Drops shapes

Neumann has adapted the pendant drop experiment (see Section II-7) to measure the surface pressure of insoluble monolayers [70]. By varying the droplet volume with a motor-driven syringe, they measure the surface pressure as a function of area in both expansion and compression. In tests with octadecanol monolayers, they found excellent agreement between axisymmetric drop shape analysis and a conventional film balance. Unlike the Wilhelmy plate and film balance, the pendant drop experiment can be readily adapted to studies in a pressure cell [70]. In studies of the rate dependence of the molecular area at collapse, Neumann and co-workers found more consistent and reproducible results with the actual area at collapse rather than that determined by conventional extrapolation to zero surface pressure [71]. The collapse pressure and shape of the pressure-area isotherm change with the compression rate [72]. 

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... 

Equation 36 must be corrected for changes in the drop shape and for the effects of the inertia of Hquid flowing through the orifice, viscous drag, etc (64). As the orifice or aperture diameter is increased, d has less effect on the drop diameter and the mean drop si2e then tends to become a function only of the system properties ... 

Impingement is corrosion caused by aerated water streams constricting metal surfaces. It is similar to erosion corrosion in which air bubbles take the place of particles. The pits formed by impingement attack have a characteristic tear drop shape. 

The degree of deformation and whether or not a drop breaks is completely determined by Ca, p, the flow type, and the initial drop shape and orientation. If Ca is less than a critical value, Cacri the initially spherical drop is deformed into a stable ellipsoid. If Ca is greater than Cacrit, a stable drop shape does not exist, so the drop will be continually stretched until it breaks. For linear, steady flows, the critical capillary number, Cacrit, is a function of the flow type and p. Figure 14 shows the dependence of CaCTi, on p for flows between elongational flow and simple shear flow. Bentley and Leal (1986) have shown that for flows with vorticity between simple shear flow and planar elongational flow, Caen, lies between the two curves in Fig. 14. The important points to be noted from Fig. 14 are these ... 

In the present paper, interfacial tensions were measured for a number of heavy crude oils at temperatures up to 200°C using the spinning drop technique. However, reliable data cannot be obtained by this or any other drop shape method because of the small density difference between heavy crudes and water which, moreover, tends to decrease as the temperature increases. This problem was overcome by using aqueous D20 instead of H20 as has been previously described [5,8,211. The influence of surfactant type and concentration, mono- and divalent cation concentrations, and pH on the attainment of low interfacial tensions are reported and discussed. 

Wendt and Fassel [2] reported early experiments with a tear-drop shaped inductively coupled plasma but later described the medium power l-3kW 18mm annular plasma now favoured in modern analytical instruments [3]. 

This latter case is the same result as Einstein calculated for the situation where slip occurred at the rigid particle-liquid interface. Cox15 has extended the analysis of drop shape and orientation to a wider range of conditions, but for typical colloidal systems the deformation remains small at shear rates normally accessible in the rheometer. The data shown in Figure 3.11 was calculated from Cox s analysis. His results have been confirmed by Torza et al.16 with optical measurements. The ratio of the viscous to interfacial tension forces, Rf, was given as ... 

Figure 11 The SUMO conjugation pathway. SUMO (open drop-shaped objects) is synthesized with a C-terminai extension. SUMO-specific isopeptidases (SENPs) cieave the C-terminai extension from the SUMO precursor to produce a mature protein with giycine at the C-terminai. The mature SUMO is activated by an E1 heterodimerconsistingof Uba2 and AOS1 in an ATP-dependent reaction. The action of E1 produces a SUMO-AMP intermediate (fiiied drop-shaped object), which is passed onto an E2 caiied Ubc9. E2 passes SUMO onto an E3 iigase, which attaches SUMO to the substrate. SUMO attachment is reversibie and can be removed by SENPs.

These derivations have been described in detail (15). However, the relationship in Equation 5 was found to be very unsuitable for the determination of yij, since the curvatures are not easily evaluated from the photographic images. Especially, the older studies were unsatisfactory, arising from the inadequate optical and photographic techniques. In a later analysis an empirical procedure was described (21) which defined a function, S, which determines the drop shape as ... 

The resulting half-tear-drop-shaped impedance (defined here as Ac/AAai(c>) at x = 0) is somewhat... 

Shape of the liquid drop (Pendant drop method) The liquid drop forms as it flows through a tubing (Figure 2.11). At a stage just before it breaks off, the shape of the pendant drop has been used to estimate y. The drop shape is photographed and, from the diameter of the shape, y can be accurately determined. 

Drop shape method (can also be used for high pressure and temperature)... 

Fic. 2. Drop shape at formation Null and Johnson model (Nl). 

Fig. 6. Different drop shapes of endotamponade materials in water (a) PFCL, (b) partial fluorinated liquid and (c) heavier than water silicone oil.

A reasonable approximation to the observed profile of many drops and bubbles is a combination of two half oblate spheroids with a common major axis and different minor axes (B8, FI). This observation has been used (Wl) to propose a model from which bubble and drop shapes can be estimated at... 

Figure 20.7 Change of mercury drop shape with size.

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. 

DYNAMIC INTERFACIAL TENSION DETERMINATION BY THE DROP SHAPE TECHNIQUE... 

---