Simulating Contact Angles in RheoCube

Carolien Vis, PhD

1 July, 2021

Across many industries, knowledge of how fluids and solids interact can be crucial to the formulation of a product. In particular, the wettability of a solid by multiple liquids can be a deciding factor in formulation research. Wettability can have a profound impact across a range of applications. Think, for example, of industrial processes such as wastewater treatment, detergency, printing, and lubrication. To make smart decisions in the lab, it is therefore important to gain as much insight into the interactions between the fluids and solids and the corresponding wettability.

Wettability, or surface wetting, is quantified by the so-called three-phase contact angle. For a solid surface that is poorly wetted by a fluid (e.g. a glass surface by an apolar oil) contact angles greater than 90° will be measured (figure 1, left). The use of a hydrophobic surface, such as polypropylene (PP), and an apolar oil, will result in a contact angle smaller than 90°, as this surface is very well wetted by the fluid (figure 1, right). 

Figure 1: Solid surface poorly wetted by droplet, resulting in contact angle >90° (left), solid surface well wetted by droplet, resulting in contact angle <90° (right).

Experimental versus Digital setup

Contact angles can be experimentally determined using an optical tensiometer, which principally consist of a plateau, a dispenser, an optical camera and a light source. A substrate, a solid surface, is immersed in a fluid and placed on the plateau. A droplet of a second fluid is placed carefully on the surface using the dispenser. The optical camera records the droplet and the contact angle is determined by tracing the contours. When a blend of fluids and or surfactants is used, the effect of the combination of components can be observed in the changing contact angle. However, the exact cause of this change remains unknown. Additional spectroscopic techniques should be used to get an idea of how the components are arranged throughout the fluid, i.e. whether a surfactant aligns on the fluid-fluid interface. 

Another method to gain more understanding on the behavior of complex fluids and fluid-particle mixtures is by running simulations. RheoCube, simulation software that is specifically designed to simulate complex fluids on the meso- and microscale, can give insights that are not easily obtained in experiments. For instance, the location and concentration of each ingredient in the simulation box can be determined, which in the lab would only be possible with the use of advanced spectroscopic techniques. But how do our models know what ingredients like each other or not? In RheoCube, chemical interactions on the mesoscale are modelled using Hansen Solubility Parameters (HSPs). Together with the molar mass, viscosity and molar density, these serve as input parameters for the Smoothed Particle Hydrodynamics (SPH) method. These HSPs are a measure of the cohesive energy density of a chemical component, split into 3 contributions; ẟD from the dispersion forces, ẟP from the polar forces and ẟH from the hydrogen-bonding forces. One of the advantages of using HSPs as input for chemical interactions is that they can be applied to a wide variety of chemical components, from fluids to polymers and from surfactants to particles. The compatibility of different chemicals is determined by their distance in HSP space. If the HSPs of two components are very much alike, they will mix very well, while if their HSPs are very much apart they will not mix at all.

To model simple contact angles in RheoCube three ingredients are required: 2 immiscible fluids, one for the droplet phase, one for the bulk phase, and a flat particle representing the solid surface. This particle is placed in the middle of the simulation box on which a droplet of a predetermined width and height is placed, the rest of the box is filled with the bulk fluid. Depending on the affinity of the particle, droplet and bulk fluids with each other based on the HSP differences, the droplet will either spread out over or repel the surface, resulting in a low or high contact angle respectively.

Simulated contact angles

To demonstrate the advantage of using RheoCube in predicting contact angles we have compared the outcome of simulations with experimental research. Here we choose to use 2 types of solid surfaces, PP and glass, together with two immiscible fluids, water and decane. After the simulation was finished, analysis was done using the Data Analysis and Visualization tool that RheoCube offers. First, the simulation box was sliced vertically through the center to visualize the particle and the droplet. From this slice a so-called heatmap was created, a 2D image showing the concentration of the components as a color gradient. Second, the surface of the particle was drawn on the heatmap followed by drawing the contour of the droplet. Finally, by fitting an ellipse to the droplet contour, and calculating the angle between the ellipse and the surface, the contact angle was determined. The resulting contact angles were compared to the ones found in experiments and reported in literature.[1] For good comparison both the contact angle of a water droplet in decane and the contact angle of a decane droplet in water were determined. 

Figure 2 shows the decane and water droplet on the PP surface after 5 ms. In these images the bulk phases are filtered out for clarity. As PP is a hydrophobic surface with HSP close to decane (see Table 1), the contact angle of the decane droplet with PP is expected to be lower than 90°. This was also shown in literature where the experimentally determined contact angle of decane on PP was found to be 49°. The contact angle determined after this simulation, 52°, was very close to the experimental value. As the HSP distance of water and PP is very big (Table 1), the contact angle is expected to be greater than 90°. And indeed, after a simulation of 5 ms, a contact angle of 145° was found, comparable to the 149° found in the experimental research. 

IngredientδD (MPa1/2)δP (MPa1/2)δH (MPa1/2)
Decane1600
Water15.51642.3
PP surface1801
Glass surface14.612.17.8
Table 1: HSPs of fluids and surfaces used in the simulations.

Figure 2: a) Visualization of a decane droplet on a PP particle in water (t=5 ms), and the corresponding contact angle as measured in the heatmap. b) Visualization of a water droplet on a PP particle in decane (t=5 ms), and the corresponding contact angle as measured in the heatmap.

For a comparison, glass was used as a more hydrophilic surface. As the exact HSP is not known for glass, the HSP of silicon dioxide (SiO2) was used (Table 1). As these values do not fully describe the chemical interactions of glass (such as the surface hydrogen bonding network) some parameterization of the individual interactions (water-glass and decane-glass) was necessary. Interactions between water and the glass surface are largely driven by hydrogen bonding networks. Although both water and glass have high δH components, their HSP distance is large and these interactions were therefore parameterized to more closely resemble the attraction between them. In the decane-glass HSP interactions, the dispersion forces (δD) are very similar, which makes them much more attractive than they are in reality. Therefore, the decane-glass interactions were parameterized to be more repulsive. 

Figure 3 shows the decane and water droplets on the glass surface after 5 ms with the bulk phases filtered out. Next to these 3D images, the corresponding contact angles are shown. The average contact angles were 117° for the decane droplet in water, and 102° for the water droplet in decane, respectively, in very good agreement with  the angles found experimentally (117° and 102°).

Figure 3: a) Visualization of a decane droplet on a glass particle in water (t=5 ms), and the corresponding contact angle as measured in the heatmap. b) Visualization of a water droplet on a glass particle in decane (t=5 ms), and the corresponding contact angle as measured in the heatmap.

Predictive power of simulations

With this, we have demonstrated the ability of RheoCube to simulate contact angles based on existing materials. Simulations, however, can be used not only to duplicate experiments performed in the lab, but also to simulate systems that cannot be so easily prepared experimentally. One such example is experimenting with solid surfaces that do not exist or are not yet synthesized in the lab. With simulations, this would be a simple matter of changing the HSPs to see what the effect would be on the contact angle. The same holds true for the use of fluids. All kinds of (potentially non-existent) fluids could be screened before choosing the ones that might be interesting to try out in the lab. Using simulations as a predictive tool reduces the number of iterations in experimental work. This will make a huge difference, not just by reducing the tedious aspects of trial-and-error work, but saving vast amounts of time and money.

References

[1] Orkun Ozkan and H Yildirim Erbil 2017 Surf. Topogr.: Metrol. Prop. 5 024002

Final Note

Not a RheoCube user yet and interested in how simulation software can progress your product development? Reach out to request your demo and speak with one of our experts today. Additionally, we have a special webinar coming up on 8 July regarding Data Visualization in Simulations via RheoCube, sign up here to attend.