Drop volume method dynamic

Since the drop volume method involves creation of surface, it is frequently used as a dynamic technique to study adsorption processes occurring over intervals of seconds to minutes. A commercial instrument delivers computer-controlled drops over intervals from 0.5 sec to several hours [38, 39]. Accurate determination of the surface tension is limited to drop times of a second or greater due to hydrodynamic instabilities on the liquid bridge between the detaching and residing drops [40],... 

The drop weight, or drop volume method (sec. 1.6) is intrinsically dynamic the time scale can be varied by applying a variable pressure on the capillary. The volume of the drop is measured as a function of time, emd theory is needed to dafve y(t). Practically speaking, this technique is convenient although the interpretation may offer problems temperature control Is simple, the accuracy is = 0.1 mN m and LG and LL Interfaces can both be studied. 

Figure 3 contains dynamic data for ff-LG received by three methods the maximum bubble pressure method in the time range 0.001 s to 100 s, the drop volume method for times in the range 5 s to 500 s, and the profile analysis tensiometer PAT l in the time range from 10 s up to several hours. 

The aim of this chapter is to present the fundamentals of adsorption at liquid interfaces and a selection of techniques, for their experimental investigation. The chapter will summarise the theoretical models that describe the dynamics of adsorption of surfactants, surfactant mixtures, polymers and polymer/surfactant mixtures. Besides analytical solutions, which are in part very complex and difficult to apply, approximate and asymptotic solutions are given and their range of application is demonstrated. For methods like the dynamic drop volume method, the maximum bubble pressure method, and harmonic or transient relaxation methods, specific initial and boundary conditions have to be considered in the theories. The chapter will end with the description of the background of several experimental technique and the discussion of data obtained with different methods. 

The principle of the drop volume method is of dynamic character and therefore, it can be used for studies of adsorption processes in the time interval of seconds up to some minutes. At small drop times a so-called hydrodynamic effect has to be considered, as discussed in many papers (Davies Rideal 1969, Kloubek 1976, Jho Burke 1983, Van Hunsel et al. 1986, Van Hunsel 1987, Miller et al. 1994a). This hydrodynamic effect appears at small drop times under the condition of constant liquid flow into the drop and gives rise to apparently higher surface tensions. Davies Rideal (1969) discussed two factors influencing the drop formation at and its detachment from the tip of a capillary the so-called "blow up" effect and a "circular current" effect inside the drop. The first effect increases the detaching drop volume and simulates a higher surface tension while the second process leads to an earlier break-off of the drop and results in an opposite effect. A schematic of these two effects on measured drop volumes is shown in Fig. 5.10. 

Fig. 5.30 Dynamic surface tension of a 0.025 mol/l pt-BPh-EOlO solution measured using the maximum bubble pressure ( ) and drop volume ( ) methods original data ( - ), corrected data ( ) according to Miller et al. (1994d)...

It has been already indicated (Fig. 7) that micelles can lead to an essential acceleration of the adsorption process. Therefore, special experimental techniques are necessary for its investigation, allowing measurements of the dynamic surface tension in a time interval of milliseconds. The maximum bubble pressure method [78, 81, 83, 89,90,93] and the oscillating jet method [77, 82, 86, 87, 88, 90, 92, 93, 156] are most frequently used for these purposes. The inclined plate method [83, 89, 90, 93], the method of constant surface dilation [85] and the drop volume method [84] have been used also for slow adsorbing surfactants. 

There are three different measurement modes available with the drop-volume method, which can yield different data. However, taking all peculiarities into consideration, the results obtained by the different procedures are the same. The dynamic version of the drop-volume method is the classical procedure for the measurement of interfacial tensions. This mode consists of creating a continuous for-... 

As mentioned above, the drop volume method is of dynamic character and it can be used for adsorption processes in the time interval of seconds up to some minutes. At small drop time, the sohydrodynamic effect has to be considered [27]. This gives rise to apparently higher surface tension. Kloubek et al. [28] used an empirical equation to account for this effect. 

Figure 12.7. Dynamic surface tension data of two diethylde-cylphosphine oxide solutions, as measured by the drop volume method (TVT2, LAUDA, Germany) in the dynamic mode , Co = 10 mol/cm O, Co = 10 mol/cm ...

In many experimental techniques used for dynamic surface-tension measurements (such as the MBP method and the drop-volume method [14,76,82]), the surface expands gradually with time. In such a case, the convective terms in Eqs. (24) and (25) carmot be neglected. Nevertheless, it can be demonstrated that with the help of the new independent variables. 

Joos, P. and Rillaerts, E. 1981. Theory on the determination of dynamic surface tension with the drop volume and maximum bubble pressure method. J. Colloid Interface Sci. 79 96-100. 

This unit will introduce two fundamental protocols—the Wilhelmy plate method (see Basic Protocol 1 and Alternate Protocol 1) and the du Noiiy ring method (see Alternate Protocol 2)—that can be used to determine static interfacial tension (Dukhin et al., 1995). Since the two methods use the same experimental setup, they will be discussed together. Two advanced protocols that have the capability to determine dynamic interfacial tension—the drop volume technique (see Basic Protocol 2) and the drop shape method (see Alternate Protocol 3)—will also be presented. The basic principles of each of these techniques will be briefly outlined in the Background Information. Critical Parameters as well as Time Considerations for the different tests will be discussed. References and Internet Resources are listed to provide a more in-depth understanding of each of these techniques and allow the reader to contact commercial vendors to obtain information about costs and availability of surface science instrumentation. 

The main advantage of the static methods is cost. The equipment needed to conduct the dynamic measurements is approximately five times as expensive as the equipment required for static measurements (- 25,000 for a drop shape and drop volume analyzer versus - 5,000 for du Noiiy and Wilhelmy instruments). This is due to the additional capability of the former instruments to determine not only interfacial tension values but also the corresponding age of the interface. For more information on equipment, costs, and suppliers, see Internet Resources. 

Modem drop volume tensiometers are connected to a computer with sophisticated software that can be used to automatically record the surface tension as a function of the true interfacial age. Adsorption kinetics experiments with the drop volume technique can be conducted using either the constant drop formation method or the quasistatic method (for details, see Commentary). The choice of the dynamic measurement method depends primarily on the time range over which the adsorption kinetics needs to be measured. 

While the quasistatic method is quite accurate, it requires a long time to determine a complete adsorption kinetics curve. This is because a new drop has to be formed at the tip of the capillary to determine one single measurement point. For example, if ten dynamic interfacial tension values are to be determined over a period of 30 min, -180 min will be required to conduct the entire measurement. On the other hand, the constant drop formation method is often limited because a large number of droplets have to be formed without interruption, which may rapidly empty the syringe. Furthermore, the critical volume required to cause a detachment of droplets depends on the density difference between the phases. If the density difference decreases, the critical volume will subsequently increase, which may exacerbate the problem of not having enough sample liquid for a complete run. 

The theoretical foundation of the drop volume technique (DVT) was developed by Lohnstein (1908, 1913). Originally, this method was only intended to determine static interfacial tension values. Over the past 20 years, the technique has received increasing attention because of its extended ability to determine dynamic interfacial tension. DVT is suitable for both liquid/liquid and liquid/gas systems. Adsorption kinetics of surface-active substances at liquid/liquid or liquid/gas interfaces can be determined between 0.1 sec and several hours (see Fig. D3.6.5). 

Provides measuring techniques of contact angle, surface tension, interfacial tension, and bubble pressure. Suitable methods for both static and dynamic inteifacial tension of liquids include du Nous ring, Wilhelmy plate, spinning drop, pendant drop, bubble pressure, and drop volume techniques. Methods for solids include sessile drop, dynamic Wilhelmy, single fiber, and powder contact angle techniques. 

Dynamic surface tensions of an aqueous l.5510" mol/cm Triton X-100 solution measured with the dynamic capillary (0), inclined plate (A,A), drop volume ( ), strip ( ) and Wilhelmy plate ( ) methods according to Rillaerts Joos (I9S2)... 

Drops of liquids have held researchers interest for many years. As mathematical curiosities for famous early fluid dynamicists, the pendant drop from a capillary provided an interesting and practical challenge. Young (1805) and Laplace (1806) independently developed the theory of surface tension and drop formation while the first analytical solutions to their theory were completed by Gauss in 1830. Much of the early woik on pendant drops involved numerous methods involving the determination of drop volume or shape with experimental techniques and using the available theory to determine surface tension of the liquid-gas interface. These methods are well detailed in the works by Adamson, Padday, and Reed Hah. ITie studies of the early researches developed into the rich and diversified field of interfacial fluid dynamics. The advancement of theory and numerical techniques has steadily increased the ability of researchers to better understand and control interfacial behaviors. 

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