Langmuir 1991, 7, 1550
1550
Notes The Capillary Rise between Two Concentric Cylinders: Supplementary Values Gerald A. Bottomley
School of Chemistry, University of Western Australia, Nedlands, 6009, Australia Receioed August 13,1990
Information presented here supplements earlier tabulated values' of the capillary rise at the annular interface between two vertical concentric cylindrical tubes. In a major criticalanalysisrecommendingthe maximum bubble pressure method of measuring surface tension, Mysels2 applied the previous tables to assess possible corrections in certain experimental circumstances. The additional capillary rise values provided graphically here may be needed by experimentalists using small-diameter inner capillaries. As previously the capillary rise (2)and inner (Y) and outer ( X ) tube radii are given in dimensionless form, so that when each is multiplied by the linearly dimensioned Laplace constant, ( 2 ~ / p g ) 1 /the ~ , dimensioned form is recovered (a,interfacialtension;p, densitydifferenceacross interface, g, acceleration due to gravity). Figure 1 shows capillary rise contours (note for 1002) as a function of inner tube radius Y and outer tube radius X, all three quantities in dimensionlessform. The spacing and range of the contours are intended to be suitable for estimates of small corrections. Below the graph's range where additional values are needed for safe interpolation, the sharply turning contours end at Y = 0 at values of X (1) Bottomley, G. A. A w t . J. Chem. 1974,27, 2297. (2) Mysels, K. J. Colloids Surf. 1990,43, 241.
Figure 1. Contour Linea giving values of lo02as a function of inner tube radius Y and outer tube radius X,all three quantities converted to dimensionless form by use of Laplace constant as defined in text.
given to high precision by Lane3being the capillary rises for an outer tube only. Acknowledgment. Some numerical processing was kindly undertaken by Dr. Orowan Sirichote at the Department of Chemistry, Prince of SongklaUniversity, HatYai,Thailand, while the author was in residence there June-July 1990. Supplementary Material Available: Numerical values on which the graph is based, further 2 values below Y = 0.04 in and somewhat beyond the X range of the graph and below Y = 0.1 for X down to 0.5, and some discussion (6 pages). Ordering information is given on any current masthead. (3) Lane, J. E. J. Colloid Interface Sci. 1973,42, 145.
0743-7463/91/2407-1550$02.50/00 1991 American Chemical Society
