R-3 Repository :: Browsing by Author "Hellums, J. David"

Browsing by Author "Hellums, J. David"

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A numerical finite difference solution to a jet impinging on a liquid surface
(1965) Fagela-Alabastro, Estrella B; Hellums, J. David
A numerical finite difference solution to the problem of a two dimensional gas jet impinging on a liquid surface at right angles has been obtained in this work. For an idealized situation of flow, the liquid surface profiles and the gas jet free streamlines were determined at several values of the parameter X corresponding to different physical situations, the parameter Y being defined as equal to 2SgVj2/gcSlb. The most recent significant works along this line are the experimental investigations performed by Banks and Chandrasekhara and that of Olmstead , the latter being an analytical solution by methods of conformal mapping. Comparison of the numerical results obtained in this paper with Olmstead's results shows very good agreement for small values of y. However, for larger values of y corresponding to higher jet velocities, the liquid profile obtained numerically has a more complicated shape. Besides a lip, the numerical solution also shows the presence of ripples on the liquid surface. This phenomenon is supported by photographs taken during experimental runs by Banks and Chandrasekhara.
A study on the resistances to oxygen transport in the microcirculation
(1993) Liu, Charles Y.; Hellums, J. David
A study on the resistances to oxygen transport in the microcirculation has been conducted. In Part I of this work, the oxygen permeability of cultured bovine aortic and human umbilical vein endothelial cell monolayers was measured directly in vitro. The monolayers were cultured on silicone rubber membranes and placed in a carefully calibrated diffusion cell immersed in a 37$\sp\circ$C waterbath. The lower and upper chambers of the diffusion cell were filled with well-stirred, degassed saline and flushed with humidified oxygen respectively. The permeability of the endothelial monolayers was determined from the rate of increase of the oxygen partial pressure in the saline, as monitored by a Clark-type polarographic electrode. The lower bound on the permeability of the cultured endothelial monolayer was determined to be 1.42 $\pm$ 0.33 (s.d.) $\times$ 10$\sp{-6}$ cm$\sp2$/sec for bovine aortic endothelial cells and 1.96 $\pm$ 0.52 (s.d.) $\times$ 10$\sp{-6}$ cm$\sp2$/sec for human umbilical vein endothelial cells. The best value of the permeability of human umbilical vein endothelial monolayers determined in this work was 8.73 $\pm$ 3.21 (s.d.) $\times$ 10$\sp{-6}$ cm$\sp2$/sec. This value of permeability indicates that the resistance to oxygen transport in the endothelium is not as high as some previous studies indicate and is not of dominant importance in determining oxygen transport to tissue. In Part II of this work, the effect of hemoglobin S (HbS) polymerization on the oxygen effective diffusivity in sickle erythrocytes was studied at 25$\sp\circ$C using the diffusion cell apparatus. The effective oxygen diffusivity in fully oxygen saturated 10.2 g/dl hemoglobin A (HbA) solution and normal erythrocytes measured in this work were in excellent agreement with prior workers' measurements of diffusivity unfacilitated by hemoglobin. Furthermore, at full oxygen saturation, the effective oxygen diffusivity was not significantly different in sickle and normal erythrocytes. However, when the average oxygen tension in the samples was decreased progressively over the time course of the experiment, the effective diffusivity was significantly different in normal erythrocytes compared to sickle erythrocytes. It can therefore be concluded that HbS polymerization has a significant effect on the resistance to oxygen transport in sickle erythrocytes not fully saturated with oxygen.
Effect of hemoglobin polymerization on the oxygen transport in hemoglobin solutions and packed cells
(1997) Budhiraja, Vikas; Hellums, J. David
The effect of hemoglobin polymerization on the facilitated transport of oxygen in systems containing polymerized hemoglobins has been studied experimentally. In part I of this work, the oxygen transport efficacy of a candidate blood substitute based on polymerized bovine hemoglobin was studied. The diffusion of dissolved oxygen in the polymerized hemoglobin samples was not different from that in the unaltered hemoglobin solutions. However, in the high oxygen tension gradient (HOTG) decreasing pO$\sb2$ experiments at 37$\sp\circ$C, while the augmented oxygen transport was almost double than that of the simple diffusive flux of oxygen in the case of the latter, it was only increased by 30% in the case of polymerized hemoglobin. The lower facilitated oxygen transport is due to the decreased diffusion coefficient as well as the decreased oxygen affinity of the polymerized hemoglobin. For lower pO$\sb2$ gradients in the range of physiological significance (constant, low oxygen tension gradient, CLOTG, experiments), the oxygen transport in the polymerized hemoglobin samples was approximately the same as in unpolymerized sample over a wide range of oxygen tensions. At lower oxygen tensions, there was a significant augmentation effect, less than in the HOTG experiment and less for the polymerized than for the unploymerized Hb. In order to further confirm the results of diffusion cell experiments, in part II of this work, the diffusion coefficients of various unpolymerized and polymerized hemoglobins were measured using the PFG NMR technique. The diffusion coefficient values were in good agreement with those estimated from the diffusion cell experiments. The effect of hemoglobin polymerization on oxygen transport in sickle erythrocytes at 37$\sp\circ$C was studied in part III of this work. HOTG and CLOTG decreasing pO$\sb2$ diffusion cell experiments conducted on packed sickle cells show negligible enhancement of oxygen transport by sickle hemoglobin. Diffusion coefficients of unpolymerized HbS in the solution phase of slowly deoxygenating sickle cells was measured using PFG NMR technique. After an initial decrease the hemoglobin diffusion coefficient stays constant suggesting that though the polymer does offer appreciable resistance, it is not very high so as to drastically reduce the diffusion of hemoglobin and oxygen.
Numerical solutions for flow development and heat transfer of variable viscosity fluids
(1963) Rosenberg, David Eugene; Hellums, J. David
The equations of change for developing flow and heat transfer in a tube were solved by an implicit numerical technique on the IBM 1620 computer. Radial heat convection and the inertial terms in the equation of momentum, which previous workers have neglected, were taken into account, along with the dependence of viscosity on temperature. The approximation that the inverse of viscosity varies linearly with temperature was used. Other fluid properties were held constant. Both parabolic and uniform entering velocity profiles were considered. The three parameters were therefore the velocity profile and the Prandtl number of the entering fluid and the ratio of the viscosity at the wall temperature to that of the entering fluid. Neglecting the variation of viscosity, the values of the local Nusselt number, parabolic entering velocity profile case, were found to coincide with the Graetz-Leveque analytic constant parabolic velocity profile solution, as did the uniform entering velocity solutions for high Prandtl numbers. For low Prandtl numbers, the uniform entering case solutions corresponded to the Graetz analytic constant uniform velocity profile solution. For moderate Prandtl numbers for the uniform entering case, the solutions corresponded to the Graetz-Leveque curve for long tubes and for short tubes fell between the Graetz-Leveque and Graetz curves. The effect of the viscosity dependence on heat transfer was found to depend on the Prandtl number, being negligible for low Prandtl numbers, and very pronounced for high Prandtl numbers. A similar effect was notided for 'pressure drop, for the parabolic case only. The pressure drop was invariant with the Prandtl number for the majority of the uniform cases. The actual dependence of heat transfer on the viscosity ratio was found to be very complicated. For large entrance to wall viscosity ratios(heating), the values for the Nusselt number approached the Graetz uniform velocity curve as an upper limit. For increasingly larger wall to entrance viscosity ratios(cooling) a similar lower limit was approached. The logarithm of the pressure drop was found to vary linearly with the logarithm of the viscosity ratio. For the uniform case, the pressure droppdecreased with increasing tube length; and for the parabolic case, it was invariant with .tube length. The results for the parabolic entering velocity case were found compatible with the experimental results of Sieder and Tate. Terms involving the radial velocity were found to be negligible for both entering profiles for long tubes. For the parabblic case only, the inertial terms in the equation of momentum were also negligible for long tubes.
Numerical solutions for laminar flow heat transfer and pressure drop in circular tubes for variable property fluids
(1963) Lehigh, Walter Robert; Hellums, J. David
A numerical solution was developed for steady state heat transfer and pressure drop through circular tubes from the coupled equations of motion and energy. The energy equation was integrated numerically by use of finite difference approximations to obtain local temperatures. Axial conduction, radial convection and viscous dissapation were neglected. The equation of motion was integrated analytically. Radial acid angular velocities were taken as zero. From a one-dimensional momentum balance in the axial direction by assumption of constant pressure drop over each small tube length, newtonian behavior and constant density throughout the radial layers, an integral expression was obtained for the axial velocity as a function of viscosity. The viscosity was considered solely as a function of temperature. Each axial step in the nemerical solution began by calculating the viscosity profile from the temperature profile by means of an empirical relationship based on an experimental fluid viscosity parameter. The fluid was assumed to enter the tube ar a uniform temperature. The velocity profile was then calculated from the viscosity profile by use, of the integrated equation of motion. The temperature profile was then extrapolated a short distance down the tube by the explicit solution of a forward step finite difference form of the energy equation. Temperature and velocity gradients were measured at the wall. For a given experimental fluid viscosity parameter the method was demonstrated on a digital computer with a series of inlet fluid temperatures and a constant tube wall temperature for small temperature driving forces. Numerically calculated values of friction factor were lower than experimentally obtained values, but approached the theoretical value predicted by newtonian flow as isothermal flow was approached. Numerically calculated values of the local Nusselt ne.nber agreed closely with the analytical solution of Yamagata for constant fluid core temperature and constant fluid density.
Oxygen transport by hemoglobin-based blood substitutes
(1997) Page, Thomas Carey; Hellums, J. David
A dual track approach has been applied to the study of oxygen transport behavior of erythrocyte/hemoglobin mixtures flowing in microvessels. The method includes experimental and theoretical modeling of the microcirculation. An experimental in vitro 27 $\mu$m diameter capillary model was developed to provide detailed oxygen flux measurements for homeglobin solutions, erythrocyte suspensions, and erythrocyte/hemoglobin solution mixtures. The experimental apparatus includes computerized data acquisiton and control coupled to a Leitz Toolmaker Microscope-based, dual wavelength microspectrophotomer. Fractional oxygen saturation may be determined for various axial positions, and the resulting experimental data have been shown to agree well with simulations calculated from previously developed theoretical models of oxygen transport in hemoglobin solutions and rbc suspensions. Direct comparison of hemoglobin solutions with rbc suspensions of the same overall hemoglobin concentration and oxygen affinity shows that hemoglobin solutions are more efficient transporters of oxygen. Experiments on polymerized hemoglobin suggests that some heme pockets may have not be available for oxygen transport. The quality and quantity of the experimental data represent a significant improvement over previous experimental designs, and the results confirm existing oxygen transport models. Ultrapurified, native and polymerized bovine hemoglobin/red blood cell mixtures were studied in the capillary. Dose response plots were generated by varying the extracellular to intracellular hemoglobin distribution ratio. Increased extracellular hemoglobin concentration increased oxygen transport efficiency for both uptake and release. When only 10% of the total hemoglobin was extracellular, half of the increased efficiency of pure hemoglobin solutions was reached. When half the hemoglobin was extracellular, the mixtures behaved like hemoglobin solutions. A mathematical model of the mixture experiments initially failed to fully predict the enhancement of oxygen uptake, but well described release experiments. Consideration of shear induced augmentation led to a new hypothesis for the relative importance of extracellular mixing in rbc/hemoglobin mixtures flowing in arteriolar sized conduits. The resulting semi-predictive model matches experimental data for a variety of conditions. This model may be used to predict performance of hemoglobin-based blood substitutes.
Receptor-specific binding of von Willebrand factor to platelets in response to shear stress
(1994) McCrary, Jeffrey Kirk; Hellums, J. David
Physical and biochemical forces convert platelets in human blood in vivo from the quiescent state as freely moving, discoid, singlets to aggregates adhering to subendothelial surfaces and secreting a wide variety of bioactive substances. Platelet aggregation, one of the essential components of hemostasis, can be caused in vitro by several chemical agonists, and by shear stress, as is found in flowing blood. Platelet aggregation at high shear stress is a receptor-mediated process requiring the binding of the plasma protein von Willebrand factor (vWf) to platelets. This study was undertaken to detect and characterize by direct measurement the binding of vWf to platelets under shear stress. Three different binding assays were developed. Two utilize radioassays for detection of vWf-platelet binding, one using radioiodinated, plasma-derived vWf multimers, the other using a novel technique which produces radiolabeled, unusually large vWf multimers from human umbilical vein cell cultures. The third assay utilizes an immunoassay technique to measure extracellular vWf concentration. Each experimental technique was verified using the platelet agonist, ristocetin. The measurements reported here constitute the first direct determination of vWf multimer binding to platelets in response to shear stress. Binding of exogenous vWf multimers to platelets is detected over the entire ranges of shear stresses and times of exposure tested (15-180 dynes/cm$\sp2$ and 15-300 seconds, respectively). It is receptor-specific, involving both platelet receptors GPIb and GPIIb/IIIa without apparent interdependence. Binding of the exogenous forms persists after long periods of shear, where platelet secretion of vWf can exceed the extent of binding of exogenous vWf, resulting in a net increase in extracellular vWf concentration. Shear stress-induced binding requires large vWf multimers, and involves the secretion of adenosine diphosphate from intraplatelet granules. These results demonstrate that vWf binds to platelet receptors GPIb and GPIIb/IIIa under levels of shear stress which cause platelet aggregation in vitro, and which correspond to arterial thrombosis occurrence in vivo. The findings discussed herein thus contribute to our understanding of the role of platelets in thrombotic disorders, and may be useful in development of methods for therapy and/or prophylaxis.
Red blood cell damage by shearing stress: a study on secondary effects in the concentric cylinder viscometer
(1970) Leverett, L. Bryon; Hellums, J. David
The causes of red cell damage in artificial prostheses have been studied by several investigators. The effects of shearing stresses on cells have been investigated in the concentric cylinder viscometer. It has been demonstrated that at high shearing rates, such as can occur in an insufficient artificial valve, red cells undergo hemolysis and morphological changes similar to those seen in vivo. There are difficulties involved in the interpretation of studies of blood trauma. The difficulties arise through the possibilities of trauma from secondary effects in addition to the damage caused by shear stress. These secondary effects were studied experimentally in a concentric cylinder viscometer. One important effect is that associated with material interaction. It is well known that cell damage can result from interaction with solid surfaces. Therefore, there is a problem distinguishing damage from surface effects as opposed to damage from any other source. The surface interaction was investigated by varying the surface to volume ratio of the concentric cylinder viscometer by a factor of 2.68. It was found that at high shear stresses, above the critical shearing stress, no effect could be observed over the range of shear stresses investigated. Another secondary effect investigated was that of centrifugal forces. This was done by adding serum albumin to the blood to vary the relative density of the plasma to the cells. This addition of albumin increases the viscosity. Therefore, blood can be subjected to the same shear stresses at lower centrifugal fields. It was found that the centrifugal field had little effect on hemolysis and that in the situation with some of the cells being neutrally buoyant there was a slight augmentation of hemolysis rates. In some concentric cylinder viscometers used for blood studied a buffer layer is provided to separate the blood undergoing shear from a gas interface. There exists the possibility of mixing between the blood undergoing shear and that in the buffer layer. This was investigated using a dual isotope tag. It was found that mixing does occur. A model is provided to account for the mixing and to calculate the true herriolysis rates. It was also found that at high rotational rates hemolysis does occur in the buffer layer. As blood is sensitive to thermal damage the heat dissipation characteristics of the concentric cylinder viscometer were investigated. Design curves were obtained for steady state and for transient operation.
Studies on cell synthesis in mixed microbial populations; log phase innocula and total oxygen demand
(1962) Shivajirao, Tipirneni; Busch, A. W.; Hellums, J. David; Read, Clark P.
A study of the effects of a log-phase seeding technique and of the oxidative assimilation relations, in soluble substrates, of mixed cultures of bacteria and protozoa, as found in a typical domestic waste water, was conducted in the Environmental Engineering Laboratory of the Rice University during the 1961-1962 academic year. These studies were part of a broad investigation of the study of the Biochemical Oxygen Demand Progression in soluble substrates. This is believed to be the first work using the log-phase seeding technique in shortening the time to the plateau in oxygen utilization and in the formulation of oxidative assimilation relationships in mixed microbial populations. Previous work on the effects of log-phase seeding and microbial assimilations generally utilized pure cultures and heavy innocula of bacteria with short incubation periods. Substrates studied in this investigation were glucose, glutamic acid, a (1:1) mixture of glucose and glutamic acid, aspartic acid, acetic acid, propionic acid, and lactose. Both Warburg and dilution techniques were utilized. The log-phase seeding technique produced a marked reduction in lag for all of the substrates and a reduction in time to reach the plateau for lactose, glutamic acid, aspartic acid, and propionic acid. The general pattern of the progression of biochemical degradation of soluble substrates in shown in graph form. The plateau in oxygen utilization was highly reproducible and was characteristic for a specific substrate. Based on the data obtained, oxidative assimilation equations were developed for the substrates under study. Theoretical plateaus occurred at 41, 40, 39, 44, 50, 52, and 41 per cent of the theoretical oxygen demand in the case of glucose, a (1:1) mixture of glucose and glutamic acid, glutamic acid, aspartic acid, acetic acid, propionic acid, and lactose, respectively. The nitrogqp supplied by the standard dilution technique for B.O.D. analysis is adequate for glucose and lactose concentrations only up to 8mg/l. At the concentrations of 12.1 mg/10 utilized in this study, the resulting nitrogen deficiency yielded low values for the plateau in oxygen uptake normally representing completion of synthesis.
The kinetics of human platelet aggregation and disaggregation in controlled shear fields
(1991) Huang, Pin Ying; Hellums, J. David
The objectives of this research are to contribute to a better understanding of human platelet involvement in vascular disease. To accomplish this, both the laser light scattering technique and the population balance equation are employed to study platelet aggregation kinetics. Platelet aggregation and related reactions are studied in the uniform, known shear stress field of a rotational viscometer. Laser light scattering gives direct information on the particle size distribution as the reactions occur. The light scattering approach has several advantages over conventional turbidimetric methods. Platelet kinetics results are interpreted by means of the population balance equation (PBE). The PBE mathematically expresses the conservation of mass for a collection of particles interacting with each other. Specifically, the PBE accounts for the formation and disappearance of platelets and platelet aggregates due to collision binding and breakage. The platelet number density distribution is determined both initially and at some later time. Then the PBE can satisfactorily match the observed particle histogram to give kinetic parameters as functions of time, platelet concentrations and magnitude of physical or chemical stimuli. These parameters provide information on adhesive forces and the rates of aggregation and disaggregation of the platelets, and platelet aggregates. These parameters infer the physical properties of platelets and platelet aggregates that are of potential value in increasing our understanding of the processes involved in thrombotic disease and/or therapy.
The motion of a sphere in an accelerating fluid inside a cylindrical tube, and an application to the seating of prosthetic aortic heart valves
(1967) Fry, Charles Max; Hellums, J. David
This work is concerned with the motion of a rigid sphere which is accelerated by an accelerating fluid inside a cylindrical tube where both the sphere and the fluid are initially at rest. The investigation is valid for laminar flow and slow sphere motion relative to the fluid. In Part I an exact solution of the Navier-Stokes equation is obtained for the flow of an incompressible Newtonian fluid in a cylindrical tube under the influence of an imposed pressure gradient which increases linearly with time. Then a one-dimensional momentum balance is used to solve the same problem. Also, since the exact solution does not converge well for very small times, a small time solution is derived using Laplace transform techniques. The solutions are compared graphically and approximate regions of validity for each are obtained. In Part II the motion of a sphere is studied where the sphere has been placed in the fluid of Part I before the fluid motion begins, so that both the sphere and the fluid are initially at rest. A lower bound is found for the velocity of the sphere with respect to the tube for each of the solutions for the fluid velocity of Part I. The results are applied to the problem of the mechanism of seating of prosthetic aortic heart valves.

Browsing by Author "Hellums, J. David"

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