Sessile drops and bubbles

The cases of the sessile drop and bubble are symmetrical, as illustrated in Fig. n-16. The profile is also that of a meniscus 0 is now positive and, as an... 

The family of so-called bounded sessile configurations, that is, sessile drops and bubbles centered at the axis, belongs to the one-parameter subfamily... 

Fig. 11-16. Shapes of sessile and hanging drops and bubbles (a) hanging drop (b) sessile drop (c) hanging bubble (d) sessile bubble.

The axisymmetric drop shape analysis (see Section II-7B) developed by Neumann and co-workers has been applied to the evaluation of sessile drops or bubbles to determine contact angles between 50° and 180° [98]. In two such studies, Li, Neumann, and co-workers [99, 100] deduced the line tension from the drop size dependence of the contact angle and a modified Young equation... 

Figure 7.6 Sessile drop and sessile bubble on a planar surface.

One can measure the maximum pressure that can be applied to a gas bubble at the end of a vertical capillary, of radius r and depth t in a liquid, before it breaks away (Figure 3.13) [143], Before break-away the bubble has the shape of a sessile drop and is described by the equation of Bashforth and Adams. The pressure in the tube is the sum of the hydrostatic pressure (Apgt) and the pressure due to surface tension. Equations have been published which allow calculation of surface tension using Bashforth-Adams and density and depth data. 

Measurements on molten metals. The maximum bubble pressure method has proved one of the most satisfactory, but sessile drops, and drop-volumes have also been used with success.2 The principal difficulty lies in the proneness of metals to form skins of oxides, or other compounds, on their surfaces and these are sure to reduce the surface tension. Unless work is conducted in a very high vacuum, a freshly formed surface is almost a necessity if the sessile bubble method is used, the course of formation of a surface layer may, if great precautions are taken, be traced by the alteration in surface tension. Another difficulty lies in the high contact angles formed by liquid metals with almost all non-metallic surfaces, which are due to the very high cohesion of metals compared with their adhesion to other substances. 

Other systems belonging to this category include sessile bubbles 2urd hanging drops and bubbles, sketched in figs. 1.11 and 12. For sessile bubbles and drops the mathematics of the curvature is the same as before the radii of curvature are given by [1.2.7 and 8). or by (1.2.11 Eind 12] and the profile is determined by [1.3.9, 12 or... 

Table 1.5 reviews the capabilities of the most common (quasi-)static methods (we excluded the very fast oscillating jet and pulsating bubble), obtaining dynamic information. Some of these are intrinsically dynamic in that the measurement requires the extension of an interface (drop weight, maximum bubble pressure), so that y(t) data can in principle be obtained when the rate of extension can be varied in a controlled fashion. Others are basically static (shapes of sessile or pendent drops and bubbles), but can be rendered dynamic by disequilibratlon. 

Figure 5.19. Contact angles, measured through the liquid, in sessile drops and captive bubbles. The vapour phase can be replaced by einother liquid.

The parameter fi is positive for oblate figures of revolution, i.e. for the meniscus in a capillary, a sessile drop, and a bubble under a plate, and is negative for prolate figures, i.e. for a pendant drop or an adjacent bubble. Bashforth and Adams (1883) reported their results as tables. For more detailed information, see for example in Adamson (1967). 

In order to measure the surface tension of solutions containing surfactants, the maximum bubble pressure, pendant drop and Wilhelmy plate (immersed at a constant depth) methods are suitable capillary rise, ring, mobile Wilhelmy plate, sessile drop and drop weight methods are not very suitable. These methods are not recommended because surfactants preferably adsorb onto the solid surfaces of capillaries, substrates, rings, or plates used during the measurement. In a liquid-liquid system, if an interfacially active surfactant is present, the freshly created interface is not generally in equilibrium with the two immiscible liquids it separates. This interface will achieve its equilibrium state after the redistribution of solute molecules in both phases. Only then can dynamic methods be applied to measure the interfacial tension of these freshly created interfaces. 

The static methods are based on studies of stable equilibrium spontaneously reached by the system. These techniques yield truly equilibrium values of the surface tension, essential for the investigation of properties of solutions. Examples of the static methods include the capillary rise method, the pendant and sessile drop (or bubble) methods, the spinning (rotating) drop method, and the Wilhelmy plate method. 

As a rule, results from the sessile drop" and maximum bubble pressure" as well as from the pendant drop" methods are preferable to results obtained from other methods for metals with very high melting points. 

For polymers interfacial and surface tensions are more practically obtainable from analysing the shapes of pendant or sessile drops or bubbles, all of which are examples of axisymmetrical drops. Bubbles may be used to obtain surface tensions at liquid/vapour interfaces over a range of temperatures and for vapours other than air. Drops can also be used to obtain vapour/liquid surface tensions but they are particularly suited to determination of liquid/liquid interfacial tensions, for example for polymer/polymer interfaces. All the methods are based on the application of equation (2.2.1). The principles are illustrated in figure 2.4, in which a sessile drop is used as the specific example. Just like for the capillary meniscus, the drop has two principal radii of curvature, R in the plane of the axis of symmetry and / 2 normal to the plane of the paper. At the apex, O, the drop is spherically symmetrical and R = Rz = b and equation (2.2.12) becomes... 

The data are a compilation of several studies and measurements were obtained from the sessile drop , maximum bubble pressure , and the pendant drop methods. The accuracy varies with both method and the study. 

Methods based on the shape of static drops or bubbles include the pendant drop method and the sessile drop or bubble method. The general procedure is to make certain measurements of the dimensions or profile. It is accurate to a few tenths of a percent. 

J. Drehch, J. D. Miller, and R. J. Good, The effect of drop (bubble) size on advancing and receding contact angles for heterogeneous and rough sohd surfaces as observed with sessile-drop and captive-bubble techniques, J. Colloid Interface Set, 179,37-50 (1996). 

The surface tension measurement techniques can be divided into the following three categories (i) Force Methods, which include the truly static methods of the capillary rise and Wilhelmy plate methods, as well as the dynamic detachment methods of the Du Nouy ring and drop weight, (ii) Shape Methods, which include the pendant or sessile drop or bubble, as well as the spinning drop methods, and (iii) Pressure Methods, which are represented by the maximum bubble pressure method. These techniques are summarized in the following sections of this chapter. 

Figure 2.2 Drop and bubble configurations for measurement of equilibrium, advancing and receding contact angles [6]. (a) Equilibrium sessile drop, (b) equilibrium pendant bubble, (c) advancing and receding drop, (d) advancing and receding bubble, (e) drop on tilted plate. L = liquid, V = vapour.

Equilibrium contact angles can be measured very simply from the profiles of liquid drops (Figure 2a) or bubbles (Figure 2b) resting on a plane surface. These methods are known as the sessile drop and captive bubble methods respectively. The contact angle may be measured indirectly by... 

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