Drop volume

This is a fairly accurate and convenient method for measuring the surface tension of a liquid-vapor or liquid-liquid interface. The procedure, in its simpli-est form, is to form drops of the liquid at the end of a tube, allowing them to fall into a container until enough have been collected to accurately determine the weight per drop. Recently developed computer-controlled devices track individual drop volumes to = 0.1 p [32]. 

Harkins and Brown [21] concluded that / should be a function of the dimensionless ratio rja or, alternatively, of where V is the drop volume. (See... 

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 automated pendant drop technique has been used as a film balance to study the surface tension of insoluble monolayers [75] (see Chapter IV). A motor-driven syringe allows changes in drop volume to study surface tension as a function of surface areas as in conventional film balance measurements. This approach is useful for materials available in limited quantities and it can be extended to study monolayers at liquid-liquid interfaces [76],... 

Piezoelecttic impulse ink-jet printers ate especially sensitive to bubbles in the ink. A bubble in the firing chamber absorbs some of the comptessional force from the flexing of the chamber wall and reduces drop volume and drop velocity, thereby affecting print quaHty. Because of the limited range of motion of the crystal, bubbles ate not readily ejected, and the loss of print quaHty owing to their presence is persistent. 

Solution. Draw into the iv diagram the characteristic curve of the fan and the duct-pressure-drop volume flow dependency. The latter is a parabola passing through the origin with the following equation ... 

To investigate the influence of swelhng of the substrate by the contacting liquid, the contact angle 6 of sessile drops of tricresylphosphate, TCP (drop volume 2 p,L, viscosity t = 70 cP, surface tension = 40.9 mN m ), has been measured as a function of time after deposition, t, on flat, smooth, horizontal surfaces of soft and rigid solids at 20°C. The method of measurement of contact angle is the same as in Section Ill.A. 

The dynamic interfacial tension behavior of reacting acidic oil-alkaline solutions has been studied for both an artificially acidified synthetic oil and a real crude oil at various concentrations [131,132] with either a drop volume tensiometer or a spinning drop tensiometer. 

S. D. Ball. Comparison of transient interfacial tension behaviours of oiUalkaline systems as measured by the drop volume and spinning drop tensiometers. PhD thesis, Ottawa Univ, 1995. 

Recently, Samec et al. [38] have investigated the same system by the video-image pendant drop method. Surface tension data from the two studies are compared in Fig. 2, where the potential scale from the study [36] was shifted so that the positions of the electrocapillary maxima coincide. The systematic difference in the surface tension data of ca. 3%, cf. the dotted line in Fig. 2, was ascribed to the inaccurate determination of the drop volume, which was calculated from the shape of the drop image and used further in the evaluation of the surface tension [38]. A point of interest is the inner-layer potential difference A (pj, which can be evaluated relative to the zero-charge potential difference A cpp c by using Eq. 

As i,d is proportional to f2/3 (drop volume is proportional to t, so its surface area is proportional to i2 3) and is also proportional to t 112 (because of the concentration gradient decreasing with x in addition to D expressed in cm2s so that D112 occurs in the equation), we obtain the relationship i,d = ktlie. 

Fig. 25. Drop size distributions f(V,p)] based on drop volume (V) obtained by repeated stretching and breakup in a journal bearing flow for different viscosity ratios (p) (left). The curves for the different distributions overlap when the distribution is rescaled (right) (Muzzio, Tjahjadi, and Ottino, 1991).

Collins and Knudsen (C6) recently reported drop-size distribution produced by two immiscible liquids in turbulent flow, and the average drop size can be calculated from these distributions. From a knowledge of the average drop size, the interfacial area per drop a and the drop volume can be calculated. The number of drops per unit volume is given by... 

Propionic acid is extracted with water from a dilute solution in benzene, by bubbling the benzene phase into the bottom of a tower to which water is fed at the top. The tower is 1.2 m high and 0.14 m2 in area, the drop volume is 0.12 cm3, and the velocity of rise is 12 cm/s. From laboratory tests the value of Kw during the formation of drops is 7.6 x 10-5 kmol/sm2 (kmol/m3) and for rising drops Kw = 4.2 x 10-5 kmol/sm2 (kmol/m3). 

Tests have been carried out on the rate of extraction of benzoic acid from a dilute solution in benzene to water, in which the benzene phase was bubbled into the base of a 25 mm diameter column and the water fed to the top of the column. The rate of mass transfer was measured during the formation of the bubbles in the water phase and during the rise of the bubbles up the column. For conditions where the drop volume was 0.12 cm3 and the velocity of rise 12.5 cm/s, the value of Kw for the period of drop formation was 0.000075 kmol/s m2 (kmol/m3), and for the period of rise 0.000046 kmol/s m2 (kmol/s m3). 

When a dispersed phase is passed through a nozzle immersed in an immiscible continuous phase, the most important variables influencing the resultant drop size are the velocity of the dispersed phase, viscosity and density of continuous phase, and the density of the dispersed phase (G2, HI, H5, M3, Nl, P5, R3, S5). In general, an increase in continuous-phase viscosity, nozzle diameter, and interfacial tension increases the drop volume, whereas the increase in density difference results in its decrease. However, Null and Johnson (N4) do not find the influence of continuous-phase viscosity significant and exclude this variable from their analysis. Contradictory findings... 

At vanishingly small flow rates, the drop volume calculated by the equalization of the buoyancy with interfacial tension gives drop volumes higher than those observed experimentally, because of the residual drop. Harkins (H2) correction has therefore to be applied to calculated drop volumes under these conditions. Thus,... 

Another force acting on the drop is due to the kinetic energy of the dispersed-phase stream, which adds to the buoyancy force. Each of these forces has been considered to be contributing to the final drop volume. Thus, the final volume becomes... 

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... 

Kalyanasundaram, Kumar, and Kuloor (K2) found the influence of dispersed phase viscosity on drop formation to be quite appreciable at high rates of flow. The increase in pd results in an increase in drop volume. To account for this, the earlier model was modified by adding an extra resisting force due to the tensile viscosity of the dispersed phase. The tensile viscosity is taken as thrice the shear viscosity of the dispersed phase, in analogy with the extension of an elastic strip where the tensile elastic modulus is represented by thrice the shear elastic modulus for an incompressible material. The actual force resulting from the above is given by 3nRpd v. 

The final drop volume can then be obtained by using Eq. (133). 

The equation of Hayworth and Treybal (H5) is semi-empirical and is based on a force balance made by expressing the various contributing forces acting on the drop as fractions of the total drop volume. This procedure is probably not wholly justified, since the exact instant at which the forces act is not known, nor is their quantitative contribution to the total volume. The model also neglects the influence of dispersed-phase viscosity. 

Fig. 22. Effect of viscosity of continuous phase on drop volume.

Fig. 23. Effect of volumetric flow rate on drop volume.

Comparison of Drop Volume Data Available in Literature with Those Calculated by the Unified Model... 

If one considers a system consisting of water (with or without added electrolyte) + oil + surfactant (with or without a cosurfactant) at equilibrium, there will most likely be present more than two phases (due to the formation of emulsion or microemulsion). The determination of the interfacial tension, Yij> between the two liquid phases is, therefore, of much importance, in order to understand the forces which stabilize these emulsions or microemulsions. The interfacial tension can be measured by using a variety of methods, as described in detail in surface chemistry text-books (1-3). If the magnitude of yij is of the order of few mN/m (=dyne/ cm), then the methods generally used are Wilhelmy plate method or the drop volume (or weight) method (1-4). However, in certain systems ultra-low (or low) interfacial tensions have been reported. Since these low values are reported to be essential in order to mo-... 

R. Kumar and N. R. Kuloor, The Formation of Bubbles and Drops Volume 9... 

Carroll, B.J, (1976). The accurate measurement of contact angle, phase contact areas, drop volume, and Laplace excess pressure in drop-on-fiber system. J. Colloid. Interface Sci. 57, 488-495. 

Print buffers 3X SSC, 3X SSC + 50% DMSO, and 3X SSC + 1.5 M betaine were evaluated at 40, 60, and 80% RH for spot intensity, spot diameter, intraspot variation, and CV (Figure 4.35). The reductions in quill drop volumes and droplet drying times were measured by video microscope and the quill reservoir volume changes determined by weight. In summary, "Solvent evaporation from the print buffer reservoir is the major factor responsible for the variations in the transfer of fluid to fhe slide surface."... 

Dilute the trials at given times after set up by adding a volume of buffer or of protein in buffer at a volume which is 5-10% of the total drop volume. 

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