Addition/Correction Cite This: Langmuir XXXX, XXX, XXX−XXX
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Correction to “Predicting the Wetting Dynamics of a Two-Liquid System” D. Seveno,* T. D. Blake, S. Goossens, and J. De Coninck Langmuir 2011, 27(24), 14958−14967 (doi: 10.1021/la2034998)
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The problem is especially acute at intermediate times when the drop is evolving from its initial spherical shape to its final one, which is also a spherical cap for a partially wetting liquid. After reanalyzing the data presented in Seveno et al.,2 we have found an error in the determination of the dynamic contact angle θd (static contact angles are correct) measured in the simulation of the spreading of a liquid droplet L1 on top of a substrate S when it is surrounded by a second liquid L2. There, we approximated the drop shape by a spherical cap and fitted the L1−L2 interface profile to a circle. The tangent to the fitted circle at the intersection with the substrate then defined the contact angle and the base radius. However, we have now found that if we fit a circle to the full L1−L2 profile we overestimate the value of the dynamic angle and we underestimate the value of the radius of contact due to the lack of precision of the spherical cap approximation. As a consequence, the measured contact line friction for the two-liquid simulation ζ12 is overestimated with respect to its real value. A more accurate procedure is to fit each half of the L1−L2 profile separately. Figure 1 shows an example for solid− liquid coupling CL1−S = 0.7 of a circle fitted to the full L1−L2 interface (left) and the result obtained by fitting each half of the profile independently (right). If we recalculate the dynamic angles and the radii of contact for all of the couplings considered in our study and use them to compute the contact-line frictions, then we reach a different conclusion from the one presented in our article. Figure 2 shows an update to Figure 9 in our article, where we compare the contact-line friction for the two-liquid system, ζ12, with the sum of frictions ζ1 and ζ2 obtained from one-liquid spreading simulations.
he measurement of the contact angle of a drop placed on a solid support is always a delicate procedure, especially when its size is small. This is also the case when one simulates the spreading of such drops at the nanoscale using, for example, molecular dynamics. The basic idea1 is first to locate as precisely as possible the edges of the drop and then to fit through these points a local or global function given by the solution of the Laplace equation, whose tangent will give the contact angle. Obviously, the smaller the system, the more one tries to use the global form to gain precision. Without gravity or when it is negligible, the Laplace equation predicts a spherical cap for the drop shape at equilibrium. To arrive at this equilibrium, the shape of the drop has changed according to the time since its initial condition. The question that arises, therefore, is the shape of the spreading drop over time. When a drop of liquid spreads over a solid substrate, the parameters that control the displacement of the molecules are the viscosity and inertia. If the molecules are not too big and the viscosity is low, the molecules move quickly over the time scale of the simulation. If the time scale of displacement of these molecules is faster than that of change in the shape of the drop, then we may assume that the shape of the drop is everywhere in local equilibrium, which means that it will be given by a spherical cap once any inertial effects have dissipated. Many simulation studies have demonstrated the validity of this approach for drops of liquid spreading in a vacuum or in a rarefied atmosphere. We have recently discovered that the problem is different when a liquid spreads within another liquid. The displacement time of the molecules at the interface then increases considerably, which makes the hypothesis of local equilibrium null and void.
Figure 1. Example of fitting the full L1−L2 profile (left) or the half L1−L2 profile (right) with a circle. Clearly, fitting the full profile with a single circle overestimates the size of the contact angles.
© 2011 American Chemical Society
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DOI: 10.1021/acs.langmuir.8b00893 Langmuir XXXX, XXX, XXX−XXX
Langmuir
Addition/Correction
Figure 2. Contact-line friction for the two-liquid system, ζ12, from the simulation with CL1−L2 = 0.6: upper data set obtained by fitting the full profile with a single circle; lower data set obtained by fitting half the profile and that obtained by simply adding ζ1 and ζ2.
Therefore, we conclude that we can model the contact-line friction for the two-liquid simulation simply as the sum of the frictions obtained in the one-liquid simulations, ζ12 = ζ1 + ζ2, and not as ζ12 = ζ1 + ζ2 + 2(ζ1ζ2)1/2 as originally proposed in our article. We thank Dr. J. C. Fernandez Toledano for pointing out this error and apologize for any inconvenience and misdirection it may have caused.
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REFERENCES
(1) De Coninck, J.; Blake, T. D. Dynamic Contact Angle; Springer Handbook of Fluid Mechanics; Springer: Berlin, 2007; pp 112−119. (2) Seveno, D.; Blake, T. D.; Goossens, S.; De Coninck, J. Predicting the wetting dynamics of a two-liquid system. Langmuir 2011, 27 (24), 14958−14967.
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DOI: 10.1021/acs.langmuir.8b00893 Langmuir XXXX, XXX, XXX−XXX
