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

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J. Adhesion Sci. Technol., Vol. 20, No.12, pp. 1333-1343 (2006) …

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

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  • 1. 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. SASA Department of Mechanical Engineering, UAE University, P.O. Box 17555, Al-Ain, United Arab Emirates Received in final form 3 July 2006 Abstract—The classic hydrodynamic wetting theory leads to a linear relationship between spreading speed and the capillary force, being determined only by the surface tension of the liquid and its viscosity. 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 on the spreading of poly(dimethylsiloxane) (PDMS) on soda-lime glass substrate and fails to account for the 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 to spread 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 the critical surface tension of wetting (γc) of the respective solid, i.e., high-γc solids caused the low surface tension 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 wets like’; 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 unquestionably an important phenomenon, which is associated with several important technologies, such as coating and adhesion. Both equilibrium and dynamic processes of wetting are essential in these technologies. Moreover, wetting is a fundamental prerequisite for 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: alshamsi@uaeu.ac.ae
  • 2. 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 of biological applications, e.g., cell separation, cell adhesion and attachment, bacterial adhesion to tooth surfaces, marine fouling and phagocytosis. Attempts to model the spreading kinetics have been pursued through various scientific disciplines, most prominent of which being physical chemistry and fluid dynamics. 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 viscosity of the liquid only. De Gennes’ model [2], Tanner’s model [4] and that proposed by Seaver and Berg [5] expressed the rate of spreading in terms of surface tension and viscosity. Nevertheless, surface tension and viscosity are properties of the spreading liquid, whereas spreading of liquids on solids is an interfacial phenomenon involving all three interfacial tensions, i.e., liquid–vapor (surface tension), solid–vapor and solid–liquid. Indeed Young’s equation describes a system of interfaces in terms of three interfacial tensions. The present theory, in general, appears to be in good agreement with the results obtained from experiments conducted on the spreading of poly(dimethylsiloxane) (PDMS) over soda-lime glass substrate and fails to account for the behavior of other liquids or spreading on other solids. The phenomenon essentially entails solid–liquid and solid–vapor interactions, which suggests that their role should be explored. The molecular kinetic theory was earlier proposed by Blake and Haynes [6]. They assumed that the leading contribution to the dissipation during spreading was due to the adsorption and desorption of molecules within the three-phase zone near the wetting line. According to Blake and Haynes [6], the velocity of the wetting line is then characterized by K, the frequency of molecular displacements, and λ, the typical length of each molecular displacement. They have established a relationship between the equilibrium contact angle and the velocity of the wetting line. The evidence in the literature suggests that the solid substrate plays a key role in spreading kinetics. For example, it was noted that PDMS droplets exhibited spreading 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 glass surface, unlike the two other liquids, ‘Admix-760’ and ‘Santicizer-405’ (Ashland Chemical, Dublin, OH, USA). To induce these liquids ‘to give a large static contact angle as desired’, the glass surface was altered by a vigorous chemical and thermal treatment. These experimental evidences suggest that solids indeed play an important role in the spreading kinetics of a liquid. This role is in fact described in Young’s equation in term of the solid–liquid interfacial tension. This arises from the molecular interaction between liquids and solids. This paper examines the role played by the solid substrate in the equilibrium spreading of liquid droplets. The set of experiments in this study used different
  • 3. Spreading of liquid drops over solid substrates 1335 types of liquids with different surface tension and viscosity values on three different solid 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 liquid was charged into a 5.0-µl syringe (SGE International, Australia). The syringe was attached to a metal stand and suspended vertically by a micromanipulator on top of the glass slide. The micromanipulator was used to adjust the position of the needle tip of the syringe carefully above the clean glass slide. The tip of the syringe was positioned a few micrometers from the surface of the glass to eliminate impact effect when 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× eyepiece magnification, placed underneath the glass slide. The camera was connected to a video recorder, which, in turn, was connected to an image analysis system (Analysis Soft Imaging System, Germany). Each data point represents an average value of at least ten measurements. The standard deviation calculated for each data point was found 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.
  • 4. 1336 A. M. Alteraifi and B. J. Sasa Table 1. List of liquids used and their viscosity µ, and surface tension γ Liquid µ (cP) γ (mN/m) Undecane 1.1 29.0 Hexadecane 3.1 32.1 Glycerol 954 67.6 Water 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 70 Poly(methyl methacrylate) (PMMA) 39 Polystyrene (PS) 33 2.1.1. Liquids. Table 1 lists the liquids used in the study. All were chemical grade liquids obtained from Fluka (Buchs, Switzerland). Deionized water with a resistivity of 18.2 M /cm was used in the study. As seen from the table, the surface tension values ranged from 29.0 mN/m to 72.2 mN/m. Surface tension values were measured with the torsion balance technique using a device obtained from White Electrical Instruments (London, UK). The measurement accuracy ranged within 0.5% error, and verified with published results in the literature [10]. The viscosity values 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 surface tension (γc) values ranged from 33 mN/m to 70 mN/m. The γc values were obtained using 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 followed by a thorough rinsing with distilled water and were further cleaned with acetone (99.5% purity, Panreac, Barcelona, Spain). The clean slides were subsequently dried in a vacuum oven at 70◦ C for 30 min, at the end of which the slides were allowed to cool under vacuum. Subsequently, the slides were carefully transferred to a desiccator, where they were stored until used. Each cleaned, dried glass slide was used only once. The effectiveness of cleaning and drying procedures on the cleanliness of glass surface morphology was assured by examining the slides before and after cleaning using a Scanning Electron Microscope (Jeol JSM5600, Japan) at 5000× magnification. The quality of surface roughness and heterogeneity was inspected by measuring contact angle hysteresis on cleaned soda-lime glass surface.
  • 5. Spreading of liquid drops over solid substrates 1337 The contact angle hysteresis was determined by taking the difference between the advancing and the receding contact angles values. For water on soda-lime glass surfaces, the measured contact angle hysteresis was found to be 6–7◦ . PMMA slides were obtained from a commercial source. PMMA slides were immersed in ethanol for 2 h. The slides were rubbed gently with a soft sponge to get rid of adhesive layer. Subsequently, the slides were rinsed with DI water and immersed in DI H2O for at least 5 min. Finally, the slides were allowed to dry in fresh air just before the start of the experiment. The effectiveness of the cleaning procedures on the cleanliness of the PMMA surface was assured by examining sample slides before and after cleaning using SEM at 5000× magnification. The quality of surface roughness and heterogeneity was determined by measuring contact angle hysteresis on cleaned PMMA surface. The measured contact angle hysteresis for water on PMMA 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 make sure that the surfaces were free from any residues and were smooth. The measured contact angle hysteresis for water on polystyrene surfaces was approximately 6◦ . It should be pointed out that although the solid surfaces used in this study were very smooth, 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 might be the cause for the observed contact angle hysteresis. 2.2. Measurements and analysis The experimental measurements were based on liquid/solid contact area. The contact area is the printout of experimental measurements for the liquid drop over solid substrate for different time intervals. The image analysis system was initially calibrated by measuring the distance between the lines of a recorded stage micrometer. The images (frames) were grabbed by the image analyzer from which the 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 ascertain that 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 the experiment was verified using the following equation, which is based on spherical cap approximation: R3 θ = R3 f θf, (1) where Rf and θf are the final equilibrium contact radius and final equilibrium contact angle, respectively. Figure 2 shows cosine of the contact angle which is obtained
  • 6. 1338 A. M. Alteraifi and B. J. Sasa 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(R3 f θf/R3 ), which is measured experimentally. A straight line with a slope of unity demonstrates clearly that volume of the droplet for all liquids was conserved at least for the duration of the experiment and that evaporation losses were indeed negligible. The importance of gravity relative to capillary forces was inspected using the Bond number, Bo [13]: Bo = ρgR2 o γ , (2) where g is the gravity acceleration, Ro is the radius of the spherical droplet before spreading and ρ is the liquid density. The Bond number was found in the range between 0.115 and 0.362 for the liquids used in this study. Since Bo < 1, capillary forces were expected to dominate gravity. The hydrodynamic theory is valid when the surface tension and viscous forces are dominant, as it basically considers that the capillary driving forces are compensated by the viscous damping forces. In this study, the inertia effects were negligible because of the low values of both Reynolds number and Weber number. First we examine the spreading kinetics of low surface tension liquids on the three solid substrates. Hexadecane and undecane were selected for their relatively low surface tension values of 32.1 and 29.0 mN/m, respectively. In addition, hexadecane and undecane have a non-polar character and are known to exhibit incomplete spreading on soda-lime glass [14]. Figures 3 and 4 show the spreading kinetics of these liquids on the three solids.
  • 7. Spreading of liquid drops over solid substrates 1339 Figure 3. Typical data for hexadecane spreading on glass, PMMA and PS. Figure 4. Typical data for undecane spreading on glass, PMMA and PS.
  • 8. 1340 A. M. Alteraifi and B. J. Sasa Table 3. Contact areas (cm2) and contact angle values (degrees) for hexadecane and undecane (low surface tension 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 0.992 PMMA 0.141 11.5 0.164 0.996 PS 0.205 6.5 0.187 0.997 Undecane Glass 0.272 4.3 0.210 0.996 PMMA 0.385 2.6 0.244 0.966 PS 0.407 2.4 0.263 0.976 The major attribute characterizing the spreading process is the equilibrium contact area. Noting that a constant volume droplet (1.5 µl) was used in all experiments, the equilibrium contact area may be taken as a measure of wettability. The macroscopic shape 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 the volume of the spreading droplet, i.e., the droplet height h = 0.5Rθ and its volume V = 0.5πhR2 . Accordingly, it is also possible to calculate the corresponding contact 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. Estimates of the equilibrium contact area drawn from Fig. 3 for hexadecane and Fig. 4 for undecane and the corresponding contact angles are summarized in Table 3. Several theoretical models [2, 4, 5] which describe the spreading of PDMS on soda-lime glass substrate are found to be in good agreement with the experimental measurements. These models which are derived on basis of different theoretical considerations give rise to closely similar results, in what appears to be the power law relation [14]. Considering the most commonly referenced model, Tanner’s law described the kinetic data in terms of the power law relation. The law is based on hydrodynamic considerations accounting for the surface tension γ and the viscosity µ of the liquid [4]. Tanner’s law: θ3 D = 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 formulated to describe the case in which equilibrium contact angle of liquids against the solid was zero. This led to a spreading law of the form: R = Ct0.1 . (5)
  • 9. Spreading of liquid drops over solid substrates 1341 Figure 5. Typical data for glycerol spreading on glass, PMMA and PS. Later modification, however, to account for the effect of the solid substrate under conditions of partial wetting, led to a shifted Tanner’s law, of the form: θ3 D − θ3 f = C Uµ γ , (6) where θf is the final equilibrium contact angle. Tanner’s constants C for the spreading of hexadecane and undecane (Figs 3 and 4) are listed in Table 3. The experimental values of C are in agreement with Tanner’s theory (R2 > 0.966). Different contributions of different solid substrates to the wetting process are evident. Equal droplets from the same liquid allowed to spread under identical conditions on three different substrates produce distinctly different behaviors. Expectedly, the equilibrium contact angles (Table 3) may be qualitatively ranked in accordance with the critical surface tension of wetting (γc) of each respective solid. Glass caused hexadecane and undecane to assume the least equilibrium spreading (largest contact angle). On the other end, PS, with the lowest γc, produced the most wetting (smallest contact angle). PMMA produced an intermediate effect. It is useful to bear in mind that hexadecane and undecane are non-polar, low surface tension liquids as is the case with polystyrene. Therefore, it is reasonable to introduce the axiom ‘like wets like’ to rationalize the equilibrium wetting of hexadecane and undecane on the three solids. This axiom is coined in analogy to the 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
  • 10. 1342 A. M. Alteraifi and B. J. Sasa 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 tension liquids) 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 0.968 PMMA 0.042 70.6 0.082 0.964 PS 0.032 104.5 0.071 0.963 Water Glass 0.076 29.3 0.110 0.967 PMMA 0.049 55.8 0.093 0.977 PS 0.036 88.2 0.078 0.982 have high surface tension of 67.6 and 72.2 mN/m, respectively. Estimates of the equilibrium contact area derived from Fig. 5 for glycerol and Fig. 6 for water and the corresponding 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 agreement with Tanner’s theory (R2 > 0.963). Noting that glycerol and water are relatively high surface tension liquids, the axiom ‘like wets like’ appears to rationalize qualitatively the equilibrium spreading of glycerol and water on the same set of solid substrates. The largest equilibrium
  • 11. Spreading of liquid drops over solid substrates 1343 spreading (smallest contact angle) was noted on glass, the least on PS and on PMMA it was intermediate. Hexadecane and undecane, low surface tension liquids, were found to exhibit equilibrium wetting that was proportional to the γc of the solid substrate. Glycerol and water, high surface tension liquids, were found to exhibit equilibrium wetting that was inversely proportional to the γc of the solids. These observations are related to Young’s equation, where cos θ = (γSV − γSL)/γLV, (7) provided that γSV is somehow related to Zisman’s γc (the critical surface tension of wetting). In a pragmatic sense, ‘like wets like’ seems to work. 4. CONCLUSIONS The present investigation provides experimental evidence that the solid substrate plays a significant role in determining equilibrium contact angle. Results show that hexadecane and undecane, low surface tension liquids, exhibit equilibrium wetting that is proportional to the γc of the solid substrate. Similarly, glycerol and water, high surface tension liquids, were found to exhibit equilibrium wetting that was inversely 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 three solids 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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