Static drops shape

Methods Based on the Shape of Static Drops or Bubbles... 

Recently, the size and shape of a liquid droplet at the molten tip of an arc electrode have been studied,12151 and an iterative method for the shape of static drops has been proposed. 216 Shapes, stabilities and oscillations of pendant droplets in an electric field have also been addressed in some investigations. 217 218 The pendant drop process has found applications in determining surface tensions of molten substances. 152 However, the liquid dripping process is not an effective means for those practical applications that necessitate high liquid flow rates and fine droplets (typically 1-300 pm). For such fine droplets, gravitational forces become negligible in the droplet formation mechanism. 

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. 

The time required to conduct an interfacial tension experiment depends largely on the properties of the surfactants and less on the chosen measurement method. A notable exception is the drop volume technique, which, due to the measurement principle, requires substantial ly more time than the drop shape analysis method. Regardless of the method used, 1 day or more may be required to accurately determine, e.g., the adsorption isotherm (unit D3.s) of a protein. This is because, at low protein concentrations, it can take several hours to reach full equilibrium between proteins in the bulk phase and those at the surface due to structural rearrangement processes. This is especially important for static interfacial tension measurements (see Basic Protocol 1 and Alternate Protocols 1 and 2). If the interfacial tension is measured before the exchange of molecules... 

Since surface forces depend on the magnimde of the area, the drops tend to be as spherical as possible. Distortions due to gravitational forces depend on the volume of the drop. In principle, it is however possible to determine the surface tension by measurement of the shape of the drop, when gravitational and surface tension forces are comparable. Two principally different methods must be taken into account. There are methods based on the shape of a static drop lying on a solid surface or a bubble adhering underneath a solid plate, and dynamic methods, based on continuously forming and falling drops. It should be noted that all the principles described here for drops are valid also for bubbles. 

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. 

During this latter stage, the only one we shall discuss here, the shape of the drop is practically the same as it is of a static drop with the same contact angle, except very close to the edges. This static shape results from the balance of vertical capillary forces and gravity. It is usually close to a spherical cap and its exact dependence is controlled by the ratio of the radius R of the wetted spot to the... 

Circle method performs a circle fitting for the detected drop profile. The static contact angle is calculated between the baseline and the tangent of flie fitted circle at the contact points, which are the two intersection points of the baseline and the fitted drop profile. 0/2 method and circle fitting method are suitable for surfaces with small contact angles or when very small drop volumes are used because they assume no gravitation effect on the drop shape. 

The extrudate surface and cross section were examined by an scanning electron microscope (SEM, Leo FE-SEM 1530). Static contact angles were measured using a sessile drop method -axisymmetric drop shape analysis-profile (ADSA-P). 

Solid Desiccants. The sohd desiccants used in dynamic appHcations fad into a class caded adsorbents (see Adsorption). Because they are used in large packed beds through which the gas or Hquid to be treated is passed, the adsorbents are formed into soHd shapes that adow them to withstand the static (fluid plus sohd head) and dynamic (pressure drop) forces imposed on them. The most common shapes are granules, extmded pedets, and beads. 

Reactors with a packed bed of catalyst are identical to those for gas-liquid reactions filled with inert packing. Trickle-bed reactors are probably the most commonly used reactors with a fixed bed of catalyst. A draft-tube reactor (loop reactor) can contain a catalytic packing (see Fig. 5.4-9) inside the central tube. Stmctured catalysts similar to structural packings in distillation and absorption columns or in static mixers, which are characterized by a low pressure drop, can also be inserted into the draft tube. Recently, a monolithic reactor (Fig. 5.4-11) has been developed, which is an alternative to the trickle-bed reactor. The monolith catalyst has the shape of a block with straight narrow channels on the walls of which catalytic species are deposited. The already extremely low pressure drop by friction is compensated by gravity forces. Consequently, the pressure in the gas phase is constant over the whole height of the reactor. If needed, the gas can be recirculated internally without the necessity of using an external pump. 

Fig. 2.3 Shapes of static bubbles and drops (a),(b) sessile (c),(d) pendant (e) floating. (Shading denotes more dense fluid in each case.)...

Although normal pulse polarography was developed mainly for analytical purposes, it is a valuable and simple method to study kinetics of not-too-fast electrode reactions. As the other controlled potential techniques, it has the advantage of being applicable to systems where only one of the redox components is present initially. The technique is closely related to d.c. polarography [11] and the expressions discussed in this section are directly applicable to the case of d.c. polarography performed with the static mercury drop electrode (SMDE) if the correction for the spherical shape of this electrode is negligible [21, 22]. 

The shape of the system curve determines the saving potentials of using variable-speed pumps. All system head curves are parabolas, but they differ in steepness and in the ratio of their static head to friction drop. The value of variable-speed pumping increases as the system head curve becomes steeper. Therefore, in mostly friction systems, the savings will be greater. 

---