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.

A simple approach for the estimation of food consumption from growth rates at different environmental conditions and its application to juvenile cod (Gadus morhua L.) of a fjordic sea loch on the west coast of Scotland

Abstract Growth and condition of fish are functions of available food and environmental conditions. This led to the idea of using fish as a “consumption sensor” for the measurement of food intake over a defined period of time. A bio-physical model for the estimation of food consumption was developed based on the von Bertalanffy model. Whereas some of the input variables of the model, the initial and final lengths and masses of a fish and the temperature within the time period considered can easily be measured, internal characteristics of the species have to be determined indirectly. Three internal parameters are used in the model: the maintenance consumption at 0°C, the temperature dependence of this consumption and the food efficiency, the percentage of the ingested food utilized. Estimates of the parameters for a given species can be determined by feeding experiments. Here, data from published feeding experiments on juvenile cod, Gadus morhua L., were used to validate the model. The average of the relative error for the food intake predicted by the model for individual fish was about 24 %, indicating that fish used the food with different efficiencies. However, grouping the fish according to size classes and temperature lowered the relative error of the predicted food intake for the group to typically 5 %. For a group containing all fish of the feeding experiment the relative prediction error was about 2 %. Zusammenfassung Wachstum und Kondition der Fische sind von der verfügbaren Nahrung und von Umweltbedingungen abhängig. Dies führte zur Idee, Fisch als „Konsum-Sensor“ für die Messung der Nahrungsaufnahme über einen definierten Zeitraum zu verwenden. Auf Grundlage des von Bertalanffy-Modells wurde ein bio-physikalisches Modell zur Schätzung der Futteraufnahme entwickelt. Während einige der Eingangsgrößen des Modells leicht gemessen werden können (Anfangs- und Endlänge und -körpermasse der Fische und die Temperatur innerhalb des betrachteten Zeitraum), können interne Parameter der betrachteten Art nur indirekt bestimmt werden. Drei interne Parameter werden in dem Modell verwendet: Die Erhaltungskonsumtion bei 0° C, die Temperaturabhängigkeit dieser Rate und der Wirkungsgrad der Nahrung (der Anteil der Nahrung ,der aufgenommen und verwendet und nicht ungenutzt wieder ausgeschieden wird). Die Modellparameter für eine bestimmte Art können durch Fütterungsversuche bestimmt werden. Um das Modell zu validieren wurden Daten aus veröffentlichten Fütterungsversuchen mit juvenilen Kabeljau (Gadus morhua L.) verwendet. Modell und Wirklichkeit weichen in der Regel voneinander ab. Der durchschnittliche relative Fehler der durch das Modell vorhergesagten Nahrungsaufnahme betrug für Einzelfische etwa 24%, was darauf hinweist, dass einzelne Fisch die Nahrung mit unterschiedlichen Wirkungsgraden verwerten. Allerdings senkte die Gruppierung der Fische nach Größenklassen und Temperatur den relativen Vorhersagefehler für die Nahrungsaufnahme der Gruppe auf etwa 5%. Für alle Fische im Fütterungsversuch ist der relative Vorhersagefehler etwa 2%.

Observations on the distribution, daytime migrations and daily food intake rates of Chaoborus flavicans (Meigen) in the Goggausee [Translation from: Carinthia II 165(85), 184-190, 1975]

The Goggausee, in spite of its modest depth (Zmax = 12 metres), shows meromictic properties: autumn and spring circulation extend only to a depth of 8 metres. The water layers below about 10 metres are constantly oxygen-free, the critical zone with at least intermittent oxygen loss lies at a depth of between 6 and 10 metres. A limnological excursion in May 1974 offered an opportunity to investigate the daily vertical migration of the species Chaoborus flavicans with reference to its food supply of zooplankton as well as the chance to carry out some preliminary experiments on its rate of food intake. Among the studied features were the planktonic depth distribution of Chaoborus flavicans and the food intake of Chaoborus larvae under experimental conditions.

Particle fluid mechanics in shear flows, acoustic waves, and shock waves

Three different categories of flow problems of a fluid containing small particles are being considered here. They are: (i) a fluid containing small, non-reacting particles (Parts I and II); (ii) a fluid containing reacting particles (Parts III and IV); and (iii) a fluid containing particles of two distinct sizes with collisions between two groups of particles (Part V).

Part I

A numerical solution is obtained for a fluid containing small particles flowing over an infinite disc rotating at a constant angular velocity. It is a boundary layer type flow, and the boundary layer thickness for the mixture is estimated. For large Reynolds number, the solution suggests the boundary layer approximation of a fluid-particle mixture by assuming W = W_p. The error introduced is consistent with the Prandtl’s boundary layer approximation. Outside the boundary layer, the flow field has to satisfy the “inviscid equation” in which the viscous stress terms are absent while the drag force between the particle cloud and the fluid is still important. Increase of particle concentration reduces the boundary layer thickness and the amount of mixture being transported outwardly is reduced. A new parameter, β = 1/Ω τ_v, is introduced which is also proportional to μ. The secondary flow of the particle cloud depends very much on β. For small values of β, the particle cloud velocity attains its maximum value on the surface of the disc, and for infinitely large values of β, both the radial and axial particle velocity components vanish on the surface of the disc.

Part II

The “inviscid” equation for a gas-particle mixture is linearized to describe the flow over a wavy wall. Corresponding to the Prandtl-Glauert equation for pure gas, a fourth order partial differential equation in terms of the velocity potential ϕ is obtained for the mixture. The solution is obtained for the flow over a periodic wavy wall. For equilibrium flows where λ_v and λ_T approach zero and frozen flows in which λ_v and λ_T become infinitely large, the flow problem is basically similar to that obtained by Ackeret for a pure gas. For finite values of λ_v and λ_T, all quantities except v are not in phase with the wavy wall. Thus the drag coefficient C_D is present even in the subsonic case, and similarly, all quantities decay exponentially for supersonic flows. The phase shift and the attenuation factor increase for increasing particle concentration.

Part III

Using the boundary layer approximation, the initial development of the combustion zone between the laminar mixing of two parallel streams of oxidizing agent and small, solid, combustible particles suspended in an inert gas is investigated. For the special case when the two streams are moving at the same speed, a Green’s function exists for the differential equations describing first order gas temperature and oxidizer concentration. Solutions in terms of error functions and exponential integrals are obtained. Reactions occur within a relatively thin region of the order of λ_D. Thus, it seems advantageous in the general study of two-dimensional laminar flame problems to introduce a chemical boundary layer of thickness λ_D within which reactions take place. Outside this chemical boundary layer, the flow field corresponds to the ordinary fluid dynamics without chemical reaction.

Part IV

The shock wave structure in a condensing medium of small liquid droplets suspended in a homogeneous gas-vapor mixture consists of the conventional compressive wave followed by a relaxation region in which the particle cloud and gas mixture attain momentum and thermal equilibrium. Immediately following the compressive wave, the partial pressure corresponding to the vapor concentration in the gas mixture is higher than the vapor pressure of the liquid droplets and condensation sets in. Farther downstream of the shock, evaporation appears when the particle temperature is raised by the hot surrounding gas mixture. The thickness of the condensation region depends very much on the latent heat. For relatively high latent heat, the condensation zone is small compared with Ʌ_D.

For solid particles suspended initially in an inert gas, the relaxation zone immediately following the compression wave consists of a region where the particle temperature is first being raised to its melting point. When the particles are totally melted as the particle temperature is further increased, evaporation of the particles also plays a role.

The equilibrium condition downstream of the shock can be calculated and is independent of the model of the particle-gas mixture interaction.

Part V

For a gas containing particles of two distinct sizes and satisfying certain conditions, momentum transfer due to collisions between the two groups of particles can be taken into consideration using the classical elastic spherical ball model. Both in the relatively simple problem of normal shock wave and the perturbation solutions for the nozzle flow, the transfer of momentum due to collisions which decreases the velocity difference between the two groups of particles is clearly demonstrated. The difference in temperature as compared with the collisionless case is quite negligible.

Growth rates of bacteria in rivers

Three different methods for determining bacterial growth rate in rivers are described. Two of the methods are for bacteria in suspension: a recirculating experimental channel method and a radioactive tracer technique using super(35)SO sub(4). The third method is for bacteria attached to surfaces and specifically considers the surface of the common duckweed Lemna minor).

Steady surface wave pattern in a shear flow

The subject under investigation concerns the steady surface wave patterns created by small concentrated disturbances acting on a non-uniform flow of a heavy fluid. The initial value problem of a point disturbance in a primary flow having an arbitrary velocity distribution (U(y), 0, 0) in a direction parallel to the undisturbed free surface is formulated. A geometric optics method and the classical integral transformation method are employed as two different methods of solution for this problem. Whenever necessary, the special case of linear shear (i.e. U(y) = 1+ϵy)) is chosen for the purpose of facilitating the final integration of the solution.

The asymptotic form of the solution obtained by the method of integral transforms agrees with the leading terms of the solution obtained by geometric optics when the latter is expanded in powers of small ϵ r.

The overall effect of the shear is to confine the wave field on the downstream side of the disturbance to a region which is smaller than the wave region in the case of uniform flows. If U(y) vanishes, and changes sign at a critical plane y = y_cr (e.g. ϵy_cr = -1 for the case of linear shear), then the boundary of this asymmetric wave field approaches this critical vertical plane. On this boundary the wave crests are all perpendicular to the x-axis, indicating that waves are reflected at this boundary.

Inside the wave field, as in the case of a point disturbance in a uniform primary flow, there exist two wave systems. The loci of constant phases (such as the crests or troughs) of these wave systems are not symmetric with respect to the x-axis. The geometric optics method and the integral transform method yield the same result of these loci for the special case of U(y) = U_o(1 + ϵy) and for large Kr (ϵr ˂˂ 1 ˂˂ Kr).

An expression for the variation of the amplitude of the waves in the wave field is obtained by the integral transform method. This is in the form of an expansion in small ϵr. The zeroth order is identical to the expression for the uniform stream case and is thus not applicable near the boundary of the wave region because it becomes infinite in that neighborhood. Throughout this investigation the viscous terms in the equations of motion are neglected, a reasonable assumption which can be justified when the wavelengths of the resulting waves are sufficiently large.