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An implicit finite-difference technique employing orthogonal curvilinear co-ordinates is used to solve the Navier–Stokes equations for peristaltic flows in which both the wall-wave curvature and the Reynolds number are finite (§2). The numerical solutions agree closely with experimental flow visualizations. The kinematic characteristics of both extensible and inextensible walls (§3) are found to have a distinct influence on the flow processes only near the wall. Without vorticity, peristaltic flow observed from a reference frame moving with the wave will be equivalent to steady potential flow through a stationary wavy channel of similar geometry (§4). Solutions for steady viscous flow (§5) are obtained from simulation of unsteady flow processes beginning from an initial condition of potential peristaltic flow. For nonlinear flows due to a single peristaltic wave of dilatation, the highest stresses and energy exchange rates (§6) occur along the wall and in two instantaneous stagnation regions in the bolus core. A series of computations for periodic wave trains reveals that increasing the Reynolds number from 2[sdot ]3 to 251 yields a modest augmentation in the ratio of flow rate to Reynolds number but induces a much greater increase in the shear stress (§7.1). The transport effectiveness is markedly reduced for pumping against a mild adverse pressure drop (§7.2). Increasing the wave amplitude will lead to the development of travelling vortices within the core region of the peristaltic flow (§7.3).

A flexible Silastic casting of the human right atrium was developed to correspond to some in vivo human right atrium hemodynamic characteristics including chamber pressures, pulsatility, fluid output, and flow velocity. Using an infusion pump, air was introduced (10 ml in 30 s) into the superior vena cava of the model and aspirated via a catheter from different positions within the model atrial chamber. The tests were carried out at atrial inclinations of 60 degrees, 80 degrees, and 90 degrees from the horizontal and compared the aspiration efficiency of a single-orificed 16-gauge catheter to a 16-gauge multiorified (5 aperatures) catheter. Optimal air aspiration occurred with the multiorificed catheter tip positioned within the area 2.0 cm below the junction of the superior vena cava (SVC) and the atrial chamber at an inclination of 80 degrees. As much as 80 per cent of the incoming air could be aspirated under these conditions. At its optimal position the single-orificed catheter gave a maximal yield of 45 to 50 per cent aspiration when the tip was positioned 3.0 cm above the SVC and atrial chamber junction. Aspiration of air from mid right atrium (4.5 cm below the SVC-atrial junction) was poor regardless of the type of catheter used or atrial inclination. These data suggest a need for reappraisal of catheter design and placement.

Some insight into the mechanism of solid-particle transport by peristalsis is sought experimentally through a two-dimensional model study (§ 2). The peristaltic wave is characterized by a single bolus sweeping by the particle, resulting in oscillatory motion of the particle. Because of fluid-particle interaction and the significant curvature in the wall wave, the peristaltic flow is highly nonlinear and time dependent.For a neutrally buoyant particle propelled along the axis of the channel by a single bolus, the net particle displacement can be either positive or negative. The instantaneous force acting upon the particle and the resultant particle trajectory are sensitive to the Reynolds number of the flow (§ 3 and 4). The net forward movement of the particle increases slightly with the particle size but decreases rapidly as the gap width of the bolus increases. The combined dynamic effects of the gap width and Reynolds number on the particle displacement are studied (§ 5). Changes in both the amplitude and the form of the wave have significant effects on particle motion. A decrease in wave amplitude along with an increase in wave speed may lead to a net retrograde particle motion (§ 6). For a non-neutrally buoyant particle, the gravitational effects on particle transport are modelled according to the ratio of the Froude number to the Reynolds number. The interaction of the particle with the wall for this case is also explored (§ 7).When the centre of the particle is off the longitudinal axis, the particle will undergo rotation as well as translation. Lateral migration of the particle is found to occur in the curvilinear flow region of the bolus, leading to a reduction in the net longitudinal transport (§ 8). The interaction of the curvilinear flow field with the particle is further discussed through comparison of flow patterns around a particle with the corresponding cases without a particle (§ 9).

In 1965, a book was published with the title Research Frontiers in Fluid Dynamics, edited by Raymond Seeger and G. Temple. It was intended to give a panoramic view of some exciting vistas in fluid dynamics. It covered the following areas: (1) High-speed aerodynamics; (2) magnetophydrodynamics (MHD); (3) physics of fluids (low or high density, low or high temperature, etc); (4) constitutive properties of fluids (viscosity, viscoelasticity, etc.); (5) oceanography and meterology; (6) astrophysical and planetary fluid mechanics; and (7) mathematical aspects and numerical aspects. A few of these areas, such as MHD, have blossomed and faded away within a short decade. Some others, such as high-speed aerodynamics, have reached maturity and hope to keep their momentum. In the intervening years, we have witnessed that a number of fields in fluid mechanics have revived from their old times into a new life; still, some have emerged with brand new growth. For instance, the subject of long waves has had a colorful development, with the result of improving our understanding of at least seven different physical phenomena, though originally the solitary water wave was its home base. Low Reynolds number flows have again received new stimuli from many needed applications such as aerosol physics, two-phase flows, rheology, geophysics of the earth interior, as well as micro and molecular biology. Oil exploration has motivated various aspects of marine-related research and development, giving ever-increasing activities in ocean engineering. The energy program, a new glamorous field by its own importance, has brought forth investigations of fluid mechanical problems pertaining to nuclear, geothermal, solar, wind, ocean wave, and other forms of energy sources. Riding on the waves of these broad movements that have carried us thus far, we now hope to forecast the future of fluid mechanics research in 1986. We may like to put the focus at a slightly different depth and ask: What will be the most significant areas of fluid mechanics that by 1986 will enjoy the best prospects of vigorous development, most rewarding not only to the fluid dynamicist but also to mankind, and by then, still offer the expectation of longevity into the 1990's? The task is almost as hard as to make a prophecy on what the political world will be in 1986.

Two dimensionless forms of the Navier-Stokes equations are derived for unsteady incompressible flows with movable boundaries. Temporal variations of flow parameters and geometry are often seen when the motions of fluid and solid are interrelated. The time-dependent boundary conditions—both geometrical and fluid mechanical—are cast into the equations, making the problems simpler for computational flow simulation. These paramaters can be viewed as the forcing functions in the Navier-Stokes equations. Two flow problems are used to demonstrate this approach, one for axisymmetrical blood flow in an artery with assisted pumping of a balloon, and the other for two-dimensional flow past a finite plate with oscillatory motion. Both cases involve active and passive (flow-induced) motions of the solid boundaries.

A study was undertaken to investigate the applicability of the arteriovenous mode of perfusion for partial support of neonatal respiration. Perigestational lambs, delivered by cesarean section, served as the animal model of respiratory distress. Arteriovenous flow was accomplished between a single umbilical artery and vein. A microchannel membrane oxygenator was used to provide partial respiratory support to the newborn lambs. Total systemic flow, pulmonary blood flow, and pulmonary vascular resistance were assessed at various rates of arteriovenous perfusion and correlated with systemic oxygenation. A reduction in right-to-left shunting of blood and pulmonary vascular resistance occurred as arterial oxygenation rose from conditions of hypoxemia to PaO2 values higher than 50 torr. Myocardial performance was not impaired at rates of arteriovenous perfusion below 30 percent of the total systemic flow, as evidenced by normal electrocardiographic tracings, pulmonary capillary wedge pressures, and central venous pressures. Arteriovenous extracorporeal membrane oxgenation (ECMO) may be particularly suitable for use in infants with hypoxia and high pulmonary vascular resistance.

is Assistant Professor of Neurological Surgery, University of Pittsburgh, He received his basic neurosurgery training at Case Western Reserve Hospital and completed a year Fellowship in Microsurgery at the University of Pittsburgh. Dr. Yonas's research areas mainly are centered on problems of cerebral ischemia; for that study he has developed a new primate stroke model. His special interests in problems of spasticity developed during his fellowship at the University of Pittsburgh, and continues to the present.

Orthogonal curvilinear mesh networks are generated numerically between the wavy walls of two-dimensional peristaltic channels. A dual iterative procedure is developed to facilitate the conformal mapping, as well as to adjust mesh dimensions when necessary to fit the boundaries of the flow region. An implicit finite-difference technique is employed to obtain transient solutions of the Navier-Stokes equations. The effects of initial conditions on the flow establishment are discussed, along with considerations of numerical accuracy. The effects of certain nonconservative difference forms of the governing equations are explored. A calculated velocity field for a two-dimensional nonlinear peristaltic flow is supported by laboratory flow observation. The present method is applicable for laminar flow in a nonuniform channel with or without wall peristalsis.

Percutaneous balloon catheters have been used to selectively catheterize and immediately control hemorrhage in 8 patients. In 2 with gastrointestinal bleeding the balloon was positioned in the splenic artery in an attempt to reduce splenic flow and temporarily decrease splanchnic blood volume. In 1 with inoperable renal carcinoma, a temporary pressure decrease resulted in hemostasis of venous bleeding. In visceral trauma control of bleeding was possible until stabilization of vital signs permitted definitive surgery. The extent and duration of occlusion varies according to clinical indications. No significant sequelae at the puncture site have been noted following catheter removal.

Three-dimensional, time-dependent, axisymmetric flows of an incompressible Newtonian fluid in an annular tube as well as in a circular one were analyzed numerically. The flow was produced from rest by a pressure drop between the inlet and the outlet of a finite, annular (or circular) tube which was rotating around its axis. An implicit finite-difference scheme of the Navier-Stokes equations was developed to obtain the time variations of three velocity components and of the pressure as boundary conditions vary. Entrance effects on the velocity field, the pressure, and the Bernoulli-sum were analyzed.

The accelerated flow of a viscous fluid due to a suddenly established discharge in a two-dimensional conduit expansion has been determined by numerical integration of the governing differential equation. The complete form of the equation for diffusion and convection of vorticity was employed. The Reynolds number of the flow, based on the prescribed disharge, was 200. The growth of the separation zone, assuming symmetric flow, was determined. Flow and vorticity pattern were calculated at short interval of time; a selection of those pattern is presented, as well a curves showing the variation with time of the principal kinematic characteristics of the unsteady flow through the expansion.

Slow motions of purely viscous fluids in a two-dimensional conduit expansion are investigated using a finite-difference numerical scheme. The important concepts in the general theory leading to the governing differential equations of the flow are briefly discussed, and the equations are reduced to a convenient form for numerical solution. Contours of stream function, vorticity, and viscosity function in the zone of separation are compared for different values of the flow behavior index, which vary from the shear-thinning, pseudoplastic, range to the shear-thickening, dilatant, range, at four values of the generalized Reynolds number: 0, 16, 32, and 48. The results of the investigation indicate that for the separated flow of power-law fluids, shear-thinning fluids develop shorter, less intense, and more viscous eddies than do shear-thickening fluids at the same Reynolds number. It is also found that the influence of the flow behavior index is different for creeping flows than for flows at higher Reynolds numbers, i.e., at R = 0 the deviation of the eddy characteristics from Newtonian behavior is greater than at higher values of the Reynolds number.

Results of calculations and experiments on the flow of a viscous liquid through an axisymmetric conduit expansion are reported. The streamlines and vorticity contours are presented as functions of the Reynolds number of the flow. The dynamic interaction between the main flow and the captive eddy between it and the walls is analysed, and it is concluded that, for laminar flow, the main role of the eddy is that of shaping the flow with a rather small energy exchange.

L'article expose les resultats de calculs effectues a l'aide d'un ordinateur electronique, interessant la zone de decollement de l'ecoulement dans un elargissement, dans un rapport de 2 a 1, d'une conduite a deux dimensions, et presente des schemas d'ecoulement, et des profils de vorticite, correspondant a des nombres de Reynolds de 0 a 333. Deux methodes ont ete employees : dans l'une, on determine directement le regime permanent a partir d'equations sans termes non permanents, et dans l'autre, on aborde la solution par un procede asymptotique, correspondant a l'integration numerique des equations presentant des termes d'acceleration localisee. A conditions egales, la methode non permanente s'est revelee stable, au point de vue du calcul, alors que la methode permanente devenait instable ; lorsque les deux methodes etaient stables, leurs resultats montraient une excellente concordance. Les equations qui ont permis de construire le schema des differences correspondant au modele mathematique ayant servi pour la presente etude, sont les equations (7) et (8), couplees par l'intermediaire des conditions aux limites. La substitution de l'equation (7) en (8) fournirait une seule equation du 4e ordre, mais l'experience du passe a demontre la grande difficulte du traitement numerique d'une telle equation. L'etude de l'ecoulement a travers l'elargissement de la conduite s'est faite par deux methodes. L'une, que nous appellerons la methode "permanente", a consiste a calculer la solution en regime permanent, a partir de l'equation (8). et sans intervention du terme non permanent ζi; l'autre methode, que nous appellerons la methode "non permanente", etait basee sur l'application de l'equation (8) "telle quelle" a l'une des solutions deja fournies par la methode permanente. La methode non perrnanente a permis le passage, sans modification des dimensions de la maille, de l'ecoulement correspondent a un nombre de Reynolds donne, a un autre ecoulement, correspondant a un nombre de Reynolds bien plus eleve (ou plus faible). Les equations aux differences finies intervenant dans la methode permanente sont les equations (9) et (10), obtenues a partir des equations (7) et (8) a l'aide de formules du genre des (11) et (12). Dans les equations aux differences finies (9) et (10) , l'indice k indique le nombre des iterations ; celles-ci se font dans le sens des j et des i croissants, ou bien, ce qui revient au meme, des y et des x croissants. Pour la methode non perrnanente, on a employe les equations (13) et (14), dans lesquelles n represente l'indice du temps. On notera que la premiere de ces deux equations indique la possibilite de calculer ζ a l'instant (n + 1) δt, a partir des valeurs stables de Ψ et de ζ a l'instant nδt, et celle de ζ a l'instant (n -1) δt. Une fois faits les calculs de ζ a l'instant (n + 1) δt, on calcule la fonction de courant par iteration, a l'aide de l'equation (14). Etant donne qu'il semblait si evident que les solutions correspondant au regime permanent s'obtiendraient plus aisement a partir d'equations sans termes non permanents, la premiere partie de la presente etude a ete consacree a l'integration des equations (9) et (10) en partant du cas-limite de la disparition des forces d'inertie, soit du cas bien connu de l'ecoulement de fluage. Ensuite, une fois determine l'ecoulement correspondant a un nombre de Reynolds donne, on a fait augmenter la valeur de ce nombre dans l'equation (10), et on a repris le calcul autant de fois qu'il fallait pour obtenir des valeurs bien etablies. A cause d'instabilites du calcul, il n'est possible, pour des dimensions de maille donnees, de poursuivre ce procede, et d'obtenir de bons resultats, que jusqu'a un certain nombre de Reynolds ; une fois ce nombre de Reynolds atteint, le passage a une maille de plus petites dimensions s'impose. L'influence des dimensions de maille, et des methodes de balayage, sur la stabilite des calculs, a ete etudiee a l'aide d'un ecoulement uniforme et perturbe, en faisant pour ce dernier des calculs correspondant a une partie de la conduite a deux dimensions. Les equations (15) a (21) representent la methode par laquelle les auteurs ont aborde les conditions aux limites. Dans toute experience reelle ayant pour objet la determination d'une zone de decollement, il est necessaire d'accelerer le fluide progressivement, a partir de son etat initial au repos. Autrement dit, on n'envisagerait guere d'etablir l'ecoulement permanent recherche d'un seul coup. Par consequent, il semble qu'un schema de calcul plus naturel, pour la determination de la zone de decollement, devrait, en principe, etre propre a reproduire, sur le modele mathematique, ce qui se passe dans le milieu physique. Cependant, ceci n'a ete fait qu'apres s'etre heurte a des difficultes insurmontables avec la methode permanente, qui de prime abord etait censee plus simple et rapide. Or, la methode non permanente s'est montree a la fois d'un maniement tout aussi aise que la methode permanente, et beaucoup plus stable. La methode permanente representait un moyen different de determiner des schemas d'ecoulement; elle servait egalement a verifier et a guider la methode non permanente, dont on preconisera neanmoins l'emploi pour toute nouvelle etude. Le procede employe a consiste a changer le nombre de Reynolds dans l'equation (13), sans modifier les valeurs de la fonction de courant aux limites, ce qui peut se concevoir comme une modification brusque de la viscosite, la valeur du debit restant constante. Les figures 2 et 3 representent une serie de schemas d'ecoulement, et les profils de vorticite correspondants, obtenus par la methode permanente. Ces figures ne correspondent qu'a une partie des calculs executes pour la gamme des nombres de Reynolds s'echelonnant de 0 jusqu'a Presque 100. Les resultats des calculs effectues a l'aide de la methode non permanente sont representes sur la figure 4, qui montre le schema d'ecoulement correspondant a R = 333, et ayant ete obtenu a partir de celui correspondant a R = 200 par un artifice consistant a changer le nombre de Reynolds dans les equations aux differences finies de 200 a 333, tout en maintenant constante la valeur du debit sans dimensions. Le schema d'ecoulement correspondent a R = 200 a ete obtenu en "accelerant" de R = 48 a R = 93,3, et ensuite de R = 93,3 a R = 200. Les schemas (a) a (e) de la figure 4 montrent, successivement, les etapes initiale, intermediaire, et finale de "l'ecoulement" du calcul, en passant de R = 200 a R = 333. Une caracteristique interessante de la croissance du tourbillon est que l'ecoulement en son interieur evolue d'une maniere qui parait realiste, en ce sens que l'observation experimentale de la scission du tourbillon en deux parties est possible, dans le cas des tourbillons de forme allongee. Des calculs imposant une acceleration reelle du debit "modele" par un elargissement, ont deja ete effectues sous la direction du deuxieme auteur de l'etude ; il s'est montre que, la aussi, le tourbillon sE scindait en deux parties, de maniere semblable a celle indiquee sur la figure 4. Le dernier schema de cette figure correspond egalement a R = 200, mais il a ete obtenu en reduisant brutalement le nombre de Reynolds de 333 a 200 ; seul y figure le tourbillon de plus petites dimensions, puisque le tourbillon se retrecit tout a fait regulierement, comme s'il restait semblable a lui-meme, sans se scindre en deux. Les figures 5 et 6 indiquent la croissance calculee de la longueur relative du tourbillon, la position du centre du tourbillon, et son intensite, due aux variations du nombre de Reynolds, respectivement de 48 a 98,3, et de 333 a 200. La figure 7 presente quatre caracteristiques de tourbillons permanents, en fonction du nombre de Reynolds ; ou y notera avec interet la croissance lineaire de la longueur du tourbillon. L'utilisation de formes discretisees des equations correspondant a l'ecoulement visqueux, lorsque l'on dispose d'ordinateurs a grande capacite et rapidite de calcul poussee met a disposition un puissant moyen pour l'etude des ecoulements resistant encore aux procedes classiques d'integration analytique. Un des avantages des modeles mathematiques est qu'ils permettent d'emmagasiner "l'ecoulement", et "d'effectuer des observations complementaires" a n'importe quel moment par la suite. C'est exactement ce qu'ont fait les auteurs, en calculant la pression, la somme de Bernoulli, les efforts normaux et tangentiels, les termes tenant compte de la qualite, de mouvement et de l'impulsion, et les equations de l'energie et du travail, correspondant a l'un des ecoulements emmagasines dans les elargissements de conduites. Les resultats de ces "observations" ont deja ete presentes en vue de leur publication.

The collapse shape and internal velocity field of an initially circular homogeneous fluid mass surrounded by a linearly stratified fluid are computed. During the initial stage of collapse, the fluid is assumed to be irrotational and inviscid while in later stages the Navier-Stokes equations are solved numerically by a modification of Chorin's primitive variable decomposition method. The final stage is analyzed by means of an asymptotic viscous long-wave theory.

The present paper represents a summary of the findings of a six month study of health care in the western Pennsylvania region, conducted by the Biotechnology Program of Carnegie-Mellon University during 1968. The study, one of six, was commissioned by the Committee on Engineering in Medicine and Biology of the National Academy of Engineering. A parallel study of Bioengineering in Pennsylvania, sponsored by the Pennsylvania Science and Engineering Foundation of the Department of Commerce, Commonwealth of Pennsylvania, was conducted simultaneously with the NAE study. Major conclusions of this paper center about the need for introduction of modern technology into the health care industry.

Changes in precordial ultrasonic Doppler patterns in dogs were compared with changes of end-tidal carbon dioxide (EtCO2) and pulmonary arterial pressure (PAP). Possible mechanisms of pulmonary arterial hypertension after air embolism in dogs are discussed. After the injection of air, an immediate change in the Doppler ultrasonic pattern was detected, including a shift of the base line. The duration of change of Doppler patterns varied depending upon the length of time that trapped air remained in the right heart. There was a delay of 15 to 30 seconds before the EtCO2 and PAP responded. In a group of dogs pretreated with 0.3 mg of propranolol per kg, there was a significant decrease in the PAP response due to induced air embolism compared to the control group (P < 0.05). We found that the Doppler ultrasonic device was the most sensitive for detecting venous air embolism at a level as low as 0.05 ml of air per kg compared to 0.25 ml/kg for the PAP and EtCO2 responses.

The effects of arteriovenous perfusion on myocardial performance, pulmonary circulatory dynamics, and organ preservation were studied in dogs in order to evaluate the applicability of arteriovenous extracorporeal membrane oxygenation for partial respiratory support. Studies were made on normally oxygenated dogs, on dogs made hypoxic by oxygen deprivation and ventilatory depression, and on dogs with pulmonary injury and moderate pulmonary hypertension induced by injection of oleic acid into the right ventricle. The latter two groups were included to assess the changes that occur in cardiopulmonary dynamics in the presence of hypoxia and pulmonary hypertension. A microchannel membrane oxygenator was employed to provide partial respiratory support to the group of animals with pulmonary injury. The results indicate that no deleterious hemodynamic changes occurred in any of the groups of animals with arteriovenous flow for periods of up to 5 hours at rates corresponding to 20 to 35% of the total cardiac output. Adequate systemic oxygenation was provided by the microchannel oxygenator at these rates of arteriovenous perfusion.

An in-vivo experimental method was developed to measure the stress-strain relationship of a spinal cord segment of anesthetized puppies. A pseudo Young’s modulus was defined for the linear region followed by a nonlinear rheological behavior for finite strain. Both the sensory response and motor function of the puppies were fully recovered within 5 days after the spinal cord segment in the first lumbar region was elongated once by 50 percent or less. The usefulness of the in-vivo experiments was further elaborated by demonstrating the large artifacts that could be associated in an in-vitro experiment.

The present study makes use of a mathematical model to investigate hemodynamic characteristics during the incipient period of the aortic flow. The analysis provides numerical results which not only support the data of Bellhouse on the pressure/flow relationship through the valve but also give a further insight into the effects of the speed and shape of the leaflet, and of the temporal variations of discharge on the flow processes. It is demonstrated that four types of discharge coefficients are needed for the hydrodynamic evaluation of pulsatile flow through both natural and prosthetic heart valves.

A new membrane oxygenator capable of effective and efficient arterialization of venous blood flowing through etched microchannels has been developed. The design flow capacity can be regulated up to 1.4 liters per minute with a priming volume of 80 cm3. The characteristics of oxygen and carbon dioxide exchange are correlated to the effective channel depth and compared with theoretical predictions. An analysis of the resistance coefficient of blood flowing through the etched microchannels shows a significant reduction (50–65%) of the apparent viscosity of blood, indicating the peripheral plasma layer effect on the microflow processes. The particulate flow results in an anomalous oxygen and carbon dioxide, exchange above theoretical predictions for homogeneous fluids.

The mathematical model of Hung (Tsai and Hung, 1984) is employed to determine the wall shear rate acting on canine carotid arteries perfused in vitro. Model equations for pulsatile flow in a deformable vessel are coupled with experimental data of dynamic pressure drop, flow rate, vessel radius and radial wall motion. Derived quantities, e.g. velocity profiles and wall shear, are obtained for vessels exposed to 'normotensive' hemodynamics, 'hypertension' simulations and perfusions in which the compliance of the vessel wall is deliberately altered. Our results indicate that wall shear varies markedly as a function of the hemodynamic environment. The effects of vessel radius vs flow rate on the development of wall shear are also demonstrated. It is found that convective processes correlate with the magnitude of wall shear in the 'hypertension' simulations. The present findings and complementary published data may explain, at least in part, the variations in vessel wall transport and endothelial cell biology we observe as a function of the hemodynamic environment. For example we have documented that the exposure of canine carotids to 'hypertensive' (vs 'normotensive') hemodynamics is associated with an increased flux of lipoproteins (LDL) into the intima and luminal media. Alternations in wall compliance, on the other hand, profoundly influence endothelial shape, orientation and cytoskeletal array.

A fully established three-dimensional blood flow in a uniform, rectangular channel with a moving wall (membrane) is calculated by using an implicit finite-difference approximation to the Navier-Stokes equations. The strength of the secondary flow, which provides a mechanism for the enhancement of oxygen transfer, is controlled by the relative motion between the membrane and the channel. The calculations simulate uniform flow establishment from rest, with and without secondary flow in a long channel.

Publisher Summary This chapter discusses a simple, systematic approach to the hydrodynamics of the ureter is proposed in the light of information theory. The main goal is to analyze the examine the hydrodynamic information conveyed by the bolus flow in the ureter and to attempt to single out parameters that are useful for the identification of normal and pathological conditions of the urinary system. It is important to determine whether the process is a Markovian one, to determine the particular chain corresponding to a given diet and given living conditions, and to define the normal transitions. The time variation of the characteristics of the bolus and the stability of the urinary system should be examined under various disturbances, which may be caused by disease, drugs, mechanical factors, or by a combination of these agents.

Time varying flows of plasma in the axial gaps between erythrocytes in a mathematical model of a capillary have been solved from the complete Navier-Stokes equations by a finite-difference method. The erythrocytes are considered to be disk-like and to span the entire lumen. Secondary flow patterns, pressure and shear distributions between the erythrocytes are obtained as a function of time, and the pressure drop is compared with previous results for steady creeping flow. The rate of oxygen transfer from the cells is calculated from a numerical solution of the convective diffusion equation.

The pressure field, the Bernoulli‐sum variation, and the different terms of the impulse‐momentum and work‐energy relations have been determined computationally for a conduit expansion of 2:1 and a Reynolds number of 48 in the narrow part of the conduit. The procedure used was the integration of an explicit discretized form of the Navier‐Stokes equations. The calculations were carried out with an IBM 7044 electronic computer. It was found that some terms of the differential and integrated forms of the basic equations were relatively small. The integrated form of the work‐energy relation can be simplified to only three of its terms. The role of the eddy was found to be essentially that of shaping the main flow, the exchange of momentum and energy with the main flow being rather small.