The shape and dynamics of deformations of viscoelastic fluids by water droplets
Graphical abstract
Introduction
The interfaces between liquids and soft materials, such as oil or water on skins, oil on feathers and furs, and water on thick oil, are as common as those between liquids and rigid solid surfaces. While much attention has been paid to studies using hard and rigid solid surfaces, less attention has been given to studies using soft surfaces. For instance, using hard and rigid solid surfaces, many studies of liquid on flat solid surfaces have provided insights on contact angle hysteresis [1], [2], [3], [4], [5], [6] and adhesion energy [7], [8], [9]. Moreover, the liquid behavior on rough or patterned surfaces, which represent more practical or common solid surfaces, have been studied extensively. Cassie, Baxter [10], and Wenzel [11] studied the apparent contact angle (measured or observed at a macroscopic level) of water droplets on rough surfaces. Many have studied the superhydrophobicity derived from micro- and/or nano-structures [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], and the stable or metastable wetting states on particular structures [12], [13], [15], [22], [23].
While the normal component of the surface tension at the three-phase boundary for the aforementioned cases is not important in the energy balance to derive Young’s equation that gives the relationship between contact angle and adhesion energy for rigid substrates, this component becomes important when it is strong enough to deform soft substrates. While most of the principles applicable to rigid surfaces are held valid, this type of deformation brings forth several additional aspects necessary in understanding the wetting phenomena on soft materials. If a droplet is placed on an initially smooth surface, the change in apparent contact angle over time is slower if the surface is soft or deformable than if it is rigid [24]. This change is affected by elasticity, modulus [24], [25], [26], [27], [28], [29], [30], and the relaxation time of polymers responding to the normal component of surface tension [31]. Though the apparent contact angle at any time after droplet deposition, θ(t), may be different from the intrinsic contact angle of the droplet before the deformation at time zero, θi, the local energy balance should be satisfied at the three-phase boundary (TPB) even during deformation. Therefore, the shape of the deformed surface and the location of the TPB are important in understanding the apparent contact angle. Theories [24], [25], [26] predict a very sharp wetting ridge at the TPB, and the direct visualization of the TPB with X-ray microscopy indeed shows very sharp ridges at submicron scales [27], satisfying the surface tension balance at the sharp ridges. The characteristics of the wetting liquid also affect the deformation. The curvature of the liquid–vapor and liquid–solid interfaces gives rise to a Laplace pressure that further deforms the soft material [32], [33], [34]. The Laplace pressure, PL is dependent on the curvature of the fluid and the surface tension of the fluid, γ, which can be related as ΔPL = 2γH. H is the mean curvature for a droplet with two different radii R1 and R2, which is expressed as H = (1/R1 + 1/R2).
Building on the efforts previously exerted in understanding the wetting phenomena of liquid droplets on soft materials, we here focus extensively on the dynamics, or time-dependence, of a spreading water droplet deposited on partially cross-linked polyacrylate polymers influenced by the different initial contact angles of water on those polymers. Most of the previous experiments studying the deformation of soft materials used thin polymer films (<100 μm) coated on rigid substrates [24], [26], [27], [35], [36], which did not allow observing the equilibrim shape of the soft surface and the liquid due to interference by the rigid substrate that resist the deformation. In this study, the thickness of our polymer film is large enough for a droplet to deform to its maximum extent, i.e., deep enough for the deformation to experimentally show the thermodynamic equilibrium shape predicted by Neumann relation (or angles). With the knowledge of the shape and angles obtained from the equilibrium state, we discuss the time evolution and shape of the TPB from the first contact of the liquid droplet on the soft polymers until true equilibrium without being hindered by the rigid substrate during deformation. We initially assumed the trend would be the same with other reports with thin films, that is, increase in the radius, height, and depth of deformation, and the decrease in the apparent contact angle. In addition, we also hypothesized that their rates would be controlled by the different intrinsic contact angles of water on soft surfaces if the rheological and other physical properties are the same because it would change the normal component of surface tension only. Therefore, we performed experiments with water droplets on two different polymers having similar rheology but different initial contact angles of water on them. The rate and shape of the deformation were observed carefully to understand the behavior of liquid on soft surfaces. In doing so, the measurements and calculation of surface tension between each phase provided important values for the conclusion. While there are other more accurate and sophisticated models for calculating surface tensions of soft solid or liquid surface [37], the Neumann angle calculation [38] is used because the purpose of this study is not to report accurate values for other material or experiments, but to explain the reasons for the observed phenomena.
Section snippets
Materials and methods
Two kinds of monomers were used in preparing the partially crosslinked polymeric fluids. One monomer, benzyl acrylate (97%, Alfa Aesar), was purchased and used without further purification. The other one, 3,4-bis(triethyl)siloxy benzyl acrylate, was synthesized in-house. The details of the synthesis can be found in Ref. [39]. The molecular structure of the monomers and the experimental scheme can be found in Fig. S2 in the Supporting Information.
After these two monomer liquids were mixed with
Identification of the phase states of the polymers
We identified the two polymers as viscoelastic polymeric fluids, because (1) the fluids flowed due to the large downward force exerted by a heavy metal piece resting on top of the polymer surfaces (refer to Fig. S3 of the Supporting Information) and (2) the raised ridges relaxed back to a flat surface at long times (>50 min) after the water droplets were removed. (Fig. S4 of the SI). With a parallel plate rheometer, we measured shear storage and loss moduli for these polymers at the temperature
Conclusions
Building upon the previous reports regarding the behavior of liquid on deformable surfaces [24], [26], [27], [35], [36], the time-evolution of the deformation process by water droplets on viscoelastic polymeric fluids was observed until it reached the equilibrium shape as predicted by Neumann [38]. While the previous studies could not observe the equilibrium shape due to using thin films with rigid materials underneath, we employed very thick viscoelastic polymeric fluid to study the dynamics
Author contribution
Dongjin Seo, Dong Woog Lee, Steve Page, Peter H. Koenig, Yonas Gizaw, and Jacob N. Israelachvili designed the experiment. Dongjin Seo, Szu-Ying Chen, Dong Woog Lee, and Alex M. Schrader performed the deformation experiments. Dongjin Seo, Dong Woog Lee, and Kollbe Ahn prepared polymers and controlled their properties. Dongjin Seo, Yonas Gizaw, and Jacob N. Israelachvili oversaw the entire research.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was supported by a grant from the Procter & Gamble Company. We acknowledge the use of the NRI-MCDB Microscopy Facility and the Spectral Laser Scanning Confocal supported by the Office of the Director, National Institutes of Health of the United States of America under Award # S10OD010610. Dong Woog Lee was supported by the Basic Science Research Program (NRF2019R1A2C2005854) funded by the National Research Foundation (NRF) of Korea, and the 2020 Research Fund (1.200092.01) of Ulsan
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