File Name: contact angle measurement and contact angle interpretation .zip
The contact angle, as a vital measured parameter of wettability of material surface, has long been in dispute whether it is affected by gravity. Herein, we measured the advancing and receding contact angles on extremely low contact angle hysteresis surfaces under different gravities G and found that both of them decrease with the increase of the gravity.
The underlying mechanism is revealed to be the contact angle hysteresis and the deformation of the liquid-vapor interface away from the solid surface caused by gradient distribution of the hydrostatic pressure. The real contact angle is not affected by gravity and cannot measured by an optical method. The measured apparent contact angles are angles of inclination of the liquid-vapor interface away from the solid surface. Furthermore, a new equation is proposed based on the balance of forces acting on the three-phase contact region, which quantitatively reveals the relation of the apparent contact angle with the interfacial tensions and gravity.
This finding can provide new horizons for solving the debate on whether gravity affects the contact angle and may be useful for the accurate measurement of the contact angle and the development of a new contact angle measurement system.
Wetting is one of the basic characteristics of solid surfaces. It is very important for processes like adhesion [ 1 ], self-cleaning [ 2 ], fluid drag reduction [ 3 ], heterogeneous nucleation [ 4 ], and the formation of coffee rings [ 5 ]. Therefore, it has attracted immense interest in a large diversity of research fields ranging from physical, biological, and environmental sciences. Owing to its complexity, wetting and the parameter used to measure it, the contact angle, have been investigated for many years [ 6 — 27 ].
Currently, thousands of papers are published annually about the topic. However, there are still fundamental questions to be answered. The relationship between the wetting and gravity is one of them. Because the disjoining pressure, resulted from the intermolecular interaction, makes the structure of three-phase contact line complicated, Benner et al.
This issue was resolved by Keller and Merchant [ 33 ], and a precise mathematical definition for the contact angle was proposed: a boundary condition to the Young-Laplace equation where the film thickness is 0. And the interfacial tensions refer to the constant, interfacial Gibbs free energies far from the contact line.
Gravity only affects the shape of the drop [ 8 — 14 ]. Recently, Bormashenko imposing the transversality conditions on the variational problem of wetting also demonstrates that gravity does not influence equilibrium contact angles [ 35 — 37 ]. This discrepancy becomes an important issue, especially in the space era, when interfacial phenomena frequently draw more attention because they are dominant events in microgravity and much different from those observed on Earth.
Extensive studies on wetting and the contact angle are beneficial for clarifying this issue. On an ideal surface, the system has a single and unique contact angle. However, for a real solid surface and a liquid, many contact angles can be measured since the system has many metastable equilibrium states, and each metastable equilibrium state corresponds to one contact angle [ 38 ].
Among these contact angles, the lowest metastable contact angle is the receding contact angle, and the highest one is the advancing contact angle [ 38 ]. They can be measured by receding and advancing liquid on a solid surface [ 7 , 38 , 39 ]. And the difference between advancing and receding contact angles is called contact angle hysteresis.
Nearly all real solid surfaces exhibit contact angle hysteresis [ 7 , 39 , 40 ]. Only a few smooth, chemically homogeneous, and inert real surfaces possess very low contact angle hysteresis [ 41 , 42 ]. They are the ones that most closely approach an ideal surface. Previous experimental studies [ 15 — 27 , 43 ] at different gravities used ordinary surfaces. Thus, the results of the effect of gravity on the contact angle may be caused by contact angle hysteresis.
To rule out this possibility, it is necessary to systematically study the relationship between the contact angle and gravity using surfaces with low contact angle hysteresis. In addition to the requirement for using low contact angle hysteresis surfaces, clarification of the relationship between the contact angle and gravity needs to consider the drop size.
Even on ideal surfaces, the contact angle is affected by the drop volume increases, due to line tension [ 9 , 44 ]. According to Equation 2 , when the drop is large enough, the effect of the line tension can be ignored [ 7 , 38 ].
Furthermore, in order for the measurement and interpretation to be meaningful, the drop must be sufficiently large compared with the size scale of heterogeneity that ensures the drop base is axisymmetric [ 45 ]. Therefore, reproducible and reliable measurement of the contact angle shall be carried out using large drops. In the literatures, it has been reported that the radius of the sessile drop should be larger than 2. In previous experimental measurements of the contact angle under different gravities, large drops were rarely used.
In general, the sessile droplet on an inclined plate real surface, not idea surface will be deformed due to the pinning of the contact line and gravity, and the contact angle will be changed by gravity [ 47 — 51 ]. This issue was widely investigated by researchers [ 47 — 51 ]. The tilt plate method is also used to measure the advancing and receding contact angle.
However, they are related to the weight of the drop. According to literature report, the advancing and receding contact angles obtained by the tilt plate method are not consistent with that obtained by the sessile drop [ 38 , 45 ].
Thus, the sessile drop method is employed in this study. The dynamic process of gravity affecting the apparent contact angle was analyzed by solving the augmented Young-Laplace equation.
The relationship between the contact angle measured by the optical method and the real contact angle was discussed. And a new equation describing the relationship between gravity and the apparent contact angle was presented. The discovery can provide new horizons for solving the debate on whether gravity affects contact angle and may be useful for the accurate measurement of the contact angle and the development of a new contact angle measurement system.
The contact angles of liquids on solid surfaces were measured under different gravities generated by a home-made specially designed long-arm centrifuge Figures 1 a and 1 b.
The contact between the liquid and solid surface takes place at point which is inside a sealed box in the contact angle measurement unit Figure 1 c.
The contact angle measurement unit Figure 1 hangs on one end of the long-arm, while an object of the same weight hangs on the other end of the long-arm for balance Figure 1 b. The liquid can be injected onto or withdrawn from the solid surface through a syringe via a remote liquid control unit Figure 1 b. From the video, the images of the sessile drops can be captured, and the contact angle can be determined from the images using the DropSnake program [ 52 ].
Most of the other surfaces also exhibited the same properties. Generally, surface roughness and chemical heterogeneity will lead to pinning of the three-phase contact line, which subsequently results in contact angle hysteresis [ 35 , 53 ]. For the PDMS 9K , the pinning effect of these small hills on the three-phase contact line may be the reason for the relatively larger contact angle hysteresis.
From Figure 2 b , it can also be seen that the apparent contact angle decreased as gravity increased, especially for the advancing contact angle. Although low contact angle hysteresis surfaces were used in this study, the contact angle hysteresis still exists. Thus, the decrease of the apparent contact angle with the increase of gravity may be related to contact angle hysteresis. For a drop on a real surface, the wetting state is generally in a metastable equilibrium state, and the most stable equilibrium state is difficult to achieve because many energy barriers need to be overcome [ 38 ].
The advancing and receding contact angles can be easily measured because of the low energy barrier [ 38 ]. Generally, additional energy can overcome the energy barrier and make the wetting state reach a more stable equilibrium state [ 38 , 45 ]. The direct result is that the additional energy decreases the advancing contact angle and increases the receding contact angle [ 38 ].
The increasing gravity may provide additional energy to make wetting reach a more stable state, so that the advancing and receding contact angles are different under different gravities. However, upon checking the data in Figure 2 b more carefully, we found that all receding contact angles do not increase with the increase of gravity as predicted by theory except receding contact angles of ethylene glycol on DMDCS and PDMS 9K.
This means that the apparent contact angle decrease relative to the increasing gravity was not only caused by contact angle hysteresis. As showed in Figures 2 b and 2 c , the apparent contact angles are affected by gravity. The direct consequence of gravity for a drop is the presence of the hydrostatic pressure, which means that the apparent contact angle under gravity is related to the hydrostatic pressure.
It can be seen that the height of the drops decreased upon increasing gravity Figure 3 b. This result means that the effect of gravity on the hydrostatic pressure is more significant than that of the drop height. The results of all hydrostatic pressure cases investigated in this research are summarized in Figure 3 d , which show that the hydrostatic pressure does increase with increasing gravity, despite the height of the drop decreasing with increasing gravity.
However, how does the hydrostatic pressure affects the apparent contact angle? In gravitational field, the diagram of the hydrostatic pressure red arrows acting on the liquid-vapor interface of the drop of the three-phase contact region is shown in Figure 3 f. As shown in Figure 3 f , the drop will be deformed due to the hydrostatic pressure, leading to a smaller contact angle as compared with that without considering gravity.
With increasing gravity, the hydrostatic pressure will increase, so that the deformation of the drop will be more significant, resulting in a smaller contact angle Figure 3 d. This is in contradiction with our experimental results.
The possible reason is that the contact angles we measured are the apparent contact angles, not the mathematically defined contact angles. They are on the liquid-vapor interface and away from the solid surface due to the low resolution of the measurement system.
If the resolution of the measurement system is high enough, we will see the real three-phase contact region. In this region, viscous resistance, resulted from the intermolecular interaction, is very high. The deformation of liquid-vapor interface caused by hydrostatic pressure can only occur in the area controlled by capillary action far away from the solid surface and the three-phase contact region.
The situation shown in Figure 3 d is just a macrosituation. In fact, the measured apparent contact angles are the angles of inclination of a certain position on the liquid-vapor interface. In order to confirm this point, it is necessary to study the relationship between droplet profile and inclination angle under different gravities. In this part, we use the method of Diaz et al. Figure 4 shows the 2D profile of a liquid-vapor interface shape in the vicinity of the contact line.
As shown in Figure 4 , there are three regions—molecular, transition, and capillary regions. The molecular region is dominated by the disjoining pressure and spatially varying interfacial free energies resulted from the molecular interaction; the capillary region is dominated by the capillarity and gravity; and in the transition region, the disjoining pressure competes with the hydrostatic pressure, and the surface tension is assumed constant.
Within the molecular region, the equation for the shape of the liquid-vapor interface is the fully augmented Young-Laplace equation [ 31 ]: where is liquid-vapor interfacial free energy, is the film thickness, is the angle of inclination of the liquid-vapor interface, is the curvature, is the disjoining pressure, is the pressure in liquid, and is the pressure in vapor. Above the molecular region, becomes a constant,. In Equation 3 , can be expressed by. For convenience, considering only the contribution from Van der Waals force, the disjoining pressure can be expressed by where is Hamaker constants, [ 54 ].
By introducing a molecular film thickness, , then,. For the liquid slice, the hydrostatic pressure at any point on the interface can be expressed by where , the equilibrium height of the drop, is a certain constant at a particular gravitational level; is the height of any point on the liquid-vapor interface. Outside the molecular region, an augmented Young-Laplace equation can be obtained by combining Equations 3 , 4 , 7 , and 8 where is the capillary length.
Integrating Equation 9 and imposing , yields the solution. Without the disjoining pressure, Equation 10 becomes the Young-Laplace equation:. Figure 5 a shows a variation of the angle of the water drop on DMDCS with the film thickness under different gravity is calculated by using Equation 10 and assuming.
Surface and Colloid Science pp Cite as. The previous chapter was largely theoretical, in that it dealt with the interpretation of contact angle results in terms of solid surface energies. It also delved into the question of how the structure of a solid surface affects the contact angle that a liquid forms on the solid. The level of structure considered there included features that are not macroscopically observed, such as microheterogeneities, or minute peaks, pits, hills, and grooves in various geometries. Their existence may be inferred from certain observations, such as contact angle hysteresis, and sometimes they can be observed directly, e. Unable to display preview. Download preview PDF.
Contact angle measurement is easily performed by establishing the tangent (angle) of a liquid drop with a solid surface at the base. The contact angle of a liquid drop on a solid surface is defined by the mechanical equilibrium of the drop under the action of three interfacial tensions (Fig.
The contact angle, as a vital measured parameter of wettability of material surface, has long been in dispute whether it is affected by gravity.
Download PDF. Wettability refers to how easily a liquid spreads over the surface of a contact lens. Clinically, this can be observed by viewing the interaction between the tears and the lens surface. The contact angle is the angle formed between a drop of liquid and the surface of the lens. Small contact angles are associated with an increased ability of the tears to spread out over the surface of a contact lens and lead to a more stable tear film. The three main laboratory techniques used to measure the contact angle of contact lenses are the sessile drop , captive bubble , and Wilhelmy plate methods, which are described in detail below.
Contact angle is one of the common ways to measure the wettability of a surface or material. Wetting refers to the study of how a liquid deposited on a solid or liquid substrate spreads out or the ability of liquids to form boundary surfaces with solid states. The wetting, as mentioned before is determined by measuring the contact angle, which the liquid forms in contact with the solids or liquids. The wetting tendency is larger, the smaller the contact angle or the surface tension is. The contact angle is an angle that a liquid creates with a solid surface or capillary walls of a porous material when both materials come in contact together. This angle is determined by both properties of the solid and the liquid and the interaction and repulsion forces between liquid and solid and by the three phase interface properties gas, liquid and solid. Those interactions are described by cohesion and adhesion forces which are intermolecular forces.
The contact angle is the angle , conventionally measured through the liquid, where a liquid — vapor interface meets a solid surface. It quantifies the wettability of a solid surface by a liquid via the Young equation. A given system of solid, liquid, and vapor at a given temperature and pressure has a unique equilibrium contact angle. However, in practice a dynamic phenomenon of contact angle hysteresis is often observed, ranging from the advancing maximal contact angle to the receding minimal contact angle. The equilibrium contact angle reflects the relative strength of the liquid, solid, and vapour molecular interaction. The contact angle depends upon the medium above the free surface of the liquid, and the nature of the liquid and solid in contact. It is independent of the inclination of solid to the liquid surface.
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The contact angle is one of the most sensitive experimental values describing a junction between three phases, being influenced by the composition and properties of contacting media as well as the structure and composition of interfaces involved. Since then, the contact angle has remained one of the most important values measured experimentally during characterization of solids and their wetting characteristics. As a result, the attention of scientists and researchers in the past two centuries has been on development of methods for accurate contact angle measurements, interpretation of experimental values and understanding of the causes of contact angle value variation and contact angle hysteresis.
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