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Quantitative Experimental Study on the Transition between Fast and Delayed Coalescence of Sessile Droplets with Different but Completely Miscible Liquids Stefan Karpitschka* and Hans Riegler Max-Planck-Institut f€ ur Kolloid und Grenzfl€ achenforschung, D-14476 Potsdam, Germany Received February 19, 2010. Revised Manuscript Received June 2, 2010 Quantitative experimental data on the coalescence behavior of sessile droplets with different but completely miscible liquids are presented. The liquids consist of various aqueous mixtures of different nonvolatile diols and carbon acids with surface tensions ranging from 33 to 68 mN/m, contact angles between 9° and 20°, and viscosities from 1 to 12 cP. Two distinctly different coalescence behaviors, a delayed and a fast regime, are found. The transition between the two behaviors is remarkably sharp. It is found that the coalescence mode depends predominantly on the differences in the surface tensions of the two droplets. If the surface tension difference exceeds ∼3 mN/m, the coalescence is delayed. If it is less, droplet fusion occurs fast. Within the investigated parameter space, the transition seems independent from droplet size, absolute values of the surface tensions, and viscosity. Certain aspects of the experimental findings are explained with the simple hydrodynamic model presented in a recent publication.
Introduction The coalescence of droplets of identical liquids has been investigated in some depth during the last decades. There have been studies with free spherical droplets contacting each other 1-4 and with pendant droplets contacting a planar liquid surface5 or contacting a sessile droplet.6 The convergence of sessile droplets has also been investigated.7-17 Generally, the coalescence of droplets is driven by the minimization of the interfacial energies. Thus, droplets with identical liquids instantaneously start to merge with each other after their first contact. The research focuses on the evolution of the surfaces in the vicinity of the contact spot as it transforms from two separated droplets into a single one. In remarkable contrast, the coalescence behavior of sessile droplets with different, nonetheless completely miscible liquids has rarely been investigated although it is even of some technological importance, e.g., in microfluidics.7,18 The coalescence *E-mail:
[email protected]. (1) Bradley, S. G.; Stow, C. D. Phil. Trans. R. Soc. London 1978, 287, 635–675. (2) Eggers, J.; Lister, J. R.; Stone, H. A. J. Fluid Mech. 1999, 401, 293–310. (3) Eggers, J. Phys. Rev. Lett. 1998, 80, 2634–2637. (4) Aarts, D. G. A. L.; Lekkerkerker, H. N. W.; Guo, H.; Wegdam, G. H.; Bonn, D. Phys. Rev. Lett. 2005, 95, 164503. (5) Thoroddsen, S. T.; Takehara, K. Phys. Fluids 2000, 12, 1265–1267. (6) Thoroddsen, S. T.; Takehara, K.; Etoh, T. G. J. Fluid Mech. 2005, 527, 85– 114. (7) Christopher, G. F.; Bergstein, J.; Poon, M.; Nguyen, C.; Anna, S. L. Lab Chip 2009, 9, 1102–1109. (8) Andrieu, C.; Beysens, D. A.; Nikolayev, V. S.; Pomeau, Y. J. Fluid Mech. 2002, 453, 427–438. (9) Gokhale, S. J.; DasGupta, S.; Plawsky, J. L.; Wayner, P. C. Phys. Rev. E 2004, 70, 051610. (10) Narhe, R.; Beysens, D.; Nikolayev, V. S. Langmuir 2004, 20, 1213–1221. (11) Narhe, R.; Beysens, D.; Nikolayev, V. S. Int. J. Thermophys. 2005, 26, 1743–1757. (12) Ristenpart, W. D.; McCalla, P. M.; Roy, R. V.; Stone, H. A. Phys. Rev. Lett. 2006, 97, 064501. (13) Nikolayev, V. S.; Gavrilyuk, S. L.; Gouin, H. Adv. Colloid Interface Sci. 2006, 302, 605–612. (14) Beysens, D. A.; Narhe, R. D. J. Phys. Chem. B 2006, 110, 22133–22135. (15) Kapur, N.; Gaskell, P. H. Phys. Rev. E 2007, 75, 056315. (16) Narhe, R. D.; Beysens, D. A.; Pomeau, Y. Euro. Phys. Lett. 2008, 81, 46002. (17) Sellier, M.; Trelluyer, E. Biomicrofluidics 2009, 3, 022412. (18) Whitesides, G. M. Nature 2006, 442(7101), 368–373.
Langmuir 2010, 26(14), 11823–11829
behavior can be quite different from that of identical liquids, because it will be affected by Marangoni flows.19 It has been found, in particular, that the coalescence can be delayed substantially. This was mentioned by Maxwell for the first time more than a century ago, although very briefly in only one sentence.20 In 1938, Bangham et al.21 presented for the first time a qualitative description of the delay of the coalescence of sessile droplets of completely miscible liquids. However, they could not really explain the findings, analyzing them only in vague terms such as caused by ”certain adsorption effects and molecular transport phenomena through the vapor phase“. Recently, we presented some more detailed (though still qualitative) experimental results and, in addition, a hydrodynamic model for the delay of the coalescence.19 We propose that the delay originates from the Marangoni convection between the two droplets, which is caused by the difference of the surface tensions of the two liquids. Our calculations show that the convective flow can induce a dynamic pressure. This pressure balances the (fusion-promoting) capillary pressure and thus keeps the droplets temporarily separated. This separation is maintained many orders of magnitude longer than the typical time for a complete droplet coalescence in the case of identical liquids. Hence, it is vindicated to distinguish between a fast coalescence of droplets with identical liquids and a delayed one in the case of different liquids. Recent results from experiments under betterdefined conditions, as well as simulations based on phase field and lubrication approximation models, qualitatively support this picture.22 Still, quantitative experimental data on the delayed coalescence have up to now not yet been presented, and many questions, including those concerning the validity of the hydrodynamic model, are still open. For Marangoni convection, a gradient in surface tension is necessary. Hence, assuming the validity of the hydrodynamic (19) Riegler, H.; Lazar, P. Langmuir 2008, 24, 6395–6398. (20) Maxwell, J. C. Encyclopedia Britannica 9th ed., 1875. (21) Banhgam, D. H.; Saweris, Z. Z. Trans. Faraday Soc. 1938, 34, 554–569. (22) Borcia, R.; Menzel, S.; Bestehorn, M.; Karpitschka, S.; Riegler, H. Physics of Fluids 2009, submitted.
Published on Web 06/17/2010
DOI: 10.1021/la1007457
11823
Article
Karpitschka and Riegler
Figure 1. Experimental setup for the observation of the coalescence behavior of two sessile droplets with different liquids. The two insets (”top view“, ”side view“) show images taken during a real experiment.
model, only liquids with sufficiently different surface tensions will lead to a delayed coalescence. On the other hand, droplets with the same liquid (same surface tension) fuse without delay. Thus, the following questions arise. What difference in surface tension is necessary to delay the coalescence? What happens if the difference in surface tension is increased continuously? Is there a continuous shift in the behavior from fast to delayed coalescence, or is there a (sharp) transition between the two modes? In other words, are fast and delayed coalescence qualitatively or only quantitatively different? In the first case, what is the minimum difference in surface tensions for the transition between fast and delayed coalescence? How important are the absolute values of the surface tensions? How important are other parameters, e.g., the viscosity, the droplet size, or the contact angle? In the following, we will address those questions and present for the first time a systematic set of quantitative experimental data. The data were obtained with a new experimental setup, which was designed specifically for the investigation of the coalescence behavior of sessile droplets. We will show that the experimental findings indeed confirm a key premise of the proposed hydrodynamic model, namely, that the difference in the surface tensions is the essential parameter that determines whether the coalescence is fast or delayed. In addition, we show that the transition between the two coalescence modes is quite sharp. Last but not least, it has to be mentioned that, besides the fundamental intellectual curiosity, there is also a strong technological motive to better understand the mechanisms behind the delay of the coalescence. It is obvious that the coalescence behavior of sessile droplets of different liquids is of immense practical importance, e.g., for ”lab-on-a-chip devices“.18
Materials and Methods Figure 1 shows a sketch of the experimental setup to study the coalescence of two sessile droplets on a planar substrate.15 All experiments were performed by first depositing droplet 1 (fluid 1) onto the substrate from the top with a syringe. Thus, location, volume, and state (between receding or advancing contact angle) of this preplaced droplet can be adjusted. Then, droplet 2 is created by pumping fluid 2 through a hole in the substrate (subfilled). Upon increasing the volume of droplet 2, its contact line will eventually come close enough to the contact line of droplet 1 to initiate the coalescence process. The droplet coalescence behavior was imaged from the top and the side. One camera inspected the sample through a macrolens from above. The sample area was homogeneously illuminated with light of a defined divergence. Therefore, the local brightness of the droplet image can be translated into the local surface 11824 DOI: 10.1021/la1007457
Figure 2. Surface tensions of the various aqueous mixtures at
20 °C.
inclination. Simultaneously, the droplets were imaged from the side with a second camera and an object-space telecentric lens. The samples were illuminated from the opposite side with light of low divergence (telecentric illumination). Therefore, the imaging scale is constant over the whole sample depth (2 cm) with a focal range covering about half of this depth. Via the simultaneous imaging from the top and the side and a proper analysis of the data, detailed information on the local droplet surface topology and the contact angles can be derived. The insets in Figure 1 show examples of imaging two droplets in the very moment of their contact taken from the top and from the side, respectively. During the experiments, the samples were kept in a closed chamber under controlled temperature, humidity, and gaseous environment. To minimize evaporation effects, the duration of the experiments was kept as short as possible (typically
