Drop number method

Instead of measuring the weight directly we may calculate it from the volume and the density the drop volume method has been applied by Harkins chiefly to the measurement of the tension between two liquid phases, and it probably falls little short in accuracy from the previous method. More frequently it has been j modified, especially for biochemical purposes, as a drop number method that is, a known volume of liquid iFallbwed oo nov. of a tube, and the number of drops formed is compared with that formed by a standard fluid. This method is necessarily very rough. 

From the foregoing considerations it will be apparent that the lower the surface tension at the oil/water interface, the smaller will be the size of the drops of oil formed in an emulsion. Donnan s drop-number method is a simple and convenient means of determining or comparing oil/detergent solution interfacial surface tension. The apparatus is shown in Fig. 9.12, in which a pipette A of about 5 ml capacity is provided with a capillary tube B... 

The Drop Number Method, because of its practical convenience and a good degree of reliability, is commonly employed for laboratory measurement of surface tension. 

Determination of surface tension of a liquid, say CCI. benzene, alcohol etc., by drop number method... 

Fig. 4.2 Electrocapillary curves of 0.1 m aqueous solutions of KF, KC1, KBr, KI and K2S04 obtained by means of the drop-time method (page 233). The slight deviation of the right-hand branch of the S042- curve is caused by a higher charge number of sulphate. (By courtesy of L. Novotny)...

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. 

The experiment was therefore varied by allowing the oil to rise through the solution in very fine drops of definite size. The change in concentration was again measured by taking the drop number before and after treatment with a known number of drops. The principle of this altered method will be easily understood from a description of the apparatus used in a third series of experiments, in which mercury in the form of fine drops was used as the adsorbent (Fig. io). 

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. 

Drop-weight method. Here, the liquid is allowed to flow out from the bottom of a capillary tube. Drops are formed which detach when they reach a critical dimension. The weight of a drop falling out of a capillary is measured. To get a precise measure, this is done for a number of drops and the total weight is divided by this number. 

For measurement of interfacial tension see also -> Wilhelmy plate (slide) method, -> drop weight method, -> ring method. There are also a number of other static and dynamic methods for the determination the interfacial tension [viii]. 

This technique is one of oldest methods for the measurement of surface and interfacial tensions between two fluids. The precursor of this method is the so-called stalagmometer method. Essentially, it consists of counting the number of drops formed from a definite amount of liquid detaching from a capillary. This drop number is then compared with values obtained for liquids of known interfacial tension. The stalagmometer method is still used in many laboratories for a first estimation of the interfacial tension of liquids. 

To determine the onset of surfactant aggregation, necessary for the calculations of the surfactant aggregation numbers, cac was determined for 0.1% PEO at various NaCl concentrations by surface tension measurements using the drop-weight method. For this puipose, an apparatus built at the department s workshop was us. ... 

Today, thanks to the fast development of computer enhanced imaging techniques and numerical fitting procedures, the accuracy and the sampling rate of drop shape methods are substantially increased. Thus, this technique is an important tool for the investigation of adsorption dynamics, and it is particularly suitable for studying processes with characteristic times from a few seconds up to hours and even longer. In fact, there is a large number of experimental studies in which the drop shape technique is used to evaluate the adsorption equilibrium properties, like adsorption isotherms and the dynamic surface tension behaviour. The method is also extensively utilised in the study of surfactants and proteins both in liquid/liquid and liquid/air systems. 

In a number of works [124-126], the model of monodisperse micelles has been used to determine the diffusivity of the micelles Joos and van Hunsel [127] have used this model to interpret experimental data for kinetics of adsorption obtained by the drop-volume method. These authors have demonstrated that the data can be fitted by means of a simpler expression for and R , which are linear with respect to the concentration see also Refs. 77, 128, and 129. In fact, every reaction mechanism reduces to a reaction of pseudo-first-order for small deviations from equilibrium see, for example, Ref. 130, Sec. 5. 

The drop volume method [341-343] requires only a buret or a syringe (Fig. 9.22). Either the volume required to form the drop, V, is measured or the number of drops formed by a measured volume of liquid is counted ... 

For larger systems, various approximate schemes have been developed, called mixed methods as they treat parts of the system using different levels of theory. Of interest to us here are quantuin-seiniclassical methods, which use full quantum mechanics to treat the electrons, but use approximations based on trajectories in a classical phase space to describe the nuclear motion. The prefix quantum may be dropped, and we will talk of seiniclassical methods. There are a number of different approaches, but here we shall concentrate on the few that are suitable for direct dynamics molecular simulations. An overview of other methods is given in the introduction of [21]. 

The correct treatment of boundaries and boundary effects is crucial to simulation methods because it enables macroscopic properties to be calculated from simulations using relatively small numbers of particles. The importance of boundary effects can be illustrated by considering the following simple example. Suppose we have a cube of volume 1 litre which is filled with water at room temperature. The cube contains approximately 3.3 X 10 molecules. Interactions with the walls can extend up to 10 molecular diameters into the fluid. The diameter of the water molecule is approximately 2.8 A and so the number of water molecules that are interacting with the boundary is about 2 x 10. So only about one in 1.5 million water molecules is influenced by interactions with the walls of the container. The number of particles in a Monte Carlo or molecular dynamics simulation is far fewer than 10 -10 and is frequently less than 1000. In a system of 1000 water molecules most, if not all of them, would be within the influence of the walls of the boundary. Clecirly, a simulation of 1000 water molecules in a vessel would not be an appropriate way to derive bulk properties. The alternative is to dispense with the container altogether. Now, approximately three-quarters of the molecules would be at the surface of the sample rather than being in the bulk. Such a situation would be relevcUit to studies of liquid drops, but not to studies of bulk phenomena. 

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