I. The effects of variations in certain parameters upon the efficiency of in vivo hemodialysis with a Kiil dialyzer. II. Interfacial structure of concurrent air-water flow in a two-inch diameter horizontal tube.

Part I

Regression analyses are performed on in vivo hemodialysis data for the transfer of creatinine, urea, uric acid and inorganic phosphate to determine the effects of variations in certain parameters on the efficiency of dialysis with a Kiil dialyzer. In calculating the mass transfer rates across the membrane, the effects of cell-plasma mass transfer kinetics are considered. The concept of the effective permeability coefficient for the red cell membrane is introduced to account for these effects. A discussion of the consequences of neglecting cell-plasma kinetics, as has been done to date in the literature, is presented.

A physical model for the Kiil dialyzer is presented in order to calculate the available membrane area for mass transfer, the linear blood and dialysate velocities, and other variables. The equations used to determine the independent variables of the regression analyses are presented. The potential dependent variables in the analyses are discussed.

Regression analyses were carried out considering overall mass-transfer coefficients, dialysances, relative dialysances, and relative permeabilities for each substance as the dependent variables. The independent variables were linear blood velocity, linear dialysate velocity, the pressure difference across the membrane, the elapsed time of dialysis, the blood hematocrit, and the arterial plasma concentrations of each substance transferred. The resulting correlations are tabulated, presented graphically, and discussed. The implications of these correlations are discussed from the viewpoint of a research investigator and from the viewpoint of patient treatment.

Recommendations for further experimental work are presented.

Part II

The interfacial structure of concurrent air-water flow in a two-inch diameter horizontal tube in the wavy flow regime has been measured using resistance wave gages. The median water depth, r.m.s. wave height, wave frequency, extrema frequency, and wave velocity have been measured as functions of air and water flow rates. Reynolds numbers, Froude numbers, Weber numbers, and bulk velocities for each phase may be calculated from these measurements. No theory for wave formation and propagation available in the literature was sufficient to describe these results.

The water surface level distribution generally is not adequately represented as a stationary Gaussian process. Five types of deviation from the Gaussian process function were noted in this work. The presence of the tube walls and the relatively large interfacial shear stresses precludes the use of simple statistical analyses to describe the interfacial structure. A detailed study of the behavior of individual fluid elements near the interface may be necessary to describe adequately wavy two-phase flow in systems similar to the one used in this work.

Joule-Thomson coefficients of propane and n-butane

Experimental Joule-Thomson measurements were made on gaseous propane at temperatures from 100 to 280˚F and at pressures from 8 to 66 psia. Joule-Thomson measurements were also made on gaseous n-butane at temperatures from 100 to 280˚ and at pressures from 8 to 42 psia. For propane, the values of these measurements ranged from 0.07986˚F/psi at 280˚F and 8.01 psia to 0.19685˚F/psi at 100˚F and 66.15 psia. For n-butane, the values ranged from 0.11031˚F/psi at 280˚F and 9.36 psia to 0.30141˚F/psi at 100˚F and 41.02 psia. The experimental values have a maximum error of 1.5 percent.

For n-butane, the measurements of this study did not agree with previous Joule-Thomson measurements made in the Laboratory in 1935. The application of a thermal-transfer correction to the previous experimental measurements would cause the two sets of data to agree. Calculated values of the Joule-Thomson coefficient from other types of p-v-t data did agree with the present measurements for n-butane.

The apparatus used to measure the experimental Joule-Thomson coefficients had a radial-flow porous thimble and was operated at pressure changes between 2.3 and 8.6 psi. The major difference between this and other Joule-Thomson apparatus was its larger weight rates of flow (up to 6 pounds per hour) at atmospheric pressure. The flow rate was shown to have an appreciable effect on non-isenthalpic Joule-Thomson measurements.

Photographic materials on pages 79-81 are essential and will not reproduced clearly on Xerox copies. Photographic copies should be ordered.

Some properties of the coefficients of cyclotomic polynomials

An explicit formula is obtained for the coefficients of the cyclotomic polynomial F_n(x), where n is the product of two distinct odd primes. A recursion formula and a lower bound and an improvement of Bang’s upper bound for the coefficients of F_n(x) are also obtained, where n is the product of three distinct primes. The cyclotomic coefficients are also studied when n is the product of four distinct odd primes. A recursion formula and upper bounds for its coefficients are obtained. The last chapter includes a different approach to the cyclotomic coefficients. A connection is obtained between a certain partition function and the cyclotomic coefficients when n is the product of an arbitrary number of distinct odd primes. Finally, an upper bound for the coefficients is derived when n is the product of an arbitrary number of distinct and odd primes.

Friction and heat transfer coefficients in smooth and rough pipes with dilute polymer solutions

Measurements of friction and heat transfer coefficients were obtained with dilute polymer solutions flowing through electrically heated smooth and rough tubes. The polymer used was "Polyox WSR-301", and tests were performed at concentrations of 10 and 50 parts per million. The rough tubes contained a close-packed, granular type of surface with roughness-height-to-diameter ratios of 0.0138 and 0.0488 respectively. A Prandtl number range of 4.38 to 10.3 was investigated which was obtained by adjusting the bulk temperature of the solution. The Reynolds numbers in the experiments were varied from =10,000 (Pr= 10.3) to 250,000 (Pr= 4.38).

Friction reductions as high as 73% in smooth tubes and 83% in rough tubes were observed, accompanied by an even more drastic heat transfer reduction (as high as 84% in smooth tubes and 93% in rough tubes). The heat transfer coefficients with Polyox can be lower for a rough tube than for a smooth one.

The similarity rules previously developed for heat transfer with a Newtonian fluid were extended to dilute polymer solution pipe flows. A velocity profile similar to the one proposed by Deissler was taken as a model to interpret the friction and heat transfer data in smooth tubes. It was found that the observed results could be explained by assuming that the turbulent diffusivities are reduced in smooth tubes in the vicinity of the wall, which brings about a thickening of the viscous layer. A possible mechanism describing the effect of the polymer additive on rough pipe flow is also discussed.