pubs.acs.org/Langmuir © 2009 American Chemical Society
Surfactant-Induced Modification of Low Weber Number Droplet Impact Dynamics Kalpak P. Gatne, Milind A. Jog, and Raj M. Manglik* Thermal-Fluids & Thermal Processing Laboratory, University of Cincinnati, Cincinnati, Ohio 45221 Received February 19, 2009. Revised Manuscript Received April 27, 2009 The effect of surfactant molecular mass transport on the normal impact and spreading of a droplet of its aqueous solution on dry horizontal substrates is investigated experimentally for a range of Weber numbers (20-100). The postimpact dynamics of film spreading and its recoil behavior are captured using high-speed real-time digital imaging. Hydrophilic (glass) and hydrophobic (Teflon) substrates were used with water and aqueous solutions of three different surfactants of varying diffusion rates and ionic characteristics: SDS (anionic), CTAB (cationic), and Triton X-100 (nonionic). Their solutions facilitate larger spread and weaker surface oscillations compared to a pure water drop colliding at the same Weber number. On a hydrophobic surface, the drop rebound and column fracture are inhibited by the presence of the surface-active agent. Besides reagent bulk properties, dynamic surface tension, surface wettability, and droplet Weber number govern the transient impact-spreading-recoil phenomena. The role of dynamic surface tension is evident in comparisons of impact dynamics of droplets of different surfactant solutions with identical equilibrium surface tension and same Weber number. It was observed that higher diffusion and interfacial adsorption rate (low molecular weight) surfactants promote higher drop spreading factors and weaker oscillations compared to low diffusion/adsorption rate (high molecular weight) surfactants.
Introduction The phenomenon of droplet impact on a surface is encountered in a variety of applications including spray coating, spray cooling, inkjet printing, deposition of thermal barrier coatings, near netshape manufacturing, aerosol drug delivery, and agro-chemical sprays.1-4 Not surprisingly, considerable work has been carried out on drop impact, spreading, and recoil behavior using analytical, experimental, and computational methods.3,5-19 A recent review by Yarin4 provides an extended discussion of the current literature and unresolved issues. For pure liquids, characterized by their thermophysical properties (in particular, density F, surface or gas-liquid interfacial tension σ, and viscosity μ), the drop-surface interactions are *To whom correspondence should be addressed. Telephone: (513) 556 5704. Fax: (513) 556 3390. E-mail:
[email protected]. (1) Asai, A.; Shioya, M.; Hirasawa, S.; Okazaki, T. J. Imaging Sci. Technol. 1993, 37, 205–207. (2) Drug Delivery to the Lung; Bisgaard, H., O’Callaghan, C., Smaldone, G. C., Eds.; Marcel Dekker: New York, 2002. (3) Jia, W.; Qiu, H. H. Exp. Therm. Fluid Sci. 2003, 27, 829–838. (4) Yarin, A. L. Annu. Rev. Fluid Mech. 2006, 38, 159–192. (5) Madejski, J. Int. J. Heat Mass Transfer 1976, 19, 1009–1013. (6) Chandra, S.; Avedisian, C. T. Proc. R. Soc. A 1991, 432, 13–41. (7) Fukai, J.; Shiiba, Y.; Yamamoto, T.; Miyatake, O.; Poulikakos, D.; Megaridis, C. M.; Zhao, Z. Phys. Fluids 1995, 7, 236–247. (8) Pasandideh-Fard, M.; Qiao, Y. M.; Chandra, S.; Mostaghimi, J. Phys. Fluids 1996, 8, 650–658. (9) Healy, W. M.; Hartley, J. G.; Abdel-Khalik, S. I. Int. J. Heat Mass Transfer 1996, 39, 3079–3082. (10) Sadhal, S. S.; Ayyaswamy, P. S.; Chung, J. N. Transport Phenomena with Drops and Bubbles; Springer: New York, 1997. (11) Mao, T.; Kuhn, D. C. S.; Tran, H. AIChE J. 1997, 43, 2169–2179. (12) Riboo, R.; Marengo, M.; Tropea, C. Atomization Sprays 2001, 11, 155–165. (13) Riboo, R.; Marengo, M.; Tropea, C. Exp. Fluids 2002, 33, 12–24. (14) Roisman, I. V.; Rioboo, R.; Tropea, C. Proc. R. Soc. A 2002, A458, 1411–1430. (15) Sikalo, S.; Marengo, M.; Tropea, C.; Ganic, E. N. Exp. Therm. Fluid Sci. 2002, 25, 503–510. (16) Sikalo, S.; Wilhelm, H. D.; Roisman, I. V.; Jakirlic, S.; Tropea, C. Phys. Fluids 2005, 17, 062103-1–12. (17) Gunjal, P. R.; Ranade, V. V.; Chaudhari, R. V. AIChE J. 2005, 51, 59–79. (18) Ukiwe, C.; Kwok, K. Y. Langmuir 2005, 21, 666–673. (19) Sikalo, S.; Ganic, E. N. Exp. Therm. Fluid Sci. 2006, 31, 97–110.
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shaped by inertia, viscous, surface tension, and gravity forces. Their dynamic influences have been scaled with Weber number (We = FV2D/σ), Reynolds number (Re = FVD/μ), Ohnesorge number [Oh=(We)1/2/Re), capillary number (Ca=μV/σ), and a parameter K = We Oh-2/5 via different experimental analyses and computational modeling.4,6,8-10,12-14,17,19 The results of drop impact behavior have been generally expressed in terms of a spreading factor φd defined as the ratio of the instantaneous spread diameter to the equivalent drop diameter just before impact (d/D), and a flattening factor φh that is given by the ratio of the instantaneous drop height or liquid film thickness to the equivalent drop diameter prior to impact (h/D); these dimensions are described in Figure 1. Theoretical models, based on applying the principle of conservation of energy between an instant of time before impact and at the maximum spread, have been proposed to predict the maximum spreading ratio.6,8,11,14,18 These models work well for predicting drop spreading but are not accurate in predicting drop recoil.16 Furthermore, the volume-of-fluid (VOF) method has been used to computationally simulate the drop impact and spreading phenomena for pure liquids on hydrophilic surfaces with reasonable success, but this has required advancing and receding contact angles data from experiments.8,16,17,20 This is reflective of the difficulty in resolving the complex liquid-soilidair interfacial interactions in a more generalized manner. Addition of small amounts of surface-active agents or surfactants in pure liquids can have a dramatic effect on liquid drop impact, spreading, recoil, and rebound phenomena.17,21-24 (20) Bussman, M.; Mostaghimi, J.; Chandra, S. Phys. Fluids 1999, 11, 1406– 1417. (21) Mourougou-Candoni, N.; Prunet-Foch, B.; Legay, F.; Vignes-Alder, M.; Wong, K. J. Colloid Interface Sci. 1997, 192, 129–141. (22) Mourougou-Candoni, N.; Prunet-Foch, B.; Legay, F.; Vignes-Alder, M. Langmuir 1999, 15, 6563–6574. (23) Zhang, X.; Basaran, O. A. J. Colloid Interface Sci. 1997, 187, 166–178. (24) Cooper-White, J. J.; Crooks, R. C.; Boger, D. V. Colloids Surf., A 2002, 210, 105–123.
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Figure 1. Schematic representation of the droplet-surface interactions.
Surfactants typically have a unique long-chain molecular structure, composed of a hydrophilic head and a hydrophobic tail. Based on their molecule’s hydrophilic part, which is ionizable, polar, and polarizable, they are generally categorized as anionics, nonionics, cationics, and zwitterionics.25 Reagent molecules in aqueous solutions naturally tend to diffuse toward and adsorb at interfaces. At an evolving gas-liquid interface, this process reduces the interfacial tension in a time-dependent manner that manifests in a dynamic surface tension behavior, and the equilibrium value is attained only after a relatively long time span.26,27 Gas-liquid interfacial tension σ of an aqueous surfactant solution typically decreases with increasing concentration until a critical micelle concentration or CMC, when the reagent molecules agglomerate to form micelles; with C g CMC, the equilibrium σ remains unchanged. The adsorption behavior of all reagents changes around their respective CMC, and their micellization is a property of each solute. Their molecular dynamics and micellar aggregation also influence the solid-liquid interface. The physisorption of reagent molecules at the solid-liquid interface changes the surface wetting behavior where the adsorption dynamics is concentration-dependent.28,29 At low concentration, adsorption may take place as individual ions. At higher concentration, formation of hemimicelles and then adsorption as reverse hemimicelles, with their polar heads oriented both toward the solid surface and liquid, renders the surface increasingly hydrophilic. As the critical micelle concentration or CMC is approached, the adsorption becomes independent of the bulk concentration, and the surfactant molecules form a bilayer on the surface to make it strongly hydrophilic. A hydrophobic surface thus becomes increasingly hydrophilic with increasing reagent concentration on its surface.30-33 The ability of surfactant molecules to diffuse and repopulate the interface is governed by their mobility.26,34 Thus, when a new (25) Holmberg, K.; J€onsson, B.; Kronberg, B.; Lindman, B. Surfactants and Polymers in Aqueous Solution, 2nd ed.; Wiley: New York, 2003. (26) Miller, C. A.; Neogi, P. Interfacial Phenomena: Equilibrium and Dynamic Effects; Marcel Dekker: New York, 1985. (27) Manglik, R. M.; Wasekar, V. M.; Zhang, J. Exp. Therm. Fluid Sci. 2001, 25, 55–64. (28) Somasundaran, P.; Krishnakumar, S. Colloids Surf., A 1997, 123-124, 491–513. (29) Fuerstenau, D. W. J. Colloid Interface Sci. 2002, 256, 79–90. (30) Bisio, P. D.; Cartledge, J. G.; Keesom, W. H.; Radke, C. J. J. Colloid Interface Sci. 1980, 78, 225–234. (31) Dobias, B.; Rybinski, W. V. In Solid-Liquid Dispersions; Dobias, B., Qiu, X., Rybinski, W. V., Eds.; Marcel Dekker: New York, 1999; Vol. 81, pp 318-470. (32) Lyklema, J. Fundamentals of Interface and Colloid Science; Academic Press: London, UK, 1991. (33) Rosen, M. J. Surfactants and Interfacial Phenomena, 3rd ed.; WileyInterscience: Hoboken, NJ, 2004. (34) Dukhin, S. S.; Kretzschmar, G.; Miller, R. Dynamics of Adsorption at Liquid Interfaces; Elsevier: Amsterdam, Holland, 1995.
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surface is created, the interfacial tension is initially close to that of the solvent and then decreases with time as the surfactant molecules diffuse and are adsorbed at the interface. Once the interface is repopulated with surfactant molecules, the surface tension reaches an equilibrium value. When the time scales of both microscale reagent diffusion and macroscale fluid motion are of the same order (∼milliseconds), the interfacial tension becomes time- and flow-dependent. Consequently, dynamic surface tension variations play an important role in governing drop impact and film-spreading phenomena for reagent-laden aqueous solutions.17,21-24 While the benefits of surfactant and polymeric additives on modifying impact dynamics have been recognized,35 the work on characterizing the associated droplet impact and postimpact spread/recoil is somewhat limited. Zhang and Basaran23 presented an analysis of the drop-impact phenomenon to suggest an influence of Marangoni stresses due to nonuniform surfactant distribution in the drop, possibly caused by the disturbance and change of area due to the impact. However, these effects have not been observed in other studies.36 Mourougou-Candoni and co-workers21,22 carried out experiments using different ionic and nonionic surfactants at 10CMC on low energy (hydrophobic) substrates. They observed that during the short-time-scale spreading there is a large change in the surface area of the drop and so the surface tension at the interface is much larger than the equilibrium value; this alludes to the relevance of the dynamic surface tension. Crooks et al.36 studied the effect of dynamic surface tension and elasticity on the droplet impact dynamics of both Newtonian and non-Newtonian fluids on hydrophobic surfaces to identify the factors that would suppress drop rebound. Using high speed photography and the VOF computational method, Gunjal et al.17 have reported that, with the reduction in surface tension, SDS solution produces larger spread on a glass substrate. In most previous studies, however, the equilibrium surface tension of different surfactant solutions varied considerably. As such, the droplets formed at a discharge orifice tended to differ in size and give rise to considerably different Weber numbers. In comparing their impact dynamics, these results thus obscure the superimposition of three effects: (i) due to the differences in the rate of diffusion and adsorption, which manifests as dynamic surface tension behavior, (ii) because of the variations in the equilibrium surface tension, and (iii) due to the variation in the drop Weber number. To isolate the effects of dynamic surface tension, surfactant solutions of identical equilibrium surface tension must be considered and the experiments should be carried out at the same Weber number. Such a systematic study is presented in this paper, where we have investigated the impact, spreading, and recoil phenomena with drops of water and solutions of three surfactants with varying diffusion rates: sodium dodecyl sulfate (SDS, anionic), cetyltrimethyl ammonium bromide (CTAB, cationic), and octylphenoxypolyethoxyethanol (Triton X-100, nonionic). For the range of Weber numbers considered in the experiments, the time scale of surfactant diffusion and that of spreading/recoil were of the same order, thereby producing a dynamic interaction between the drop evolution and reagent transport and adsorption. For example, SDS and CTAB solutions have nearly the same equilibrium surface tension but significantly different relaxation rates at 2CMC. On the other hand, CTAB and Triton X-100 solutions have similar relaxation rates, but the latter has a much lower equilibrium surface tension (35) Bergeron, V.; Bonn, D.; Martin, J. Y.; Vovelle, L. Nature 2000, 405, 772– 775. (36) Crooks, R.; Cooper-Whitez, J.; Boger, D. V. Chem. Eng. Sci. 2001, 56, 5575–5592.
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compared to CTAB at 2 CMC. These reagent solutions thus provide an effective basis for investigating the dynamic surface tension effects by comparing their respective droplet-impactspreading-recoil/column fracture dynamics on both hydrophilic and hydrophobic surfaces. The characteristic phenomena for water and surfactant solutions are delineated via temporal variations of the drop or film spreading and flattening factors, as well as photographic visualization of the impact-spreading-recoil processes. It should further be noted that the low Weber numbers range in the experiments of this study was chosen to ensure that the drop impact process did not result in splashing. In the case of additivefree pure liquids, several different empirical correlations have been proposed in the literature to predict the onset of instabilities and splashing. For example, Mundo et al.37 have reported a threshold value of (We1/2Re1/4) > 57.7 for the onset of splashing. This restricts the Weber number range to below about 100 for water and the surfactant solution droplets considered here. This avoids the additional uncertainties introduced by splashing, and lends to a more controlled investigation that centers around the rather complex phenomena of interfacial molecular transport of surfactants and the concomitant effects on droplet spreading via the dynamic interfacial adsorption and/or physisorption behavior of the reagents.
Experimental Procedure and Apparatus Figure 2 depicts a schematic of the experimental apparatus, where carefully controlled droplets are generated using a precision syringe that has provision for interchangeable needles for varying the orifice diameter and hence the drop size. The syringe was mounted on a measurable and calibrated vertical stand, and it could be lowered or raised so as to release the droplet from different predetermined heights. A microscope slide (commercial glass) was used as the hydrophilic surface, whereas the hydrophobic substrate was prepared by wrapping the microscope slide with Teflon tape. The substrates were cleaned with water and ethanol, wiped with nonabrasive, lint-free wipes, and then allowed to dry completely before carrying out the experiment. They were placed on a leveling table, which controls its horizontal alignment that is also perpendicular to the drop trajectory. The dropsurface interactions were captured using a digital high-speed high-resolution camera system (Hi-Dcam-II version 3.0; NAC Image Technology) with a lens that provides a magnification of 8. The camera was aligned at 0 to the substrate orientation so as to obtain a frontal view of the drop impact. A focusing, singleended parabolic aluminized reflector lighting system (daylight PAR; ARRI) along with a glossy white reflector was used for providing sharply contrasting and continuous lighting. With the camera frame rate set at 2000 fps and a shutter speed of 1/4000, sequential images of a single drop impact were captured in real time. These were digitally contrasted and analyzed with an imageprocessing software (Image-Pro plus 4.0; Media Cybernetics) in order to measure the droplet shapes, sizes, and temporal evolution. The droplet size (preimpact diameter, and postimpact film spread and its thickness) was obtained on an equivalent volume-average basis. For example, in determining the preimpact drop diameter, measurements were made at several different angular diameters on the drop-face image (digitally enhanced and enlarged) using four different images just before impact and their composite average calculated for the final value. A similar averaging was employed to obtain the drop-film spread and thickness after impact. The droplet velocity and hence its Weber number were varied and controlled by changing the height from (37) Mundo, C.; Sommerfeld, M.; Tropea, C. Int. J. Multiphase Flow 1995, 21, 151–173.
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Figure 2. Schematic of the experimental apparatus. which the drop of a given size (function of orifice needle diameter) was released. The velocity was measured from two consecutive images just before impact by resolving the difference between the relative drop position and the time lapse (0.5 ms precision) between the two respective frames. Each experiment was repeated three times so as to ensure reproducibility and accuracy of measurements of the drop-impact spatial-temporal evolution. The test fluids were prepared by dissolving weighed samples of additives in distilled, deionized water to get the desired concentration [wppm]. For powder additives, sample weights were measured on a precision electronic weighing machine of (0.1 mg accuracy; for additives in liquid form, precision syringes (volumetric ranges: 0-0.1 mL ( 0.002 mL, 0-1.0 mL ( 0.01 mL, and 0-20 mL ( 1.0 mL) were used for sample volumes, and the corresponding weight evaluated by the known value of specific gravity. All the solutions were aged and remixed sufficiently so as to ensure complete homogenization prior to carrying out the drop-impact and spread dynamics experiments. Based on a sampling cumulative-error-propagation method, the maximum uncertainty in the surfactant concentration in the prepared test solutions was determined to be (1.6% for powder surfactants and (2.8% for liquid surfactants. In the case of the drop diameter and velocity measurements, the maximum sampling uncertainty was found to be (1.38% and (1.31%, respectively. The consequent uncertainty in evaluating the Weber number is (2.35%, and (1.90% in the Reynolds number. Finally, uncertainties in the droplet-film spread and flattening measurements are (1.47% and (3.51%, respectively. More details of the measurement methods, precision, and uncertainty analysis are available in Manglik et al.27 and Gatne.38
Results and Discussion Experiments were conducted with aqueous solutions of three surfactants, namely, sodium dodecyl sulfate (SDS, anionic, MW= 288.3), cetyltrimethyl ammonium bromide (CTAB, cationic, MW = 364.5), and octylphenoxypolyethoxyethanol (Triton X-100, nonionic, MW = 625) to explore their respective postimpact drop dynamics on the following two substrates: glass (hydrophilic) and Teflon (hydrophobic). The surfactants have different molecular weights and ionic nature, and their relevant physicochemical properties at a nominal room temperature of 23 C are listed in Table 1. The variations in equilibrium surface tension with concentration C for their aqueous solutions at 23 C are plotted in Figure 3 from the data of Zhang and Manglik.39,40 The surface tension is seen to decrease in all cases with increasing surfactant concentration to asymptotically attain a minimum constant value beyond the CMC. The CMCs for the three (38) Gatne, K. P. M. S. Thesis, University of Cincinnati, 2006. (39) Zhang, J.; Manglik, R. M. J. Heat Transfer 2004, 126, 34–42. (40) Zhang, J.; Manglik, R. M. J. Heat Transfer 2005, 127, 684–691.
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Article Table 1. Physicochemical Properties of Surfactants
surfactant name chemical formula ionic nature MW ethylene oxide (EO) groups appearance CMC equilibrium surface tension σ at CMC manufacturer
SDS C12H15SO4 anionic 288.3 0 white powder ∼2500 wppm 38.0 mN/m Fisher
Figure 3. Surface tension variation with concentration for different surfactant solutions.
surfactants at 23 C, as obtained from the lower asymptotic inflection point on the equilibrium adsorption isotherm, are ∼2500 wppm for SDS, ∼400 wppm for CTAB, and ∼200 wppm for Triton X-100. The concomitant equilibrium surface tension values are 38.0, 38.3, and 33.1 mN/m, respectively. For exploring the role of dynamic surface tension, as dictated by the relative molecular mobility of each reagent, surfactant solutions in water were prepared so that each of them had the same value of the equilibrium surface tension (42.5 mN/m). Their corresponding concentrations were identified from the adsorption isotherms given in Figure 3, and in all cases the concentrations were significantly lower than their respective CMC values. When a new surface is created in a reagent-laden aqueous solution, a finite time is required for the additive molecular adsorption to reach an equilibrium state between the surface concentration and bulk concentration. This time-dependent surfactant adsorption at the air-liquid interface gives rise to the dynamic surface tension behavior, which, however, eventually reduces to the equilibrium condition after a long time period.27,41,42 This is clearly illustrated in Figure 4 where the variation of interfacial tension σ with surface age τ is depicted for the three surfactant solutions based on data of Zhang and Manglik;39,40 here the values for σ at very small times are extrapolated using the method of Hua and Rosen.43 The time scale to reach the equilibrium value (total relaxation) at the newly created interface is of the same order (∼100 ms) as that for droplet impact and recoil with We ∼ 20-100 and D ∼ 2-3 mm diameter drops. The dynamic surface tension relaxation rather than the equilibrium or static value, therefore, becomes the more critical determinant of the concomitant surface-spread dynamics. The time-dependent process is primarily related to the interfacial adsorption and molecular mobility or diffusion of the reagent, which is a function of its molecular weight. A lower molecular weight surfactant adsorbs (41) Iliev, T. H.; Dushkin, C. D. Colloid Polym. Sci. 1992, 270, 370–376. (42) Chang, C.-H.; Franses, E. I. Colloids Surf., A 1995, 100, 1–45. (43) Hua, X. Y.; Rosen, M. J. J. Colloid Interface Sci. 1988, 124, 652–659.
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CTAB C19H42BrN cationic 364.5 0 white powder ∼400 wppm 38.3 mN/m Sigma-Aldrich
Triton X-100 C14H21(OCH2CH2)9-10OH nonionic 624 (average) 9-10 clear liquid ∼200 wppm 33.1 mN/m Union Carbide
Figure 4. Surface tension variation with surface age for different surfactant solutions.
faster than its higher molecular weight counterpart, and this is seen in the faster interfacial tension relaxation of SDS solution in comparison with that for CTAB or Triton X-100 solutions in Figure 4. At the liquid-solid interface, on the other hand, the change in wetting characteristics can be inferred from a measurement of the contact angle θ. Based on the data of Zhang and Manglik,39,40 the variation of θ/θwater with concentration C for the three surfactant solutions is graphed in Figure 5. While θ/θwater is seen to decrease with increasing C in all solutions, in the case of ionic surfactants (SDS and CTAB), a lower plateau is attained around their respective CMC. This is in concurrence with the general physisorption characteristics of ionics at the solid-liquid interface,29,40 whereby micellar bilayers start to form on the surface and obviate any further change in wetting. In aqueous nonionic surfactant (Triton X-100) solution, on the other hand, the contact angle data attains a constant value much below the CMC. Because direct interactions of their polar chains are generally weak, nonionics tend to build and rebuild adsorption layers with C
