Harkins correction factor

Fig. 12.4 Harkins correction factor for formation of drops or bubbles, accounting for residual volume retained at the orifice when detachment occurs.

Harkins and Jordan [43] found, however, that Eq. 11-26 was generally in serious error and worked out an empirical correction factor in much the same way as was done for the drop weight method. Here, however, there is one additional variable so that the correction factor/ now depends on two dimensionless ratios. Thus... 

Greek Letters correction factor of Harkins and Brown [Eq. (132)]... 

The correction factor /3 allows for the non-vertical direction of the tension forces and for the complex shape of the liquid supported by the ring at the point of detachment hence, it depends on the dimensions of the ring and the nature of the interface. Values of / have been tabulated by Harkins and Jordan145, they can also be calculated from the equation of Zuidema and Waters146. 

The correction factor < > is required because on detachment (a) the drop does not completely leave the tip, (b) the surface tension forces are seldom exactly vertical and (c) there is a pressure difference across the curved liquid surface147. (f> depends on the ratio r/Vm. Values of have been determined empirically by Harkins and Brown148,149. It can be seen that values of r/Vm between about 0.6 and 1.2 are preferable (Figure 4.8). 

However, Harkins and Jordan (1930) found that Eq. (6.94) is not precise and proposed an empirical correction factor, which depends on two dimensionless ratios... 

Values of the correction factor / were tabulated by Harkins and Jordan [see Eq. (5.7)], and a theoretical account of / was given by Freud and Freud [11]. 

A correction factor has to be applied to the measured surface tension according to a method of Harkins and Jordan [44], which has been justified theoretically by Freud and Freud [45]. Table 5 [45] shows the details of measurements for four liquids Tl is the surface tension directly obtained from the force and /l is the corrected value. The correction factor (F) is a function of R V and RJr where R is the radius... 

The interfacial tension can be obtained by measuring the force needed to remove the ring from the interface between two immiscible liquids. Because the densities of the two liquids are not greatly different, a large volume of the lower liquid is raised above the interface and quite a deep layer of the upper liquid is needed to contain it the Harkins-Jordan correction factor is now larger. 

A Kriiss K6 tensiometer with a platinum du Noiiy ring was used during the surface tension measurements, and the experiments were performed at a temperature of 20 °C. Concentrated surfactant solutions were prepared, and the pH was adjusted with sodium hydroxide or hydrochloric acid. The samples were prepared by dilution with Milli-Q water, buffered to the appropriate pH. The sample volumes were approximately 13 ml and the surface area of the samples were ca 15.5 cm. The surface tension was measured directly after pouring the liquid into the sample vessel. The surface tension value for each sample was multiplied by the appropriate correction factor, according to Harkins and Jordan. [7] The cmc was found at the break point in the surface tension versus concentration plot. 

For precise measurements, the use of a correction factor is extremely important when using this method. That is, the surface tension can be written as y = Xobs// where /obs is the observed surface tension obtained from equation 11.6 and / is a correction factor (defined in this manner so that / < 1). The need for this correction factor arises from the fact that a portion of the liquid contained in the drop remains attached to the tube when the drop detaches itself (as shown schematically in Figure 11.3), and thus the measured drop weight is less than the actual drop weight. Values of this correction factor have been empirically tabulated as a function of by Harkins and Brown (4), as well as Lando and Oakley (5). 

Zhang Z, Mori Y. (1993) Formulation of the Harkins-Brown correction factor for drop-volume description. Ind Eng Chem Res 32 2950—2952. 

The main premise of both models is that a successful theory should predict the correct cosmic abundances of all nuclides. This idea, that abundances hold the clue to nucleogenesis probably stems from a proposal by Harkins (1931) in 1915 that the abundance of an element depends on two factors ... 

---