Metabolism of Plasmodium berghei. I. Krebs cycle

The free parasites of Plasmodium berghei, obtained from infected cells of rats using an antiserum method, were investigated to study the operation of Krebs cycle. P. berghei was found to respire only with succinate; pyruvate, and other substrates of the Krebs cycle were not oxidized. The presence of a succinate dehydrogenase and a functioning cytochrome oxidase system was demonstrated. Cell-free extracts of free parasites showed the presence of enzymes for the utilization of C4 dicarboxylic acids; other enzymes of the Krebs cycle could not be detected. P. berghei differs from other species of Plasmodium in this respect.

Sapientia, 1968, Vol. XXIII, nº 90 (número completo)

Contenido: La ubicación de la inteligencia / Octavio N. Derisi – La libertad en la filosofía de la integralidad / Alberto Caturelli – Conocimiento y ser / José I. Alcorta – Notas y comentarios -- Bibliografía

Alvará, por que Vossa Magestade ha por bem conceder aos Conservadores da Companhia Geral do Grão Pará, e Maranhão, a mesma jurisdicção de que goza o Conservador da Junta do Commercio destes Reinos, e seus domínios para se evitarem mais efficazmente os contrabandos, que se fazem à dita Companhia; determinando,que o producto das tomadias que se fizerem se applique ametade a favor dos denunciantes, e a outra ametade a favor da mesma Companhia; tudo na forma assima declarada : para Vossa Magestade ver / Joaquim José Borralho, o fez

Ao alto do título: Conde de Oeyras.

Alvará, por que V. Magestade ha por bem ampliar os privilegios, que na Instituição da Junta da Administração da Companhia Geral do Grão Pará, e Maranhão, lhe tinha concedido; na forma, que nelle se declara : para Vossa Magestade ver / Joaquim Joseph Borralho o fez

Ao alto do título: Sebastião Joseph de Carvalho e Mello.

Sea surface temperature and the distribution and apparent abundance of skipjack (Katsuwonus pelamis) in the Eastern Pacific Ocean, 1951-1968

ENGLISH: Isograms of sea surface temperature (OC) have been produced for 1949-1968 for the areas of the eastern Pacific Ocean in which the majority of the skipjack catch is taken. These are in the immediate coastal zone, California (35° N) to Chile (20 0 S), and the Revillagigedo and Galapagos Islands groups. Skipjack occurrence and apparent abundance (as CSDF, i.e., catch per standard days fishing, standardized in purse-seiner units) for 1951-1968 were then superimposed on the surface temperature isograms. Results show that skipjack occur at surface temperatures> 17° C but with the majority between 20°-30° C. Apparent abundance at CSDF > 1 ton/day is normally Iimited to 20°29° C water, except in two areas in certain years; from the Gulf of Tehuantepec to Cape Mala rates of 1-9 tons/day are relatively common at 29°-30° C, and off Chimbote (Peru) occasionally >9 tons/day are recorded down to 18° C. As expected there were no apparent relationships between annual thermal conditions in the coastal zone and skipjack abundance (total catch or indices of abundance) in the same or 2 subsequent years. An Appendix to the report determines the quantitative relationships between surface temperature and skipjack abundance in relatively small areal strata in Baja California waters in 1955 and 1958. Relationships generally appeared significant and opposite in these years when temperatures were respectively anomalously cold and warm. SPANISH: Se han producido isogramas de la temperatura de la superficie del mar (OC) para 1949-1968 correspondientes a las áreas del Océano Pacífico oriental en donde se obtiene la mayor parte de la captura de barrilete. Estas se encuentran ubicadas en la zona costanera inmediata, desde California (35°N) hasta Chile (200S) y en las Islas Revillagigedo y Galápagos. La ocurrencia de barrilete y su abundancia aparente (expresada como CDSP standardizada en unidades de cerqueros) para 1951-1968 fueron luego superpuestas en los isogramas de la temperatura superficial. Los resultados demuestran que el barrilete aparece en temperaturas superficiales de > 17°C pero la mayoría entre los 20°C-30°C. La abundancia aparente de la CDSP > 1 tonelada/día se limita normalmente a aguas de 20°-29°C, excepto en dos áreas en ciertos años; desde el Golfo de Tehuantepec a Cabo Mala las tasas de 1-9 toneladas/día son relativamente comunes en los 29°-30°C, y frente a Chimbote (Perú) se registran ocasionalmente> 9 toneladas/día a una temperatura tan fría como de 18°C. Como era de esperarse no existió una relación aparente entre las condiciones térmicas anuales de la zona costanera y la abundancia del barrilete (captura total o índices de abundancia) en el mismo año o en los 2 años siguientes. Un Apéndice del informe determina la relación cuantitativa entre la temperatura superficial y la abundancia del barrilete en un estrato de áreas relativamente pequeño en las aguas de Baja California en 1955 y 1968. Las relaciones generalmente aparecieron significativas y opuestas en esos años cuando las temperaturas fueron respectivamente anómalamente frías y calientes. (PDF contains 53 pages.)

Migrations of yellowfin tuna in the Eastern Pacific Ocean as determined from tagging experiments initiated during 1968-1974

ENGLISH: Data from tagging experiments initiated during 1968-1974 in the eastern Pacific Ocean were used to study the migrations of yellowfin tuna in that area. The map method, the parallel-area method, and the Jones method were employed in the analyses. The map method gives a useful impression of the distances and directions traveled, but does not express these parameters in quantitative terms. The parallel-area method is particularly useful for determining whether or not there is net movement in particular directions, i.e. inshore-offshore, east-west, or north-south. The first of these is of particular interest, as the incidence of smaller fish is much higher in the catches made inshore than in those made offshore, and it is desirable to know whether this is due to relatively greater abundance or to relatively greater vulnerability of the smaller fish in the inshore areas. If the former were the case an offshore movement of the fish as they grew older would probably be detected. Such a movement was not detected, however, so it appears likely that the differences in the catches of smaller fish in the inshore and offshore areas are due mainly to differences in vulnerability. Few or no east-west or north-south tendencies in the movements of the fish were detected. The Jones method indicates that the movement is not random, but reveals no pronounced directional tendencies. SPANISH: Se emplearon los datos de los experimentos de marcado, iniciados en el Océano Pacífico oriental durante 1968-1974 para estudiar los desplazamientos del atún aleta amarilla en esa zona. En los análisis se emplearon los métodos cartográficos, de las zonas paralelas y de Jones. El método cartográfico ofrece una idea útil sobre la distancia y dirección de los desplazamientos, pero no expresa estos parámetros en términos cuantitativos. El método de las zonas paralelas es particularmente conveniente para determinar si existe o nó un desplazamiento neto en una dirección especial, es decir, hacia la costa-fuera de la costa, este-oeste o norte-sur. El primero de éstos tiene un interés especial, ya que la incidencia de peces más pequeños es muy superior en las capturas realizadas cerca de la costa que en las de mar afuera, y se desea conocer si ésto se debe a la abundancia relativamente superior o a las vulnerabilidad relativamente mayor de los pequeños peces en las zonas costeras. Si el caso fuera el primero, se podría descubrir probablemente un movimiento de los peces mar afuera a medida que crecen. Sin embargo, no se ha descubierto tal movimiento, así que es probable que las diferencias en las capturas de peces pequeños en las zonas costeras y mar afuera se deban principalmente a diferencias en la vulnerabilidad. Se descubrió poca o ninguna tendencia en los peces a desplazarse este-oeste o norte-sur. El método de Jones indica que el movimiento no es aleatorio, pero no revela una tendencia pronunciada a orientarse direccionalmente.

Part I. On the breaking of nonlinear dispersive waves. Part II. Variational principles in continuum mechanics

A model equation for water waves has been suggested by Whitham to study, qualitatively at least, the different kinds of breaking. This is an integro-differential equation which combines a typical nonlinear convection term with an integral for the dispersive effects and is of independent mathematical interest. For an approximate kernel of the form e^(-b|x|) it is shown first that solitary waves have a maximum height with sharp crests and secondly that waves which are sufficiently asymmetric break into "bores." The second part applies to a wide class of bounded kernels, but the kernel giving the correct dispersion effects of water waves has a square root singularity and the present argument does not go through. Nevertheless the possibility of the two kinds of breaking in such integro-differential equations is demonstrated.

Difficulties arise in finding variational principles for continuum mechanics problems in the Eulerian (field) description. The reason is found to be that continuum equations in the original field variables lack a mathematical "self-adjointness" property which is necessary for Euler equations. This is a feature of the Eulerian description and occurs in non-dissipative problems which have variational principles for their Lagrangian description. To overcome this difficulty a "potential representation" approach is used which consists of transforming to new (Eulerian) variables whose equations are self-adjoint. The transformations to the velocity potential or stream function in fluids or the scaler and vector potentials in electromagnetism often lead to variational principles in this way. As yet no general procedure is available for finding suitable transformations. Existing variational principles for the inviscid fluid equations in the Eulerian description are reviewed and some ideas on the form of the appropriate transformations and Lagrangians for fluid problems are obtained. These ideas are developed in a series of examples which include finding variational principles for Rossby waves and for the internal waves of a stratified fluid.

I. Spectroscopic evidence for slow vibrational relaxation in excited electronic states of diatomics in rare gas solids. II. Static crystal field effects in the electronic spectra of isotopically mixed benzene crystals

Part I

Studies of vibrational relaxation in excited electronic states of simple diatomic molecules trapped in solid rare-gas matrices at low temperatures are reported. The relaxation is investigated by monitoring the emission intensity from vibrational levels of the excited electronic state to vibrational levels of the ground electronic state. The emission was in all cases excited by bombardment of the doped rare-gas solid with X-rays.

The diatomics studied and the band systems seen are: N₂, Vegard-Kaplan and Second Positive systems; O₂, Herzberg system; OH and OD, A ²Σ⁺ - X²II_i system. The latter has been investigated only in solid Ne, where both emission and absorption spectra were recorded; observed fine structure has been partly interpreted in terms of slightly perturbed rotational motion in the solid. For N₂, OH, and OD emission occurred from v' > 0, establishing a vibrational relaxation time in the excited electronic state of the order, of longer than, the electronic radiative lifetime. The relative emission intensity and decay times for different v' progressions in the Vegard-Kaplan system are found to depend on the rare-gas host and the N₂ concentration, but are independent of temperature in the range 1.7°K to 30°K.

Part II

Static crystal field effects on the absorption, fluorescence, and phosphorescence spectra of isotopically mixed benzene crystals were investigated. Evidence is presented which demonstrate that in the crystal the ground, lowest excited singlet, and lowest triplet states of the guest deviate from hexagonal symmetry. The deviation appears largest in the lowest triplet state and may be due to an intrinsic instability of the ³B_1u state. High resolution absorption and phospho- rescence spectra are reported and analyzed in terms of site-splitting of degenerate vibrations and orientational effects. The guest phosphorescence lifetime for various benzene isotopes in C₆D₆ and sym-C₆H₃D₃ hosts is presented and discussed.

I. Quantum mechanics of one-dimensional two-particle models. II. A quantum mechanical treatment of inelastic collisions

Part I

Solutions of Schrödinger’s equation for system of two particles bound in various stationary one-dimensional potential wells and repelling each other with a Coulomb force are obtained by the method of finite differences. The general properties of such systems are worked out in detail for the case of two electrons in an infinite square well. For small well widths (1-10 a.u.) the energy levels lie above those of the noninteresting particle model by as much as a factor of 4, although excitation energies are only half again as great. The analytical form of the solutions is obtained and it is shown that every eigenstate is doubly degenerate due to the “pathological” nature of the one-dimensional Coulomb potential. This degeneracy is verified numerically by the finite-difference method. The properties of the square-well system are compared with those of the free-electron and hard-sphere models; perturbation and variational treatments are also carried out using the hard-sphere Hamiltonian as a zeroth-order approximation. The lowest several finite-difference eigenvalues converge from below with decreasing mesh size to energies below those of the “best” linear variational function consisting of hard-sphere eigenfunctions. The finite-difference solutions in general yield expectation values and matrix elements as accurate as those obtained using the “best” variational function.

The system of two electrons in a parabolic well is also treated by finite differences. In this system it is possible to separate the center-of-mass motion and hence to effect a considerable numerical simplification. It is shown that the pathological one-dimensional Coulomb potential gives rise to doubly degenerate eigenstates for the parabolic well in exactly the same manner as for the infinite square well.

Part II

A general method of treating inelastic collisions quantum mechanically is developed and applied to several one-dimensional models. The formalism is first developed for nonreactive “vibrational” excitations of a bound system by an incident free particle. It is then extended to treat simple exchange reactions of the form A + BC →AB + C. The method consists essentially of finding a set of linearly independent solutions of the Schrödinger equation such that each solution of the set satisfies a distinct, yet arbitrary boundary condition specified in the asymptotic region. These linearly independent solutions are then combined to form a total scattering wavefunction having the correct asymptotic form. The method of finite differences is used to determine the linearly independent functions.

The theory is applied to the impulsive collision of a free particle with a particle bound in (1) an infinite square well and (2) a parabolic well. Calculated transition probabilities agree well with previously obtained values.

Several models for the exchange reaction involving three identical particles are also treated: (1) infinite-square-well potential surface, in which all three particles interact as hard spheres and each two-particle subsystem (i.e. BC and AB) is bound by an attractive infinite-square-well potential; (2) truncated parabolic potential surface, in which the two-particle subsystems are bound by a harmonic oscillator potential which becomes infinite for interparticle separations greater than a certain value; (3) parabolic (untruncated) surface. Although there are no published values with which to compare our reaction probabilities, several independent checks on internal consistency indicate that the results are reliable.

Part I. Coenzyme B12 as a hydroformylation-type catalyst. Part II. Mechanisms of hydrogen transfer in the methylmalonyl coenzyme a mutase reaction

Part I

The mechanism of the hydroformylation reaction was studied. Using cobalt deuterotetracarbonyl and 1-pentene as substrates, the first step in the reaction, addition of cobalt tetracarbonyl to an olefin, was shown to be reversible.

Part II

The role of coenzyme B₁₂ in the isomerization of methylmalonyl coenzyme A to succinyl coenzyme A by methylmalonyl coenzyme A mutase was studied. The reaction was allowed to proceed to partial completion using a mixture of methylmalonyl coenzyme A and 4, 4, 4-tri-²H-methylmalonyl coenzyme A as substrate. The deuterium distribution in the product, succinyl coenzyme A, was shown to best fit a model in which hydrogen is transferred from C-4 of methylmalonyl coenzyme A to C-5’ of the adenosyl moiety of coenzyme B₁₂ in the rate determining step. The three hydrogens at the 5’-adenosyl position of the coenzyme B₁₂ intermediate are then able to become enzymatically equivalent before hydrogen is transferred from the coenzyme B₁₂ intermediate to form succinyl coenzyme A.

I. The effect of N,N,N',N' -tetramethylethylenediamine on the Schlenk Equilibrium. II. The nature of the Di-Grignard reagent

I. The influence of N,N,N’,N’-tetramethylethylenediamine on the Schlenk equilibrium

The equilibrium between ethylmagnesium bromide, diethylmagnesium, and magnesium bromide has been studied by nuclear magnetic resonance spectroscopy. The interconversion of the species is very fast on the nmr time scale, and only an averaged spectrum is observed for the ethyl species. When N,N,N’,N’-tetramethylethylenediamine is added to solutions of these reagents in tetrahydrofuran, the rate of interconversion is reduced. At temperatures near -50°, two ethylmagnesium species have been observed. These are attributed to the different ethyl groups in ethylmagnesium bromide and diethylmagnesium, two of the species involved in the Schlenk equilibrium of Grignard reagents.

II. The nature of di-Grignard reagents

Di-Grignard reagents have been examined by nuclear magnetic resonance spectroscopy in an attempt to prove that dialkylmagnesium reagents are in equilibrium with alkylmagnesium halides. The di-Grignard reagents of compounds such as 1,4-dibromobutane have been investigated. The dialkylmagnesium form of this di-Grignard reagent can exist as an intramolecular cyclic species, tetramethylene-magnesium. This cyclic form would give an nmr spectrum different from that of the classical alkylmagnesium halide di-Grignard reagent. In dimethyl ether-tetrahydrofuran solutions of di-Grignard reagents containing N N,N,N’,N’-Tetramethylethylenediamine, evidence has been found for the existence of an intramolecular dialkylmagnesium species. This species is rapidly equilibrating with other forms, but at low temperatures, the rates of interconversion are reduced. Two species can be seen in the nmr spectrum at -50°. One is the cyclic species; the other is an open form.

Inversion of the carbon at the carbon-magnesium bond in di-Grignard reagents has also been studied. This process is much faster than in corresponding monofunctional Grignard reagents.

I. The crystal structure of potassium bis(tricyanovinyl)amine. II. Nuclear magnetic resonance studies of alkali halide solutions. III. Elucidation of the intramolecular hydrogen bond in acetylacetone by the deuterium isotope effect on the chemical shift of the bridge hydrogen

Part I

Potassium bis-(tricyanovinyl) amine, K⁺N[C(CN)=C(CN)₂]₂^-, crystallizes in the monoclinic system with the space group Cc and lattice constants, a = 13.346 ± 0.003 Å, c = 8.992 ± 0.003 Å, B = 114.42 ± 0.02°, and Z = 4. Three dimensional intensity data were collected by layers perpendicular to b* and c* axes. The crystal structure was refined by the least squares method with anisotropic temperature factor to an R value of 0.064.

The average carbon-carbon and carbon-nitrogen bond distances in –C-CΞN are 1.441 ± 0.016 Å and 1.146 ± 0.014 Å respectively. The bis-(tricyanovinyl) amine anion is approximately planar. The coordination number of the potassium ion is eight with bond distances from 2.890 Å to 3.408 Å. The bond angle C-N-C of the amine nitrogen is 132.4 ± 1.9°. Among six cyano groups in the molecule, two of them are bent by what appear to be significant amounts (5.0° and 7.2°). The remaining four are linear within the experimental error. The bending can probably be explained by molecular packing forces in the crystals.

Part II

The nuclear magnetic resonance of ⁸¹Br and ¹²⁷I in aqueous solutions were studied. The cation-halide ion interactions were studied by studying the effect of the Li⁺, Na⁺, K⁺, Mg⁺⁺, Cs⁺ upon the line width of the halide ions. The solvent-halide ion interactions were studied by studying the effects of methanol, acetonitrile, and acetone upon the line width of ⁸¹Br and ¹²⁷I in the aqueous solutions. It was found that the viscosity plays a very important role upon the halide ions line width. There is no specific cation-halide ion interaction for those ions such as Mg⁺⁺, Di⁺, Na⁺, and K⁺, whereas the Cs⁺ - halide ion interaction is strong. The effect of organic solvents upon the halide ion line width in aqueous solutions is in the order acetone ˃ acetonitrile ˃ methanol. It is suggested that halide ions do form some stable complex with the solvent molecules and the reason Cs⁺ can replace one of the ligands in the solvent-halide ion complex.

Part III

An unusually large isotope effect on the bridge hydrogen chemical shift of the enol form of pentanedione-2, 4(acetylacetone) and 3-methylpentanedione-2, 4 has been observed. An attempt has been made to interpret this effect. It is suggested from the deuterium isotope effect studies, temperature dependence of the bridge hydrogen chemical shift studies, IR studies in the OH, OD, and C=O stretch regions, and the HMO calculations, that there may probably be two structures for the enol form of acetylacetone. The difference between these two structures arises mainly from the electronic structure of the π-system. The relative population of these two structures at various temperatures for normal acetylacetone and at room temperature for the deuterated acetylacetone were calculated.

I. The effect of droplet solidification upon two-phase flow in a rocket nozzle. II. A kinetic theory investigation of some condensation-evaporation phenomena by a moment method

Part I:

The perturbation technique developed by Rannie and Marble is used to study the effect of droplet solidification upon two-phase flow in a rocket nozzle. It is shown that under certain conditions an equilibrium flow exists, where the gas and particle phases have the same velocity and temperature at each section of the nozzle. The flow is divided into three regions: the first region, where the particles are all in the form of liquid droplets; a second region, over which the droplets solidify at constant freezing temperature; and a third region, where the particles are all solid. By a perturbation about the equilibrium flow, a solution is obtained for small particle slip velocities using the Stokes drag law and the corresponding approximation for heat transfer between the particle and gas phases. Singular perturbation procedure is required to handle the problem at points where solidification first starts and where it is complete. The effects of solidification are noticeable.

Part II:

When a liquid surface, in contact with only its pure vapor, is not in the thermodynamic equilibrium with it, a net condensation or evaporation of fluid occurs. This phenomenon is studied from a kinetic theory viewpoint by means of moment method developed by Lees. The evaporation-condensation rate is calculated for a spherical droplet and for a liquid sheet, when the temperatures and pressures are not too far removed from their equilibrium values. The solutions are valid for the whole range of Knudsen numbers from the free molecule to the continuum limit. In the continuum limit, the mass flux rate is proportional to the pressure difference alone.

Part I. Synchronization of the cell division cycle of HeLa cells in suspension cultures. Part II. Studies on chromosomal proteins of HeLa cells during the cell division cycle

Part I

These studies investigate the potential of single and double treatments with either 5-fluorodeoxyuridine of excess thymidine to induce cell division synchrony in suspension cultures of HeLa cells. The patterns of nucleic acid synthesis and cell proliferation have been analyzed in cultures thus synchronized. Several changes in cell population during long incubation with 5-fluorodeoxyuridine or excess thymidine are also described. These results are subjected to detailed evaluation in terms of the degree and quality of synchrony finally achieved.

Part II

Histones and non-histone proteins associated with interphase and metaphase chromosomes of HeLa cells have been qualitatively and quantitatively analyzed. Histones were fractionated by chromatography on Amberlite CG-50 and further characterized by analytical disc electrophoresis and amino acid analysis of each chromatographic fraction. It is concluded that histones of HeLa cells are comprised of only a small number of major components and that these components are homologous to those of other higher organisms. Of all the histones, arginine-rich histone III alone contains cysteine and can polymerize through formation of intermolecular disulfide bridges between histone III monomers.

A detailed comparison by chromatography and disc electrophoresis established that interphase and metaphase histones are made up of similar components. However, certain quantitative differences in proportions of different histones of interphase and metaphase cells are reported. Indirect evidence indicates that a certain proportion of metaphase histone III is polymerized through intermolecular disulfide links, whereas interphase histone III occurs mainly in the monomeric form.

Metaphase chromosomes are associated with an additional acid-soluble protein fraction which is absent from interphase chromosomes. All of these additional acid-soluble proteins of metaphase chromosomes are shown to be non-histones and it is concluded that the histone/DNA ratio is identical in interphase and metaphase chromosomes. The bulk of acid-soluble non-histone proteins of metaphase chromosomes were found to be polymerized through disulfide bridges; corresponding interphase non-histone proteins displayed no evidence of similar polymerization.

The factors responsible for the condensed configuration and metabolic inactivity of metaphase chromosomes are discussed in light of these findings.

The relationship between histone and DNA synthesis in nondividing differentiated chicken erythrocyte cells and in rapidly dividing undifferentiated HeLa cells is also investigated. Of all the histones, only arginine-rich histones are synthesized in mature erythrocytes. Histone synthesis in HeLa cells was studied in both unsynchronized and synchronized cultures. In HeLa cells, only part of the synthesis of all histone fractions is dependent on concurrent DNA synthesis, whereas all histones are synthesized in varying degrees even in the absence of DNA synthesis.

I. Stokes flow past a thin screen. II. Viscous flows past porous bodies of finite size

Part I

The slow, viscous flow past a thin screen is analyzed based on Stokes equations. The problem is reduced to an associated electric potential problem as introduced by Roscoe. Alternatively, the problem is formulated in terms of a Stokeslet distribution, which turns out to be equivalent to the first approach.

Special interest is directed towards the solution of the Stokes flow past a circular annulus. A "Stokeslet" formulation is used in this analysis. The problem is finally reduced to solving a Fredholm integral equation of the second kind. Numerical data for the drag coefficient and the mean velocity through the hole of the annulus are obtained.

Stokes flow past a circular screen with numerous holes is also attempted by assuming a set of approximate boundary conditions. An "electric potential" formulation is used, and the problem is also reduced to solving a Fredholm integral equation of the second kind. Drag coefficient and mean velocity through the screen are computed.

Part II

The purpose of this investigation is to formulate correctly a set of boundary conditions to be prescribed at the interface between a viscous flow region and a porous medium so that the problem of a viscous flow past a porous body can be solved.

General macroscopic equations of motion for flow through porous media are first derived by averaging Stokes equations over a volume element of the medium. These equations, including viscous stresses for the description, are more general than Darcy's law. They reduce to Darcy's law when the Darcy number becomes extremely small.

The interface boundary conditions of the first kind are then formulated with respect to the general macroscopic equations applied within the porous region. An application of such equations and boundary conditions to a Poiseuille shear flow problem demonstrates that there usually exists a thin interface layer immediately inside the porous medium in which the tangential velocity varies exponentially and Darcy's law does not apply.

With Darcy's law assumed within the porous region, interface boundary conditions of the second kind are established which relate the flow variables across the interface layer. The primary feature is a jump condition on the tangential velocity, which is found to be directly proportional to the normal gradient of the tangential velocity immediately outside the porous medium. This is in agreement with the experimental results of Beavers, et al.

The derived boundary conditions are applied in the solutions of two other problems: (1) Viscous flow between a rotating solid cylinder and a stationary porous cylinder, and (2) Stokes flow past a porous sphere.