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.

I. Studies on bacteriophage DNA's and minicircular DNA's in M. lysodeikticus and E. coli 15. II. Flow dichroism of DNA solutions

Part I

Chapter 1.....A physicochemical study of the DNA molecules from the three bacteriophages, N1, N5, and N6, which infect the bacterium, M. lysodeikticus, has been made. The molecular weights, as measured by both electron microscopy and sedimentation velocity, are 23 x 10⁶ for N5 DNA and 31 x 10⁶ for N1 and N6 DNA's. All three DNA's are capable of thermally reversible cyclization. N1 and N6 DNA's have identical or very similar base sequences as judged by membrane filter hybridization and by electron microscope heteroduplex studies. They have identical or similar cohesive ends. These results are in accord with the close biological relation between N1 and N6 phages. N5 DNA is not closely related to N1 or N6 DNA. The denaturation T_m of all three DNA's is the same and corresponds to a (GC) content of 70%. However, the buoyant densities in CsCl of Nl and N6 DNA's are lower than expected, corresponding to predicted GC contents of 64 and 67%. The buoyant densities in Cs₂SO₄ are also somewhat anomalous. The buoyant density anomalies are probably due to the presence of odd bases. However, direct base composition analysis of N1 DNA by anion exchange chromatography confirms a GC content of 70%, and, in the elution system used, no peaks due to odd bases are present.

Chapter 2.....A covalently closed circular DNA form has been observed as an intracellular form during both productive and abortive infection processes in M. lysodeikticus. This species has been isolated by the method of CsC1-ethidium bromide centrifugation and examined with an electron microscope.

Chapter 3.....A minute circular DNA has been discovered as a homogeneous population in M. lysodeikticus. Its length and molecular weight as determined by electron microscopy are 0.445 μ and 0.88 x 10⁶ daltons respectively. There is about one minicircle per bacterium.

Chapter 4.....Several strains of E. coli 15 harbor a prophage. Viral growth can be induced by exposing the host to mitomycin C or to uv irradiation. The coliphage 15 particles from E. coli 15 and E, coli 15 T^- appear as normal phage with head and tail structure; the particles from E. coli 15 TAU are tailless. The complete particles exert a colicinogenic activity on E.coli 15 and 15 T^-, the tailless particles do not. No host for a productive viral infection has been found and the phage may be defective. The properties of the DNA of the virus have been studied, mainly by electron microscopy. After induction but before lysis, a closed circular DNA with a contour length of about 11.9 μ is found in the bacterium; the mature phage DNA is a linear duplex and 7.5% longer than the intracellular circular form. This suggests the hypothesis that the mature phage DNA is terminally repetitious and circularly permuted. The hypothesis was confirmed by observing that denaturation and renaturation of the mature phage DNA produce circular duplexes with two single-stranded branches corresponding to the terminal repetition. The contour length of the mature phage DNA was measured relative to φX RFII DNA and λ DNA; the calculated molecular weight is 27 x 10⁶. The length of the single-stranded terminal repetition was compared to the length of φX 174 DNA under conditions where single-stranded DNA is seen in an extended form in electron micrographs. The length of the terminal repetition is found to be 7.4% of the length of the nonrepetitious part of the coliphage 15 DNA. The number of base pairs in the terminal repetition is variable in different molecules, with a fractional standard deviation of 0.18 of the average number in the terminal repetition. A new phenomenon termed "branch migration" has been discovered in renatured circular molecules; it results in forked branches, with two emerging single strands, at the position of the terminal repetition. The distribution of branch separations between the two terminal repetitions in the population of renatured circular molecules was studied. The observed distribution suggests that there is an excluded volume effect in the renaturation of a population of circularly permuted molecules such that strands with close beginning points preferentially renature with each other. This selective renaturation and the phenomenon of branch migration both affect the distribution of branch separations; the observed distribution does not contradict the hypothesis of a random distribution of beginning points around the chromosome.

Chapter 5....Some physicochemical studies on the minicircular DNA species in E. coli 15 (0.670 μ, 1.47 x 10⁶ daltons) have been made. Electron microscopic observations showed multimeric forms of the minicircle which amount to 5% of total DNA species and also showed presumably replicating forms of the minicircle. A renaturation kinetic study showed that the minicircle is a unique DNA species in its size and base sequence. A study on the minicircle replication has been made under condition in which host DNA synthesis is synchronized. Despite experimental uncertainties involved, it seems that the minicircle replication is random and the number of the minicircles increases continuously throughout a generation of the host, regardless of host DNA synchronization.

Part II

The flow dichroism of dilute DNA solutions (A₂₆₀≈0.1) has been studied in a Couette-type apparatus with the outer cylinder rotating and with the light path parallel to the cylinder axis. Shear gradients in the range of 5-160 sec.^-1 were studied. The DNA samples were whole, "half," and "quarter" molecules of T4 bacteriophage DNA, and linear and circular λb₂b₅c DNA. For the linear molecules, the fractional flow dichroism is a linear function of molecular weight. The dichroism for linear A DNA is about 1.8 that of the circular molecule. For a given DNA, the dichroism is an approximately linear function of shear gradient, but with a slight upward curvature at low values of G, and some trend toward saturation at larger values of G. The fractional dichroism increases as the supporting electrolyte concentration decreases.

Studies on the role of histones in the structure and function of chromatin

Studies on the dissociation of histones from chromatin by increasing concentrations of sodium deoxycholate (DOC) have shown that histrone II is removed at lowest concentrations of DOC, while slightly higher concentrations remove histones III and IV. Still higher concentrations remove histone I.

The complete separation of chromatin and ¹⁴C-DOC by sucrose sedimentation indicated that the binding of DOC to chromatin is readily and completely reversible.

The dissociation of histones from chromatin by increasing concentrations of related cholanic acids and some of their conjugated derivatives were studied. The results suggested that the driving force for the interaction between the cholanic acid anion and histones is the lowering of the activity coefficient of the cholanic acid anion which occurs when it is partially removed from solution by interaction with hydrophobic regions of the positively charged histones.

The role of histones in the structure of chromatin has been studied by comparing the effects of selective removal of histones from chromatin by increasing concentrations of DOC with those caused by NaCl (removes histone I at lowest concentrations, while higher concentrations remove histones II, III, and IV). Properties studied included thermal denaturation, sedimentation velocity, flow dichroism, relaxation times of molecules oriented in a flow field, and the irreversible disruption of a 130 S, cross-linked component of sheared chromatin. The data indicated that none of the structural or chemical parameters with which these properties are correlated show a dependence on the presence of one particular histone fraction.

The template activity (ability to prime a 0.2 M KC1 DNA-dependent RNA synthesis system catalyzed by E. coli RNA polymerase) increases from that of native chromatin (approximately 25 per cent of that pure DNA) to that of pure DNA in a fashion which shows a nearly linear relationship to the amount of histone coverage of the template. The precipitability of partially dehistonized chromatin samples in 0.15 M NaCl shows a large dependence on the presence of histone I.

Mass transfer from a cylinder to an air stream in axisymmetrical flow (an experimental study)

Mass transfer from wetted surfaces on one-inch cylinders with unwetted approach sections was studied experimentally by means of the evaporation of n-octane and n-heptane into an air stream in axisymmetrical flow, for Reynolds numbers from 5,000 to 310,000. A transition from the laminar to the turbulent boundary layer was observed to occur at Reynolds numbers from 10,000 to 15,000. The results were expressed in terms of the Sherwood number as a function of the Reynolds number, the Schmidt number, and the ratio of the unwetted approach length to the total length. Empirical formulas were obtained for both laminar and turbulent regimes. The rates of mass transfer obtained were higher than theoretical and experimental results obtained by previous investigators for mass and heat transfer from flat plates.

On the transport properties of fluid-particle flow

The hydrodynamic forces acting on a solid particle in a viscous, incompressible fluid medium at low Reynolds number flow is investigated mathematically as a prerequisite to the understanding of transport processes in two-phase flow involving solid particles and fluid. Viscous interaction between a small number of spherical particles and continuous solid boundaries as well as fluid interface are analyzed under a “point-force” approximation. Non-spherical and elastic spherical particles in a simple shear flow area are then considered. Non-steady motion of a spherical particle is briefly touched upon to illustrate the transient effect of particle motion.

A macroscopic continuum description of particle-fluid flow is formulated in terms of spatial averages yielding a set of particle continuum and bulk fluid equations. Phenomenological formulas describing the transport processes in a fluid medium are extended to cases where the volume concentration of solid particles is sufficiently high to exert an important influence. Hydrodynamic forces acting on a spherical solid particle in such a system, e.g. drag, torque, rotational coupling force, and viscous collision force between streams of different sized particles moving relative to each other are obtained. Phenomenological constants, such as the shear viscosity coefficient, and the diffusion coefficient of the bulk fluid, are found as a function of the material properties of the constituents of the two-phase system and the volume concentration of solid. For transient heat conduction phenomena, it is found that the introduction of a complex conductivity for the bulk fluid permits a simple mathematical description of this otherwise complicated process. The rate of heat transfer between particle continuum and bulk fluid is also investigated by means of an Oseen-type approximation to the energy equation.

Fast Lattice Green's Function Methods for Viscous Incompressible Flows on Unbounded Domains

In this thesis, a collection of novel numerical techniques culminating in a fast, parallel method for the direct numerical simulation of incompressible viscous flows around surfaces immersed in unbounded fluid domains is presented. At the core of all these techniques is the use of the fundamental solutions, or lattice Green’s functions, of discrete operators to solve inhomogeneous elliptic difference equations arising in the discretization of the three-dimensional incompressible Navier-Stokes equations on unbounded regular grids. In addition to automatically enforcing the natural free-space boundary conditions, these new lattice Green’s function techniques facilitate the implementation of robust staggered-Cartesian-grid flow solvers with efficient nodal distributions and fast multipole methods. The provable conservation and stability properties of the appropriately combined discretization and solution techniques ensure robust numerical solutions. Numerical experiments on thin vortex rings, low-aspect-ratio flat plates, and spheres are used verify the accuracy, physical fidelity, and computational efficiency of the present formulations.