Spreading of liquid drops over solid substrates like wets like- Eng.Bashar Sasa

J. Adhesion Sci. Technol., Vol. 20, No. 12, pp. 1333–1343 (2006) VSP 2006.Also available online - www.brill.nl/jast

Spreading of liquid drops over solid substrates:‘like wets like’

ABDULLATIF M. ALTERAIFI ∗ and BASHAR J. SASADepartment of Mechanical Engineering, UAE University, P.O. Box 17555, Al-Ain, United ArabEmirates

Received in final form 3 July 2006

Abstract—The classic hydrodynamic wetting theory leads to a linear relationship between spreadingspeed and the capillary force, being determined only by the surface tension of the liquid and itsviscosity. Both equilibrium and dynamic processes of wetting are important in adhesion phenomena.The theory appears to be in good agreement with the results generated from experiments conducted onthe spreading of poly(dimethylsiloxane) (PDMS) on soda-lime glass substrate and fails to account forthe behavior of other liquids. In this study, the spreading kinetics of four different liquids (hexadecane,undecane, glycerol and water) was determined on three different solids, namely, soda-lime glass,poly(methyl methacrylate) (PMMA) and polystyrene (PS). Droplets from the same liquid allowed tospread under identical conditions on three different substrates produce distinctly different behaviors.The results show that the equilibrium contact angles are qualitatively ranked in accordance with thecritical surface tension of wetting (γc) of the respective solid, i.e., high-γc solids caused the low surfacetension liquids to assume the least equilibrium spreading (largest contact angle). On the other end,low-γc solids with the lowest surface tension liquid produce the most wetting (smallest contact angle).The results suggest that equilibrium spreading could be explained on the basis of the axiom ‘like wetslike’; in other words, polar surfaces tend to be wetted by polar liquids and vice versa.

Keywords: Droplet; spreading kinetics; surface tension; partial wetting.

1. INTRODUCTION

Spontaneous spreading of liquids over solid surfaces (‘wetting’) is unquestionablyan important phenomenon, which is associated with several important technologies,such as coating and adhesion. Both equilibrium and dynamic processes of wettingare essential in these technologies. Moreover, wetting is a fundamental prerequisitefor several applications; for example, in paint films, composites, adhesives, paper

∗To whom correspondence should be addressed. Tel.: (971-50) 631-2100. Fax: (971-3) 762-3158.E-mail: [email protected]

1334 A. M. Alteraifi and B. J. Sasa

manufacture, printing, fiber manufacture, pharmaceutical tablets, cosmetics, deter-gency, water purification and oil recovery. In addition, it is important in a number ofbiological applications, e.g., cell separation, cell adhesion and attachment, bacterialadhesion to tooth surfaces, marine fouling and phagocytosis.

Attempts to model the spreading kinetics have been pursued through variousscientific disciplines, most prominent of which being physical chemistry and fluiddynamics. Recent reviews of the literature on spreading dynamics by Marmur [1],de Gennes [2] and several other contributors to a more recent book edited by Berg[3] attest to the continual interest in the subject.

Several theories deal with the spreading kinetics of liquids on solid substrates,most of which relate the rate of spreading to the surface tension, and the viscosityof the liquid only. De Gennes’ model [2], Tanner’s model [4] and that proposedby Seaver and Berg [5] expressed the rate of spreading in terms of surfacetension and viscosity. Nevertheless, surface tension and viscosity are propertiesof the spreading liquid, whereas spreading of liquids on solids is an interfacialphenomenon involving all three interfacial tensions, i.e., liquid–vapor (surfacetension), solid–vapor and solid–liquid. Indeed Young’s equation describes a systemof interfaces in terms of three interfacial tensions. The present theory, in general,appears to be in good agreement with the results obtained from experimentsconducted on the spreading of poly(dimethylsiloxane) (PDMS) over soda-limeglass substrate and fails to account for the behavior of other liquids or spreadingon other solids. The phenomenon essentially entails solid–liquid and solid–vaporinteractions, which suggests that their role should be explored.

The molecular kinetic theory was earlier proposed by Blake and Haynes [6]. Theyassumed that the leading contribution to the dissipation during spreading was dueto the adsorption and desorption of molecules within the three-phase zone near thewetting line. According to Blake and Haynes [6], the velocity of the wetting lineis then characterized by K , the frequency of molecular displacements, and λ, thetypical length of each molecular displacement. They have established a relationshipbetween the equilibrium contact angle and the velocity of the wetting line.

The evidence in the literature suggests that the solid substrate plays a key rolein spreading kinetics. For example, it was noted that PDMS droplets exhibitedspreading kinetics on soda-lime glass that was very different from that on Teflon [7].Also in Hoffman’s experiments [8] PDMS was found to spread readily on the glasssurface, unlike the two other liquids, ‘Admix-760’ and ‘Santicizer-405’ (AshlandChemical, Dublin, OH, USA). To induce these liquids ‘to give a large staticcontact angle as desired’, the glass surface was altered by a vigorous chemical andthermal treatment. These experimental evidences suggest that solids indeed play animportant role in the spreading kinetics of a liquid. This role is in fact describedin Young’s equation in term of the solid–liquid interfacial tension. This arises fromthe molecular interaction between liquids and solids.

This paper examines the role played by the solid substrate in the equilibriumspreading of liquid droplets. The set of experiments in this study used different

Spreading of liquid drops over solid substrates 1335

types of liquids with different surface tension and viscosity values on three differentsolid substrates (glass, poly(methyl methacrylate) (PMMA) and polystyrene (PS)).

2. EXPERIMENTAL

2.1. Materials

The experimental setup is shown in Fig. 1. To conduct the experiment, the liquidwas charged into a 5.0-µl syringe (SGE International, Australia). The syringe wasattached to a metal stand and suspended vertically by a micromanipulator on top ofthe glass slide. The micromanipulator was used to adjust the position of the needletip of the syringe carefully above the clean glass slide. The tip of the syringe waspositioned a few micrometers from the surface of the glass to eliminate impact effectwhen the droplet was released. The droplet volume was selected to be 1.5 µl so,that gravity effect was negligible [9].

The solid substrate was placed on an optical stand within the focus of a half-inch CCD digital video camera (JVC TK-c1380, Japan), with 10× eyepiecemagnification, placed underneath the glass slide. The camera was connected to avideo recorder, which, in turn, was connected to an image analysis system (AnalysisSoft Imaging System, Germany). Each data point represents an average value of atleast ten measurements. The standard deviation calculated for each data point wasfound to be less than 6%. All experiments were carried out at ambient conditions,i.e., 25 ± 1◦C and 47 ± 3% RH.

Figure 1. Sketch of the experimental setup for contact area measurements.


Table 1.List of liquids used and their viscosity µ, and surface tension γ

Liquid µ (cP) γ (mN/m)

Undecane 1.1 29.0Hexadecane 3.1 32.1Glycerol 954 67.6Water 0.9 72.2

The viscosity data were obtained from [10].

Table 2.Solid surfaces used and their γc values [12]

Solid γc (mN/m)

Soda-lime glass 70Poly(methyl methacrylate) (PMMA) 39Polystyrene (PS) 33

2.1.1. Liquids. Table 1 lists the liquids used in the study. All were chemicalgrade liquids obtained from Fluka (Buchs, Switzerland). Deionized water with aresistivity of 18.2 M�/cm was used in the study. As seen from the table, the surfacetension values ranged from 29.0 mN/m to 72.2 mN/m. Surface tension values weremeasured with the torsion balance technique using a device obtained from WhiteElectrical Instruments (London, UK). The measurement accuracy ranged within0.5% error, and verified with published results in the literature [10]. The viscosityvalues ranged from 0.9 cP to 954 cP [10].

2.1.2. Solids. Table 2 lists the solids used in the study: soda-lime glass,poly(methyl methacrylate) (PMMA) and polystyrene (PS). The critical surfacetension (γc) values ranged from 33 mN/m to 70 mN/m. The γc values were obtainedusing the Zisman approach [11] using a series of non-polar and non-volatile liquids,and were in agreement with published results in the literature [12].

The dry soda-lime glass slides (26 × 26 mm) (Menzel-Glaser, Geschnitten,Germany) were cleaned by immersing in chromic acid solution for 4 h followedby a thorough rinsing with distilled water and were further cleaned with acetone(99.5% purity, Panreac, Barcelona, Spain). The clean slides were subsequentlydried in a vacuum oven at 70◦C for 30 min, at the end of which the slides wereallowed to cool under vacuum. Subsequently, the slides were carefully transferredto a desiccator, where they were stored until used. Each cleaned, dried glass slidewas used only once. The effectiveness of cleaning and drying procedures on thecleanliness of glass surface morphology was assured by examining the slides beforeand after cleaning using a Scanning Electron Microscope (Jeol JSM5600, Japan)at 5000× magnification. The quality of surface roughness and heterogeneity wasinspected by measuring contact angle hysteresis on cleaned soda-lime glass surface.


The contact angle hysteresis was determined by taking the difference between theadvancing and the receding contact angles values. For water on soda-lime glasssurfaces, the measured contact angle hysteresis was found to be 6–7◦. PMMAslides were obtained from a commercial source. PMMA slides were immersed inethanol for 2 h. The slides were rubbed gently with a soft sponge to get rid ofadhesive layer. Subsequently, the slides were rinsed with DI water and immersedin DI H2O for at least 5 min. Finally, the slides were allowed to dry in fresh airjust before the start of the experiment. The effectiveness of the cleaning procedureson the cleanliness of the PMMA surface was assured by examining sample slidesbefore and after cleaning using SEM at 5000× magnification. The quality of surfaceroughness and heterogeneity was determined by measuring contact angle hysteresison cleaned PMMA surface. The measured contact angle hysteresis for water onPMMA surfaces was approximately 7◦.

A clean lab sheet of polystyrene obtained from Barloworld Scientific (Stafford-shire, UK) was used in this study. Sheets were examined under an SEM to makesure that the surfaces were free from any residues and were smooth. The measuredcontact angle hysteresis for water on polystyrene surfaces was approximately 6◦. Itshould be pointed out that although the solid surfaces used in this study were verysmooth, they may still have a very small percentage of chemical heterogeneity prob-ably due to contamination from the coating material or dust in the air. This mightbe the cause for the observed contact angle hysteresis.

2.2. Measurements and analysis

The experimental measurements were based on liquid/solid contact area. Thecontact area is the printout of experimental measurements for the liquid dropover solid substrate for different time intervals. The image analysis system wasinitially calibrated by measuring the distance between the lines of a recorded stagemicrometer. The images (frames) were grabbed by the image analyzer from whichthe contact area was digitized and measured as a function of time.

3. RESULTS AND DISCUSSION

Before discussing the experimental results obtained, it is important to ascertainthat droplet volume was conserved and thus evaporation losses were negligible.Additionally, gravitational forces should be considered.

For incompressible liquids, the conservation of volume for the duration of theexperiment was verified using the following equation, which is based on sphericalcap approximation:

R3θ = R3f θf, (1)

where Rf and θf are the final equilibrium contact radius and final equilibrium contactangle, respectively. Figure 2 shows cosine of the contact angle which is obtained


Figure 2. Cosine of contact angles for the liquids used in this study plotted in terms of equation (1)to verify that evaporation losses are negligible during the experiment.

using spherical cap approximation plotted versus cos(R3f θf/R

3), which is measuredexperimentally. A straight line with a slope of unity demonstrates clearly thatvolume of the droplet for all liquids was conserved at least for the duration of theexperiment and that evaporation losses were indeed negligible.

The importance of gravity relative to capillary forces was inspected using theBond number, Bo [13]:

Bo = ρgR2o

γ, (2)

where g is the gravity acceleration, Ro is the radius of the spherical droplet beforespreading and ρ is the liquid density. The Bond number was found in the rangebetween 0.115 and 0.362 for the liquids used in this study. Since Bo < 1, capillaryforces were expected to dominate gravity. The hydrodynamic theory is valid whenthe surface tension and viscous forces are dominant, as it basically considers thatthe capillary driving forces are compensated by the viscous damping forces. In thisstudy, the inertia effects were negligible because of the low values of both Reynoldsnumber and Weber number.

First we examine the spreading kinetics of low surface tension liquids on the threesolid substrates. Hexadecane and undecane were selected for their relatively lowsurface tension values of 32.1 and 29.0 mN/m, respectively. In addition, hexadecaneand undecane have a non-polar character and are known to exhibit incompletespreading on soda-lime glass [14]. Figures 3 and 4 show the spreading kineticsof these liquids on the three solids.


Figure 3. Typical data for hexadecane spreading on glass, PMMA and PS.

Figure 4. Typical data for undecane spreading on glass, PMMA and PS.


Table 3.Contact areas (cm2) and contact angle values (degrees) for hexadecane and undecane (low surfacetension liquids) on glass, PMMA and PS

Liquid Solid Contact Contact Tanner’s R2

area angle constant C

(cm2) (equation (3))

Hexadecane Glass 0.081 23.9 0.131 0.992PMMA 0.141 11.5 0.164 0.996PS 0.205 6.5 0.187 0.997

Undecane Glass 0.272 4.3 0.210 0.996PMMA 0.385 2.6 0.244 0.966PS 0.407 2.4 0.263 0.976

The major attribute characterizing the spreading process is the equilibrium contactarea. Noting that a constant volume droplet (1.5 µl) was used in all experiments, theequilibrium contact area may be taken as a measure of wettability. The macroscopicshape of the spreading droplet may be approximated by spherical cap geometry [2].This approximation has been used to relate the contact angle to the radius and thevolume of the spreading droplet, i.e., the droplet height h = 0.5Rθ and its volumeV = 0.5πhR2. Accordingly, it is also possible to calculate the correspondingcontact angle based on the spherical cap relationship, i.e.,

θ = 4V/πR3, (3)

where V is the droplet volume and R is the radius of the contact area. Estimatesof the equilibrium contact area drawn from Fig. 3 for hexadecane and Fig. 4 forundecane and the corresponding contact angles are summarized in Table 3.

Several theoretical models [2, 4, 5] which describe the spreading of PDMS onsoda-lime glass substrate are found to be in good agreement with the experimentalmeasurements. These models which are derived on basis of different theoreticalconsiderations give rise to closely similar results, in what appears to be the powerlaw relation [14]. Considering the most commonly referenced model, Tanner’s lawdescribed the kinetic data in terms of the power law relation. The law is based onhydrodynamic considerations accounting for the surface tension γ and the viscosityµ of the liquid [4]. Tanner’s law:

θ3D = C

Uµ

γ, (4)

where θD is the dynamic contact angle, U is the interline velocity and C is a non-dimensional parameter that has to be determined empirically, was first formulatedto describe the case in which equilibrium contact angle of liquids against the solidwas zero. This led to a spreading law of the form:

R = Ct0.1. (5)


Figure 5. Typical data for glycerol spreading on glass, PMMA and PS.

Later modification, however, to account for the effect of the solid substrate underconditions of partial wetting, led to a shifted Tanner’s law, of the form:

θ3D − θ3

f = CUµ

γ, (6)

where θf is the final equilibrium contact angle. Tanner’s constants C for thespreading of hexadecane and undecane (Figs 3 and 4) are listed in Table 3. Theexperimental values of C are in agreement with Tanner’s theory (R2 > 0.966).

Different contributions of different solid substrates to the wetting process areevident. Equal droplets from the same liquid allowed to spread under identicalconditions on three different substrates produce distinctly different behaviors.

Expectedly, the equilibrium contact angles (Table 3) may be qualitatively rankedin accordance with the critical surface tension of wetting (γc) of each respectivesolid. Glass caused hexadecane and undecane to assume the least equilibriumspreading (largest contact angle). On the other end, PS, with the lowest γc, producedthe most wetting (smallest contact angle). PMMA produced an intermediate effect.It is useful to bear in mind that hexadecane and undecane are non-polar, lowsurface tension liquids as is the case with polystyrene. Therefore, it is reasonableto introduce the axiom ‘like wets like’ to rationalize the equilibrium wetting ofhexadecane and undecane on the three solids. This axiom is coined in analogy tothe famous rule ‘like dissolves like’ in physical chemistry.

Secondly, we examine the spreading behaviors of glycerol and water on soda-lime glass, PMMA, and PS, which are shown in Figs 5 and 6. These two liquids


Figure 6. Typical data for water spreading on glass, PMMA and PS.

Table 4.Contact areas (cm2) and contact angle values (degrees) for glycerol and water (high surface tensionliquids) on glass, PMMA and PS

Liquid Solid Contact Contact Tanner’s R2

area angle constant C

(cm2) (equation (3))

Glycerol Glass 0.086 26.5 0.104 0.968PMMA 0.042 70.6 0.082 0.964PS 0.032 104.5 0.071 0.963

Water Glass 0.076 29.3 0.110 0.967PMMA 0.049 55.8 0.093 0.977PS 0.036 88.2 0.078 0.982

have high surface tension of 67.6 and 72.2 mN/m, respectively. Estimates of theequilibrium contact area derived from Fig. 5 for glycerol and Fig. 6 for water and thecorresponding contact angle values are summarized in Table 4. Tanner’s constants C

for the spreading of glycerol and water (Figs 5 and 6) are listed in Table 4. Hence,for the determined values of C, the experimental measurements are in agreementwith Tanner’s theory (R2 > 0.963).

Noting that glycerol and water are relatively high surface tension liquids, theaxiom ‘like wets like’ appears to rationalize qualitatively the equilibrium spreadingof glycerol and water on the same set of solid substrates. The largest equilibrium


spreading (smallest contact angle) was noted on glass, the least on PS and on PMMAit was intermediate.

Hexadecane and undecane, low surface tension liquids, were found to exhibitequilibrium wetting that was proportional to the γc of the solid substrate. Glyceroland water, high surface tension liquids, were found to exhibit equilibrium wettingthat was inversely proportional to the γc of the solids. These observations are relatedto Young’s equation, where

cos θ = (γSV − γSL)/γLV, (7)

provided that γSV is somehow related to Zisman’s γc (the critical surface tension ofwetting). In a pragmatic sense, ‘like wets like’ seems to work.

4. CONCLUSIONS

The present investigation provides experimental evidence that the solid substrateplays a significant role in determining equilibrium contact angle. Results show thathexadecane and undecane, low surface tension liquids, exhibit equilibrium wettingthat is proportional to the γc of the solid substrate. Similarly, glycerol and water,high surface tension liquids, were found to exhibit equilibrium wetting that wasinversely proportional to the γc of the solids. Therefore, the axiom ‘like wets like’appears to rationalize the equilibrium wetting of both types of liquids on all threesolids used.

REFERENCES

1. A. Marmur, Adv. Colloid Interface Sci. 19, 75–102 (1983).2. P. G. de Gennes, Rev. Modern Phys. 57, 827–863 (1985).3. J. C. Berg (Ed.), Wettability. Marcel Dekker, New York, NY (1993).4. L. H. Tanner, J. Phys. D. 12, 1473–1484 (1979).5. A. Seaver and J. Berg, J. Appl. Polym. Sci. 52, 431–435 (1994).6. T. D. Blake and J. M. Haynes, J. Colloid Interface Sci. 30, 421–423 (1969).7. V. A. Ogarev, T. N. Timonina, V. V. Arslanov and A. A. Trapeznikov, J. Adhesion. 6, 337–355

(1974).8. R. L. Hoffman, J. Colloid Interface Sci. 50, 228–241 (1975).9. A. M. Cazabat, Contemp. Phys. 28, 347–364 (1987).

10. R. Reid, J. Prausnitz and B. Poling, The Properties of Gases and Liquids, 4th edn. McGraw-Hill,New York, NY (1987).

11. W. Zisman, Adv. Chem. 43, 1 (1964).12. D. Myers, Surfaces, Interfaces, and Colloids. Wiley, New York, NY (1999).13. C. W. Extrand, J. Colloid Interface Sci. 157, 72–76 (1993).14. A. M. Alteraifi, D. Sherif and A. Moet, J. Colloid Interface Sci. 264, 221–227 (2003).

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Spreading of liquid drops over solid substrates like wets like- Eng.Bashar Sasa