Drop detachment time

Initially, a drop with a specific volume is very rapidly formed at the tip of the syringe. The drop volume is slightly smaller than the critical volume that corresponds to the equilibrium interfacial tension at which the drop would ordinarily detach. The drop will therefore remain attached to the tip surface. As surface-active material adsorbs at the liquid interface, the interfacial tension decreases and the drop will eventually detach. The time required between drop formation and drop detachment is the so-called drop detachment time. If the time required to form the drop is small compared to the drop detachment time, then the drop detachment time can be set equal to the effective age of the interface. Gradually, reducing the drop volume will increase the time required for the drop to detach. The drop detachment time and thus the age of the interface can be varied between 10 sec and 30 min. 

From the data presented (Miller et al. 1994a) it can be concluded that the drop detachment time t is the characteristic parameter for the observed hydrodynamic effects at small drop times and... 

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. 

The correction represented by the sample at S, is not perfect because the time delay tp is not infinitely small. In the case of the DME we can improve this by means of the excitation signal shown in Figure 5.8a, which is a modification of the original. Here we use two drops, one in which we apply a pulse, and one where no pulse is employed. The difference in the two signals just prior to drop detachment represents a much better estimate of the current due to the... 

Usually, the syringe simply needs to be lowered until the tip is submerged in the primary fluid. Note that in some drop volume tensiometers, the final resting position of the holder may need to be adjusted manually. The drop formed at the tip of the syringe must be located just above the LED detector so that the detachment time cart be determined accurately. 

The continuous formation of drops, however, can lead to substantial errors in obtained adsorption kinetic data. For short drop formation times, hydrodynamic effects have to be taken into account. At large flow rates, the measured drop volume at the moment of detachment must be corrected. This is because a finite time is required for the drop meniscus to be disrupted and the drop to detach. Even though the volume has already reached its critical value, fluid may still flow from the reservoir into the drop. The volume of the drop is thus larger than its measured value, which leads to larger calculated interfacial tension values. The shorter the drop formation time is, the larger the error w i 11 be. K1 oubek et al. (1976) were the first to quantify this effect by introducing a corrected critical drop volume, Vc ... 

A further method relies on the fact that the natural drop time of a dropping mercury electrode is proportional to the interfacial tension [18]. Again, drop birth can be detected electrically by the sudden change in impedance, so the method is easily automated. Unlike the other methods there is no adequate theory describing the mechanism of drop detachment, so the proportionality constant is again obtained by calibration with a solution of known properties. The method is extremely sensitive to vibrations and impurities, and consequently it is difficult to obtain results better than 1%. Also as a dropping mercury electrode is used, the system is dynamic and may not be in equilibrium if the rate of adsorption is slow. Similarly, capacitance measurements will be frequency dependent if adsorption is slow compared with the period of a.c. perturbation, and this provides a useful check of whether equilibrium is obtained. 

The time dependent surface tension decay was measured according to the drop-volume technique as outlined by Tornberg [18,19]. The automatization procedure according to Arnebrant and Nylander [20] was employed. In this method surface tension reduction by macromolecules during adsorption at the air-water interface is measured by formation of drops of certain volumes. Time for detachment of the droplets is recorded. Surface tension calculated [19, 20] was plotted against detachment time and the value attained after 2000 seconds was set as the equilibrium value. The surface tension of the solutions is still decreasing after this period of time, but the rate of decrease is small, less than 0.05 mNm" per 100 seconds. The maximum error in surface tension values is 1.5%. 

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],... 

This model considers the drop formation to take place in two stages, the expansion stage when the drop inflates at the nozzle tip and the detachment stage when the drop rises, forms a neck, and finally gets detached from the nozzle. The first stage is assumed to end when the buoyancy becomes equal to the interfacial tension force. For the termination of the second stage two conditions have been used, which result in two values of time of detachment. The lower of the two values is employed for calculation. 

When the static drop stage is passed, the drop starts rising with varying velocity, but still maintaining its connection with the nozzle through a neck. As further liquid is pumped into the drop during the time of detachment tc also, the final drop volume becomes... 

The integration constant for Eq. (138) is calculated by imposing the condition v = 0, when t — 0. At detachment, the condition v = (l/2)v c is applied and the corresponding time of detachment (t = tc) is evaluated. This model is useful only when the distance between the detachment drop and the residual drop is negligible. 

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. 

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