishing ahorizontal nanofluidic film, so the nanofluid cannot spontaneouslyspread. Liu et al. [28] also theoretically showed that the three-phase contact angle affects the inner contact line velocity in thebeginning stages and the velocity will be independent of the con-tact angle once a horizontal nanofilm is established when the con-tact angle is less than 2�.

Table 3 shows the oil/nanofluid/solid three-phase contact angleand oil detachment times on different substrates with the 0.25 vol-ume fraction of the PNF. Table 3 indicates that the nanofluid film

Time (min)0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

Fric

tiona

l coe

ffic

ient

0.0

0.5

1.0

1.5

2.0

2.5

0.15 PNF0.20 PNF0.25 PNF

Fig. 8. The calculated frictional coefficients from the experimental data for volumefractions 0.15, 0.20, and 0.25 of the PNF. The dashed line represents the averagevalue.

28 S. Lim et al. / Journal of Colloid and Interface Science 470 (2016) 22–30

can be established on hydrophilic substrate surfaces exertingnanofluid spreading, such as glass and mica substrates with lowcontact angles; therefore, the detachment of the oil drop doesnot occur on the stainless steel or gold plates because they exhibithigh contact angles.

3.4. The effect of salinity on oil detachment

Table 4 illustrates the effects of the salinity (0.25 wt% NaCl) onthe IFT, oil detachment time, and inner contact line velocity. Table 4shows that the inner contact line velocity is smaller and oil detach-ment time is longer in the presence of a higher salinity when theIFT decreased from 17 ± 1.7 mN/m to 8.6 ± 0.3 mN/m. The reduc-tion of the oil/nanofluid interfacial tension decreases the capillarypressure, which operates as a resistance force during the nanofluidspreading process. However, the second virial coefficient of thePNF in presence of a high salinity is significantly decreased[3,34]. The reduction of the second virial coefficient decreasesthe osmotic pressure of the PNF, thereby decreasing the structuraldisjoining pressure of the nanofluids, which is the driving force forthe nanofluid spreading dynamics [27]. Since the structural dis-joining pressure is a more dominant driving force than the capil-lary resistance force when the nanoparticle layering occurs, wecan expect a slower oil drop detachment with a higher salinity.

3.5. The effect of temperature

The glass substrate was dried in air for 12 h at 25 �C and the oiladhesion time on glass was 3 days. Table 5 shows the oil detachmenttimes on the glass substrate at 25, 35, and 50 �C using the 0.20 vol-ume fraction of the PNF. As we see in Table 5, the time required forthe oil detachment decreased as the temperature increased.

When we increased the temperature, the oil detachment acceler-ated due to the reduction in the oil/PNF interfacial tension and oilviscosity, which are the resistance forces for oil detachment. In addi-tion, the osmotic pressure of the PNF increases with the temperature[35], which means there is increase in the structural disjoining pres-sure. All of these factors accelerate the nanofluid spreading dynam-ics, so the spreading is enhanced at a higher temperature.

3.6. Modeling of the outer and inner contact line velocity andcomparison with measurement

3.6.1. Prediction of the outer contact line velocityWhen a liquid droplet is placed on a solid substrate, the unbal-

anced forces at the three-phase contact line drive spreading ordewetting of the liquid from the non-equilibrium shape to theequilibrium shape. Several studies related to a mechanism of the

Table 4Oil detachment time and inner contact line velocity using the 0.20 volume fraction ofthe PNF in water and in brine at 25 ± 1 �C.

PNF in water PNF in brine

IFT (mN/m) 17 ± 1.7 8.6 ± 0.3Oil detachment time (min) 1.5 ± 0.3 2.7 ± 0.3Inner contact line velocity (mm/min) 0.11 ± 0.02 0.084 ± 0.005

Table 5The IFT and oil detachment times from the glass substrate at 25, 35, and 50 �C usingthe 0.20 volume fraction of the PNF.

Temperature (�C) IFT (mN/m) Oil detachment time (min)

25 17 ± 1.7 80–11035 13 ± 0.4 54–7250 12 ± 0.4 22–32

spreading or dewetting of the liquid droplet (such as a pure liquid,surfactant solution, and nanofluid) have appeared in the literature[28,36–45]. In the classical approaches for a pure liquid, two typesof frictional forces for the outer contact line movement have beenproposed. The first one is the friction based on the hydrodynamicapproach which stems from the dissipation due to the viscousflows originating in the core of the droplet [37,38]. The other oneis the friction based on the molecular kinetics approach, whichconcentrates on the molecular energy dissipation in the vicinityof the three-phase contact line [36,39–43].

Recently, there has been a discussion in the literature about athird approach for elucidating a liquid’s wetting and dewettingthat focuses on the evaporation/condensation mechanism nearthe three-phase contact line [44,45]. According to this thirdapproach, the increased meniscus profile near the three- phasecontact line leads to the condensation of the liquid, resulting inthe additional spreading of the liquid.

In general, it was found that the molecular dissipation prevailswhen the contact angle is relatively large in the initial stages of thedroplet spreading and the hydrodynamic dissipation dominateswhen the contact angle is small when the liquid droplet is closeto equilibrium [41].

In the present analysis, we used Eq. (3) to consider frictionalforce [39,46] while analyzing the conventional outer contact linevelocity.

�dRdt

¼ 1fceqðcos heq � cos hdynÞ ð3Þ

where dR=dt is the outer contact line velocity, f is the frictional coef-ficient, ceq is the equilibrium oil/nanofluid interfacial tension, heq isthe equilibrium contact angle, and hdyn is the dynamic contact angle.This equation describes the outer contact line movement that isexerted by the out-of-balance surface tension force and resistedby the frictional force. Unfortunately, there is no independentmethod to directly measure the frictional coefficient.

In our study, we tried to estimate the frictional coefficient usingthe outer contact radius data with the three different volume frac-tions of the PNF (shown in Fig. 6).

First, we obtained the outer contact radius as a function of time,RðtÞ, for the volume fractions 0.15, 0.20, and 0.25 of the PNF. Sec-ond, we took the time derivative of the radius to obtain the expres-sion for the outer contact line velocity, dR=dt of each volumefraction as a function of time. Finally, since we knew the equilib-rium interfacial tension between the oil and polymeric nanofluid,the equilibrium contact angle, and dynamic contact angle from

S. Lim et al. / Journal of Colloid and Interface Science 470 (2016) 22–30 29

the side view during the oil detachment, we estimated the averagevalue of the frictional coefficient with the dR=dt values from thethree different experimental data using Eq. (3).

Fig. 8 shows the estimated frictional coefficients from the threedifferent experiments. Note that the estimated frictional coefficientis almost independent of the time and the volume fractions of thePNF. Based on the estimated data, the average value of the fric-tional coefficient is f ¼ 0:52� 0:15ð31:2� 4:7 Pa sÞ.

Using the average value of the frictional coefficient, we pre-dicted the outer contact line velocity of the nanofluids for three dif-ferent volume fractions with time and compared these results withexperimental data (shown in Fig. 9).

In Fig. 9, the calculated outer contact line velocity using Eq. (3)shows fair agreement with the experimental data for the volumefractions 0.15, 0.20, and 0.25 of the PNF. This result indicates thatthe conventional outer contact line movement is driven by theimbalance of the three surface forces; the contribution of the struc-tural disjoining pressure to the outer contact radius velocity isnegligible.

3.6.2. Prediction of the inner contact line velocityWe conducted a theoretical calculation based on the work done

by Trokhymchuk et al. [33] to estimate the structural disjoiningpressure, PðhÞ, for the 1st layer of nanoparticles. We used an accu-rate analytical expression to calculate the structural disjoiningpressure based on a solution of the Ornstein–Zernike equation(using the PY closure of the hard sphere model):

PðhÞ ¼ P0 cosðxhþu2Þe�jh þP1e�dðh�dÞ for h P d ð4Þwhere P0;P1;x;u2;j, and d are dependent parameters of the par-ticle volume fraction of nanoparticles, /, in the bulk fitted as cubicpolynomials and d is the diameter of the nanoparticles. The polyno-mial expression for the parameters is given in Ref. [32]. The struc-tural disjoining pressure was calculated with a known diameter ofthe nanoparticles and the volume fraction of the nanoparticles withEq. (4). With consideration to the structural disjoining pressure’sability to advance the inner contact line’s movement, Liu et al.[28] developed a semi-empirical expression for calculating theinner contact line velocity of the nanofluid as a function of thenanoparticle size and volume fraction (described in Eq. (5)).

Vc

mm=min¼ 24;605

/

ðd=nmÞ1:105� 1268

ðd=nmÞ2� 50ðd=nmÞþ7:5607

( )224

35

60e3ceqlf

ð5Þ

Time (min)0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

Out

er c

onta

ct li

ne v

eloc

ity (m

m/m

in) -14

-12

-10

-8

-6

-4

-2

0

0.15 PNF0.20 PNF0.25 PNFModel prediction 0.15 PNFModel prediction 0.20 PNFModel prediction 0.25 PNF

Fig. 9. Comparison of the outer contact line velocity calculated from the modelwith the experimental measured values at different PNF volume fractions (square:0.15, triangle: 0.20, and circle: 0.25).

where Vc is the inner contact line velocity, / is the nanoparticle vol-ume fraction, d is the diameter of the nanoparticle, e is the filmaspect ratio which is defined as e ¼ H=L;H is the thickness of thefilm, L is the length of the film, and lf is the nanofluid film viscosity.This equation is valid when the structural force dominates the cap-illary force. Eq. (5) can be explained in the following manner. Theterm related to the nanoparticle size and volume fraction in Eq.(5) comes from the structural force of the nanoparticles in thewedge film. It is a driving force term with respect to the enhancednanofluid spreading. The term related to the film viscosity plays arole as a resistant force, that is, a high film viscosity prevents theenhanced movement of the contact line.

Liu et al. [28] also provided an expression to estimate the filmviscosity as a function of the nanoparticle volume fraction usingthe Frenkel equation [47] considering the energy barrier betweentwo adjacent nanoparticles. We followed the same procedure andobtained the film viscosity expression of the PNF, shown in Eq.(6). The detailed procedures to achieve the film viscosity expres-sion are described in Ref. [28].

lf ¼ 16:3 � expð26:2/3:93e Þ ð6Þ

In order to evaluate the inner contact line velocity, we neededto determine the film aspect ratio, e. In our previous study, an arbi-trary value for the film aspect ratio was selected (e = 0.01) to esti-mate the inner contact line velocity. As a result, the film viscosityof the nanofluids was overestimated (�300 cp) [28]. In our presentanalysis, instead of using an arbitrary value for e, we selected thelength of the nanofluidic film, L based on the film size from thetop view in the experiment; its value is around 0.12 mm(L ffi 0.12 mm). The height of the film, H was assumed based onthe one layer of the nanoparticles combined with double layerthickness of the glass substrate at a neutral pH [48]: H ffi 285 lm.Thus, we chose e ffi 0.00237 as the film aspect ratio to calculatethe inner contact line velocity using Eq. (5) and compared it tothe experimental data for the three different volume fractions ofthe PNF shown in Fig. 6. The calculated structural disjoining pres-sure, inner contact line velocity, and film viscosity with a knownnanoparticle size, volume fraction, and the experimentally mea-sured velocity are summarized in Table 6.

Table 6 clearly shows that the inner contact line movementadvances with increasing volume fraction of the PNP, which exertsa higher structural disjoining pressure. The calculated velocityfrom Eq. (4) agrees fairly well with the experimentally measuredvalue. As we expected, the model predicts that the inner contactline velocity increases with the increase of the nanoparticle vol-ume fraction. The calculated film viscosity also increases withthe increased nanoparticle volume fraction from 0.15 to 0.25, indi-cating that the contribution of the resistance force due to the filmviscosity is insignificant for the concentration range used in ourexperiment. Therefore, we can conclude that the increase in theinner contact line velocity is mainly due to the increase of thenanofluid structural force with the increasing nanofluidconcentration.

Table 6The summarized table of the calculated structural disjoining pressure using Eq. (4),film viscosity using Eq. (6), inner contact line velocity using Eq. (5), and theexperimentally measured velocity.

Volumefractionof PNP

Structuraldisjoiningpressure (Pa)

Filmviscosity(cp)

Velocitymodelprediction(mm/min)

Velocityexperimentalmeasurement(mm/min)

0.15 5001 16.5 0.036 0.052 ± 0.0110.20 16,325 17.1 0.113 0.11 ± 0.020.25 70,252 18.3 0.170 0.14 ± 0.01

30 S. Lim et al. / Journal of Colloid and Interface Science 470 (2016) 22–30

4. Conclusions

This paper is a continuation of our previous studies on thespreading of nanofluids on solid substrates. The present study isspecifically aimed at elucidating the effects of several parameterson the motion of the inner and outer contact lines such as thenanofluid concentration, temperature, salinity, hydrophilicity ofthe substrate, drying time of the substrate, and oil adhesion timeon the substrate. The conclusions of this study can be summarizedas follows:

1. The increase in the nanoparticle volume fraction, temperature,and hydrophilicity of the substrate accelerates the motion ofthe inner contact line.

2. The salinity has an adverse effect on the spreading dynamics bydecreasing the osmotic pressure of the nanofluid.

3. The motion of the outer contact line also decreases upon theincrease in the drying time and oil adhesion time on thesubstrate.

4. The velocity of the inner contact line is faster for the non-equilibrated system than for the pre-equilibrated oil/nanofluidsystem.

5. The molecular kinetic theory model prediction for the outercontact line agrees fairly well with the experimentally mea-sured values.

6. Our previous theoretical analysis based on the structural dis-joining pressure predicts the measured values of the inner con-tact line velocity fairly well.

7. The time of the oil drop detachment from the solid substratedecreases upon the increase in the nanoparticle volume frac-tion, temperature, and hydrophilicity of the solid substrate.However, the time of detachment increases upon the increasein the salinity of the nanofluid, drying time, and oil adhesiontime on the substrate.

In conclusion, a systematic study of these and other parametersis warranted to further establish the effects of these parameters onthe spreading dynamics of the nanofluid on the solid substrate.

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