Drop methods equilibrium surface tension

Pendant or Sessile Drop Method The surface tension can be easily measured by analyzing the shape of a drop. This is often done by optical means. Assuming that the drop is axially symmetric and in equilibrium (no viscous and inertial effects), the only effective forces are gravity and surface or interfacial forces. In this case, the Young-Laplace equation relates the shape of the droplet to the pressure jump across the interface. Surface tension is, then, measured by fitting the drop shape to the Young-Laplace equation. Either a pendant or a sessile drop can be used for surface tension measurement. The pendant drop approach is often more accurate than the sessile drop approach since it is easier to satisfy the axisymmetric assumption. Similar techniques can be used for measuring surface tension in a bubble. 

A number of methods are available for the measurement of surface and interfacial tension of liquid systems. Surface tension of liquids is determined by static and dynamic surface tension methods. Static surface tension characterises the surface tension of the liquid in equilibrium and the commonly used measurement methods are Du Notiy ring, Wilhelmy plate, spinning drop and pendant drop. Dynamic surface tension determines the surface tension as a function of time and the bubble pressure method is the most common method used for its determination. 

In recent years, several theoretical and experimental attempts have been performed to develop methods based on oscillations of supported drops or bubbles. For example, Tian et al. used quadrupole shape oscillations in order to estimate the equilibrium surface tension, Gibbs elasticity, and surface dilational viscosity [203]. Pratt and Thoraval [204] used a pulsed drop rheometer for measurements of the interfacial tension relaxation process of some oil soluble surfactants. The pulsed drop rheometer is based on an instantaneous expansion of a pendant water drop formed at the tip of a capillary in oil. After perturbation an interfacial relaxation sets in. The interfacial pressure decay is followed as a function of time. The oscillating bubble system uses oscillations of a bubble formed at the tip of a capillary. The amplitudes of the bubble area and pressure oscillations are measured to determine the dilational elasticity while the frequency dependence of the phase shift yields the exchange of matter mechanism at the bubble surface [205,206]. 

Abstract The interfacial properties of tracheal aspirate from infants with untreated neonatal respiratory distress syndrome (NRDS), and NRDS infants after therapy with the exogenous surfactant Curosurf were assessed. The interfacial characteristics of the aspirate (equilibrium surface tension, maximal and minimal surface tension during lateral compression-decompression cycles) were determined with the pendant drop method. Our results show that the tracheal aspirate of infants with untreated NRDS had high equilibrium, maximal and minimal surface tension values. In contrast, the samples from infants, treated with Curosurf , showed lower surface tension values, suggesting that the application of Curosurf improves the composition and the properties of the pulmonary surfactant in the infant lung. 

The dynamic surface tension of [3-casein solutions at three concentrations 5 10, 10 and 10 mol/1 are shown in Fig. 14. As one can see the results from the two methods differ significantly. For the bubble the surface tension decrease starts much earlier. The surface tensions at long times, and hence the equilibrium surface tension from the bubble experiment are lower than those from the drop. However, the establishment of a quasi-equilibrium for the drop method is more rapid at low (3-casein concentrations while at higher P-casein concentrations this process is more rapid for the bubble method. This essential difference between solutions of proteins and surfactants was discussed in detail elsewhere [50]. In brief, it is caused by simultaneous effects of differences in the concentration loss, and the adsorption rate, which both lead to a strong difference in the conformational changes of the adsorbed protein molecules. 

Abstract The effect of interaction between proteins and amphiphiles on the surface tension reduction have been measured by the drop-volume method. The equilibrium surface tension reduction isotherms at the air/water interface of serum albumin and of ovalbumin in sodium dodecylsulphate and of ovalbumin in 1-monocaproin are reported. The surface tension reduction isotherms of the proteins in the anionic amphiphile solutions exhibit plateau regions, which have been interpreted in terms of different states of protein-amphiphile interaction in the bulk solution. Any interaction between ovalbumin and the monoglyceride is not reflected in the surface tension isotherm. At increased amphiphile concentration the protein seems to be replaced by 1-monocaproin in the surface. 

The Wilhelmy plate method [323,324], the sessile drop method [328,340], and the capillary height method [325-328] measure equilibrium surface tension, if sufficient time is allowed for the adsorption of surfactant molecules at the surface to attain the state of equilibrium. The Wilhelmy plate method measures the force exerted on a vertical plate partially immersed in the liquid (Fig. 9.20). If wetting of the plate is complete, the force, F, is proportional to the surface tension, y, and the circumference, L. of the plate ... 

As we shall have occasion to note in dealing with solutions, the composition of the surface phase is very different from that of the bulk liquid. When a liquid interface is newly formed the system is unstable until the surface phase has acquired its correct excess or deficit of solute by diffusion from or into the bulk of the solution. This process of diffusion is by no means instantaneous and, as has been observed in discussing the drop weight method, several minutes may elapse before equilibrium is established. In the ripple method the surfece is not renewed instantaneously but may be regarded as undergoing a series of expansions and contractions, thus we should anticipate that the value of the surface tension of a solution determined by this method would lie between those determined by the static and an ideal dynamic method respectively. 

The profiles of pendant and sessile bubbles and drops are commonly used in determinations of surface and interfacial tensions and of contact angles. Such methods are possible because the interfaces of static fluid particles must be at equilibrium with respect to hydrostatic pressure gradients and increments in normal stress due to surface tension at a curved interface (see Chapter 1). It is simple to show that at any point on the surface... 

In order to calculate polymer/filler interaction, or more exactly the reversible work of adhesion characterizing it, the surface tension of the polymer must also be known. This quantity is usually determined by contact angle measurements or occasionally the pendant drop method is used. The former method is based on the Young, Dupre and Eowkes equations (Eqs. 21,8, and 10), but the result is influenced by the surface quality of the substrate. Moreover, the surface (structure, orientation, density) of polymers usually differs from the bulk, which might bias the results. Accuracy of the technique maybe increased by using two or more liquids for the measurements. The use of the pendant drop method is limited due to technical problems (long time to reach equilibrium, stability of the polymer, evaluation problems etc.). Occasionally IGC is also used for the characterization of polymers [30]. 

Equation (46), one form of the Gibbs equation, is an important result because it supplies the connection between the surface excess of solute and the surface tension of an interface. For systems in which y can be determined, this measurement provides a method for evaluating the surface excess. It might be noted that the finite time required to establish equilibrium adsorption is why dynamic methods (e.g., drop detachment) are not favored for the determination of 7 for solutions. At solid interfaces, 7 is not directly measurable however, if the amount of adsorbed material can be determined, this may be related to the reduction of surface free energy through Equation (46). To understand and apply this equation, therefore, it is imperative that the significance of r2 be appreciated. 

Sitting or pendent drop. Both methods involve the determination of the shape of the drop in mechanical equilibrium. The shape is determined by the balance between gravitation and surface tensional forces. If gravitation is negligible the shape is always spherical irrespective of the surface tension. 

The dynamic methods depend on the fact that certain vibrations of a liquid cause periodic extensions and contractions of its surface, which are resisted or assisted by the surface tension. Surface tension therefore forms an important part, or the whole, of the restoring force which is concerned in these vibrations, and may be calculated from observations of their periodicity. Dynamic methods include determination of the wave-length of ripples, of the oscillations of jets issuing from non-circular orifices, and of the oscillations of hanging drops. Dynamic methods may measure a different quantity from the static methods, in the case of solutions, as the surface is constantly being renewed in some of these methods, and may not be old enough for adsorption to have reached equilibrium. In the formation of ripples there is so little interchange of material between the surface and interior, and so little renewal of the surface, that the surface tension measured is the static tension ( 12. ... 

Surface tensions of low-energy surfaces like many polymers are often determined from contact angle measurements. A review of the method and its application to polymer science was written by Koberstein [ 107], In equilibrium, the contact angle of a liquid drop on a solid surface is given by the Young equation ... 

Surface tension measurement. Adsorption titration, also called soap titration, (2.3) was carried out by the drop volume method at different polymer concentrations. The equivalent concentration of salt was held constant. The amount of emulsifier necessary to reach the critical micelle concentration (CMC) in the latex was determined by each titration. The total weight of emulsifier present in the latex is the weight of emulsifier in the water plus the weight of emulsifier adsorbed. The linear plot of emulsifier concentration (total amount of emulsifier corresponding to the end-point of each titration) versus polymer concentration gives the CMC as the intercept and the slope determines the amount of emulsifier adsorbed on the polymer surface in equilibrium with emulsifier in solution at the CMC (E ). 

The surface area expansion process in Figure 3.5 must obey the basic thermodynamic reversibility rules so that the movement from equilibrium to both directions should be so slow that the system can be continually relaxed. For most low-viscosity liquids, their surfaces relax very rapidly, and this reversibility criterion is usually met. However, if the viscosity of the liquid is too high, the equilibrium cannot take place and the thermodynamical equilibrium equations cannot be used in these conditions. For solids, it is impossible to expand a solid surface reversibly under normal experimental conditions because it will break or crack rather than flow under pressure. However, this fact should not confuse us surface tension of solids exists but we cannot apply a reversible area expansion method to solids because it cannot happen. Thus, solid surface tension determination can only be made by indirect methods such as liquid drop contact angle determination, or by applying various assumptions to some mechanical tests (see Chapters 8 and 9). 

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. 

The threshold of the equilibrium state can generally be reached slowly, and thus the surface tension values obtained by semi-static methods closely resemble those obtained by static ones. The rate of approaching the equilibrium state should be optimized in each system, in order to avoid lengthy measurements and to obtain surface tension values as close to the equilibrium ones as possible. Among the most common semi-static methods are the method of maximum pressure, the du Noiiy ring method and the drop-weight method. 

In the applications of the capillary pressure tensiometry deseribed, an equivalent to Eq. (4.119) is used in the two particular cases in which either the surface tension (pressure derivative method) or the drop curvature (expanded drop method) are constant. In other applications, like the expanding or growing drop methods developed respectively by Nagarajan and Wasan and McLeod and Radke, respectively [25, 154], the capillary pressure is monitored while the surface area is increasing continuously. In these methods APcap changes due to the variation of the drop radius and of the interfacial tension caused by the dilation of the surface which put the system in a state out of the adsorption equilibrium. The problem is that area change, flow in the bulk phases, and the adsorption kinetics of the present surface active compounds have to be considered in a model simultaneously. 

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