Showing papers in "Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences in 1954"

Experiments on a Gravity-Free Dispersion of Large Solid Spheres in a Newtonian Fluid under Shear

Abstract: Dispersions of solid spherical grains of diameter D = 0.13cm were sheared in Newtonian fluids of varying viscosity (water and a glycerine-water-alcohol mixture) in the annular space between two concentric drums. The density σ of the grains was balanced against the density ρ of the fluid, giving a condition of no differential forces due to radial acceleration. The volume concentration C of the grains was varied between 62 and 13 %. A substantial radial dispersive pressure was found to be exerted between the grains. This was measured as an increase of static pressure in the inner stationary drum which had a deformable periphery. The torque on the inner drum was also measured. The dispersive pressure P was found to be proportional to a shear stress λ attributable to the presence of the grains. The linear grain concentration λ is defined as the ratio grain diameter/mean free dispersion distance and is related to C by λ = 1 ( C 0 / C ) 1 2 − 1 where C 0 is the maximum possible static volume concentration. Both the stresses T and P , as dimensionless groups T σ D 2 /λη 2 , and P σ D 2 /λη 2 , were found to bear single-valued empirical relations to a dimensionless shear strain group λ ½ σ D 2 (d U /d y )lη for all the values of λ C = 57% approx.) where d U /d y is the rate of shearing of the grains over one another, and η the fluid viscosity. This relation gives T α σ ( λ D ) 2 ( dU / dy ) 2 and T ∝ λ 1 2 η d U / dy according as d U /d y is large or small, i.e. according to whether grain inertia or fluid viscosity dominate. An alternative semi-empirical relation F = (1+λ)(1+½λ)ηd U /d y was found for the viscous case, when T is the whole shear stress. The ratio T/P was constant at 0·3 approx, in the inertia region, and at 0.75 approx, in the viscous region. The results are applied to a few hitherto unexplained natural phenomena.

On Sound Generated Aerodynamically. II. Turbulence as a Source of Sound

Abstract: The theory of sound generated aerodynamically is extended by taking into account the statistical properties of turbulent airflows, from which the sound radiated (without the help of solid boundaries) is called aerodynamic noise. The theory is developed with special reference to the noise of jets, for which a detailed comparison with experiment is made (§7 for subsonic jets, §8 for supersonic ones). The quadrupole distribution of part I (Lighthill 1952) is shown to behave (see §3) as if it were concentrated into independent point quadrupoles, one in each ‘average eddy volume’. The sound field of each of these is distorted, in favour of downstream emission, by the general downstream motion of the eddy, in accordance with the quadrupole convection theory of part I. This explains, for jet noise, the marked preference for downstream emission, and its increase with jet velocity. For jet velocities considerably greater than the atmospheric speed of sound, the ‘Mach number of convection’ M c may exceed I in parts of the jet, and then the directional maximum for emission from these parts of the jet is at an angle of sec -1 ( M c ) to the axis (§8). Although turbulence without any mean flow has an acoustic power output, which was calculated to a rough approximation from the expressions of part I by Proudman (1952) (see also § 4 below), nevertheless, turbulence of given intensity can generate more sound in the presence of a large mean shear (§ 5). This sound has a directional maximum at 45° (or slightly less, due to the quadrupole convection effect) to the shear layer. These results follow from the fact that the most important term in the rate of change of momentum flux is the product of the pressure and the rate of strain (see figure 2). The higher frequency sound from the heavily sheared mixing region close to the orifice of a jet is found to be of this character. But the lower frequency sound from the fully turbulent core of the jet, farther downstream, can be estimated satisfactorily (§7) from Proudman’s results, which are here reinterpreted (§5) in terms of sound generated from combined fluctuations of pressure and rate of shear in the turbulence. The acoustic efficiency of the jet is of the order of magnitude 10 -4 M 5 , where M is the orifice Mach number. However, the good agreement, as regards total acoustic power output, with the dimensional considerations of part I, is partly fortuitous. The quadrupole convection effect should produce an increase in the dependence of acoustic power on the jet velocity above the predicted U 8 law. The experiments show that (largely cancelling this) some other dependence on velocity is present, tending to reduce the intensity, at the stations where the convection effect would be absent, below the U 8 law. At these stations (at 90° to the jet) proportionality to about U 6.5 is more common. A suggested explanation of this, compatible with the existing evidence, is that at higher Mach numbers there may be less turbulence (especially for larger values of nd / U , where n is frequency and d diameter), because in the mixing region, where the turbulence builds up, it is losing energy by sound radiation. This would explain also the slow rate of spread of supersonic mixing regions, and, indeed, is not incompatible with existing rough explanations of that phenomenon. A consideration (§6) of whether the terms other than momentum flux in the quadrupole strength density might become important in heated jets indicates that they should hardly ever be dominant. Accordingly, the physical explanation (part I) of aerodynamic sound generation still stands. It is re-emphasized, however, that whenever there is a fluctuating force between the fluid and a solid boundary, a dipole radiation will result which may be more efficient than the quadrupole radiation, at least at low Mach numbers.

The Dispersion of Matter in Turbulent Flow through a Pipe

Abstract: The dispersion of soluble matter introduced into a slow stream of solvent in a capillary tube can be described by means of a virtual coefficient of diffusion (Taylor 1953a) which represents the combined action of variation of velocity over the cross-section of the tube and molecluar diffusion in a radial direction. The analogous problem of dispersion in turbulent flow can be solved in the same way. In that case the virtual coefficient of diffusion K is found to be 10$\cdot $1av$\_{\ast}$ or K = 7$\cdot $14aU $\surd \gamma $. Here a is the radius of the pipe, U is the mean flow velocity, $\gamma $ is the resistance coefficient and v$\_{\ast}$ 'friction velocity'. Experiments are described in which brine was injected into a straight $\frac{3}{8}$ in. pipe and the conductivity recorded at a point downstream. The theoretical prediction was verified with both smooth and very rough pipes. A small amount of curvature was found to increase the dispersion greatly. When a fluid is forced into a pipe already full of another fluid with which it can mix, the interface spreads through a length S as it passes down the pipe. When the interface has moved through a distance X, theory leads to the formula S$^{2}$ = 437aX(v$_{\ast}$/U). Good agreement is found when this prediction is compared with experiments made in long pipe lines in America.

The stability of the plane free surface of a liquid in vertical periodic motion

Abstract: A vessel containing a heavy liquid vibrates vertically with constant frequency and amplitude. It has been observed that for some combinations of frequency and amplitude standing waves are formed at the free surface of the liquid, while for other combinations the free surface remains plane. In this paper the stability of the plane free surface is investigated theoretically when the vessel is a vertical cylinder with a horizontal base, and the liquid is an ideal frictionless fluid making a constant angle of contact of 90° with the walls of the vessel. When the cross-section of the cylinder and the frequency and amplitude of vibration of the vessel are prescribed, the theory predicts that the m th mode will be excited when the corresponding pair of parameters (p m , q m ) lies in an unstable region of the stability chart; the surface is stable if none of the modes is excited. (The corresponding frequencies are also shown on the chart.) The theory explains the disagreement between the experiments of Faraday and Rayleigh on the one hand, and of Matthiessen on the other. An experiment was made to check the application of the theory to a real fluid (water). The agreement was satisfactory; the small discrepancy is ascribed to wetting effects for which no theoretical estimate could be given.

Conditions under Which Dispersion of a Solute in a Stream of Solvent can be Used to Measure Molecular Diffusion

Abstract: It is shown that an assumption made in the author’s previous discussion (Taylor 1953) can be presented as a result of analysis. The conditions under which an approximate solution of the equations for diffusion in a moving fluid can be used to interpret longitudinal dispersion of a solute in a stream of solvent flowing through a tube is given as 4L/a - > a Ua /D > 6.9. Here U is the mean velocity, a the radius of the tube, D the coefficient of molecular diffusion. L is the length of tube over which appreciable changes of concentration occur.

The Heat Transport and Spectrum of Thermal Turbulence

Abstract: In this paper a theoretical investigation is made of various properties of the steady-state inhomogeneous turbulent convection of heat in a fluid between horizontal conducting surfaces. An upper limit to the heat transport is found subject to the constraint that some minimum eddy size exists which is effective in this transport. The spectrum of convecting motions, the mean thermal gradients at each point and the eddy conductivity are then determined in terms of the minimum eddy size. The relation between the boundary conditions and eddy size is studied by an extension of the work of Pellew & Southwell using the mean thermal gradients deduced when n 0 modes of motion are present to establish the Rayleigh number at which the ( n 0 +1)th mode first becomes unstable. In a final section the spectra and mean-square values of the fluctuating velocity and temperature fields are estimated from the Boussinesq form of the hydrodynamic equations. The previously reported experimental heat transports are within 10% of those predicted. The discrete transitions are within the error limits of the observations. However, further data must be mgathered to justify the use of minimum eddy size as a defining parameter in situations of geophysical scale.

On the Theory of Superconductivity: The One-Dimensional Case

Abstract: The one-dimensional case of free electrons interacting with lattice displacements is solved by a self-consistent method. It is found that for a certain range of the interaction parametera single sinusoidal lattice displacement is strongly excited in the lowest level of the system. Its wave-length is such as to create an energy gap in the single-electron energy spectrum with all states below it filled, and all above it empty. This periodic lattice displacement plays the role of an ‘inner field’ and leads to periodic fluctuation in the electronic density in such a way that the two stabilize each other. In an infinite medium described by a periodic boundary condition they are not fixed absolutely in space, but only relative to each other. Excitation of electrons across the gap leads to a decrease in both the electronic density fluctuations and the width of the gap. The whole system, electrons plus lattice displacements, can move through the lattice without being disturbed provided the velocity v is sufficiently small. The inertia of this system is equal to that of all electrons augmented by a term due to the lattice displacements. Elastic scattering of individual electrons which normally leads to the residual resistance is impossible if v is sufficiently small. The linear specific heat of normal electrons is eliminated and replaced by an exponential term.

The Formation of Cracks as a Result of Plastic Flow

Abstract: The stresses round a piled-up group of dislocations are investigated with reference to the initiation of a crack. A crack should form when the group consists of about 1000 dislocations piled up under a stress of the magnitude occurring in a cold-worked metal. The stress system due to the crack is obtained. The crack will have a stable equilibrium length, but this length is likely to be determined by the amount of plastic flow which takes place round the tip of the crack.

The field and radiation impedance of mechanical radiators on the free surface of a semi-infinite isotropic solid

Abstract: The problem of wave-motion in a semi-infinite solid has been studied by several workers in connexion with seismological disturbances. In a classic paper (1904), Lamb investigated the propagation of vibrations over the surface of a semi-infinite isotropic solid, due to the application of force at a point or along a line in the free surface. A related problem is studied by Lapwood (I 949) who considers the case of an infinitely long dilating line-source situated parallel to and just below the free surface. Both authors obtain solutions in the form of definite integrals which they evaluate asymptotically to obtain the various components of the field at points on or near the surface at large distances from the source. In a more recent paper by Margery Newlands (I 952) this work has been extended to include the case of a source situated in a thin surface layer and propagating into a semi-infinite solid. The static problem of the distortion of a semi-infinite solid by stresses on the free surface was investigated by Boussinesq in a series of papers (1878-83) and by Love (1929). In the present paper Lamb's method has been adapted to furnish definite-integral representations of the field at an arbitrary point in a semi-infinite isotropic solid, due to prescribed periodic stresses on the free surface, the particular stress distributions considered here being such as would be produced by certain types of electro-mechanical transducer. Asymptotic formulae are obtained for the field at infinity, and the results for the various displacement components are presented in the form of polar diagrams. To obtain the radiation impedance integral expressions are derived for the mean displacement over the part of the surface which lies beneath the source; these expressions have been evaluated by numerical quadrature in a number of cases and a table shows the corresponding values of the radiation impedance.

The response of laminar skin friction and heat transfer to fluctuations in the stream velocity

Abstract: The laminar boundary layer in two-dimensional flow about a cylindrical body, when the velocity of the oncoming flow relative to the body oscillates in magnitude but not in direction, is analyzed mathematically. It is found that the maxima of skin friction at any point anticipate the maxima of the stream velocity, because the pressure gradient needed to speed up the main stream locally produces a given percentage increase in the slow flow near the wall sooner than it can do so in the main stream itself. For each point on the body surface there is a critical frequency $\omega \_{0}$, such that for frequencies $\omega $ > $\omega \_{0}$ the oscillations are to a close approximation ordinary 'shear waves' unaffected by the mean flow; the phase advance in the skin friction is then 45 degrees. For frequencies $\omega $ < $\omega \_{0}$, on the other hand, the oscillations are closely approximated as the sum of parts proportional to the instantaneous velocity and acceleration of the oncoming stream; the phase advance in the skin friction is then tan$^{-1}$ ($\omega /\omega \_{0}$). The part depending on the instantaneous velocity may be called the quasi-steady part of the oscillations. The coefficient of the acceleration of the oncoming stream in the frictional drag of the body may be called the frictional component of the virtual mass. For a flat plate in a stream of speed V, $\omega \_{0}$ = 0$\cdot $6 V/x at a distance x from the leading edge. If c is the length of the plate, its transient motion parallel to itself is governed solely by quasi-steady forces and this added virtual mass provided that $\omega $c/V < 0$\cdot $6. The frictional component of the virtual mass of a flat plate or any thin obstacle is found to be approximately 0$\cdot $5 times the mass of the fluid in the boundary layer's 'displacement area'; it is suggested that the coefficient may need to be increased to about 0$\cdot $8 for turbulent layers. When the body surface is hot, the maxima in heat transfer from it tend to lag behind those of the stream velocity, as a result of thermal inertia, but this is counteracted to some extent by the effect of convection by the phase-advanced velocities near the wall. For layers with a favourable gradient in the mean flow, one finds that the tendency to lag predominates. For the Blasius layer, however, the two effects appear to cancel out fairly closely; and for layers with adverse pressure gradient in the main stream there seems to be phase advance at the lower frequencies. At frequencies well above $\omega \_{0}$ there is always a phase lag of 90 degrees, but the amplitude of heat-transfer fluctuations is then much reduced, even though that of the skin friction fluctuations is increased. Special attention is paid to the phase lag in the heat transfer from a heated circular wire in a fluctuating stream, in the range of Reynolds number for which a laminar boundary layer exists. Curves for the amplitude and phase of the heat-transfer fluctuations as a function of frequency are given in figure 4, from calculations for the layer of nearly uniform thickness, which covers the front quadrant of the wire, and across which most of the fluctuating part of the heat transfer is believed to occur. For frequencies small compared with $\omega _{0}$ = 20V/d (where d is the diameter), the departure of the heat-transfer fluctuations from their quasisteady form consists essentially of a time lag of the order of 0$\cdot $2d/V.

The magnetic anisotropy of cobalt

Abstract: A modified form of the magnetic balance previously designed by one of us, is described. In this apparatus the gradient is made independent of the magnetizing field. With such an apparatus measurements have been made on the variation of the intensity of magnetization with magnetic field for single-crystal specimens cut along appropriate crystal axes, both for the hexagonal close-packed and face-centred cubic cobalt. Such measurements enable the magnetic anisotropy constants to be determined. The nature of the phase change from close-packed hexagonal to face-centred cubic occurring at about 400° C is such that single crystals can be cut at room temperature, which will transform to give single crystals of known orientation in the face-centred cubic phase. The values of the magnetic anistropy constants for the hexagonal phase for various temperatures are compared with those of earlier determinations and fair agreement is found. Measurements on the face-centred cubic phase were made every 50° C in the temperature range 500 to 1000° C; at the latter temperature the material became magnetically isotropic. For face-centred cubic cobalt it was found that the crystal directions in order of increasing difficulty of magnetization are [111], [110] and [100], as is the case for nickel. Moreover, the value of the anisotropy constant k 1 obeys the same empirical law, giving the variation with temperature, as nickel. The similarity in the magnetic behaviour of these two ferromagnetics having the same crystal structure is thus evident.

The crystal structure of polyethylene terephthalate

Abstract: If it is assumed that the density of amorphous regions in partly crystalline material is the same as that of the entirely amorphous material (1.335), the proportion by weight of crystals in ordinary drawn yam (density 1-39) is 48 %, and in specimens of the highest recorded density (1.41) it is 64-5%. These figures are, however, lower limits; if, as is likely, the density of amorphous regions in partly crystalline specimens is lower than 1-335, the proportions of crystalline material are higher than the figures given. The positions of atoms in the crystals have been deduced from the relative intensities of X-ray diffractions; approximate positions were found by trial-and-error methods, and refinement was then effected by calculations of electron densities, using the three-dimensional Fourier synthesis method. The molecules are nearly planar in configuration. Distances between atoms in neighbouring molecules are all normal Van der Waals contact distances; there is therefore no structural evidence for any unusually strong forces between the molecules. This conclusion is in agreement with that based on an estimate of the cohesion energy, which is very nearly the same as that of a comparable aliphatic polyester, polyethylene adipate. The high melting-point of polyethylene terephthalate in comparison with aliphatic polyesters is therefore not due to strong forces between the molecules; it is attributed to the

The behaviour of sulphur in silicate and aluminate melts

Abstract: As part of a general programme of research on the nature of inorganic melts, a study has been made of the manner in which sulphur is held in liquid silicates and aluminates. Mixtures of CaO-SiO 2 , MgO-SiO 2 , FeO-SiO 2 , CaO-Al 2 O 3 and CaO-SiO 2 -Al 2 O 3 have been brought into equilibrium, at temperatures between 1350 and 1650°C, with gas phases made by mixing H 2 , CO 2 and SO 2 at room temperature. It has been shown that, when p O 2 is less than about 10 –5 atm, a sulphur atom can only enter the melt by displacing a suitable oxygen atom. The sulphur is then held in the slag entirely as sulphide, its concentration being controlled by the general equilibrium, ½S 2 + (O)melt = ½O 2 + (S)melt. When p O 2 is greater than about 10 -3 atm, the sulphur is held as sulphate and the corresponding equilibrium is ½S 2 + 3/2O 2 + (O)melt = (SO 4 )melt∙ In the binary silicate melts there must be three kinds of oxygen atoms present: those bonded to two silicon atoms, those bonded to one silicon and those unattached to silicon. Their proportions are presumably connected by an equilibrium of the type O 2– + ⋮ Si-O-Si ⋮ = 2(⋮ Si-O¯). From the manner in which both the sulphide and sulphate equilibria depend upon the proportions of metal oxide present, it appears that only the oxygen atoms which are unattached to silicon are of importance so far as these equilibria are concerned. The potential capacity of a melt to hold sulphur as sulphide is expressed as its sulphide capacity C s = (wt. % S) ( p O 2 ) ½ /( p s 2 ) ½ . For binary silicate and aluminate melts there is a close parallelism between the value of this capacity and the activity of the basic metal oxide. The activity coefficients for CaS have been found to be the same as for CaSO 4 and approximately constant in CaO-SiO 2 mixtures. The sulphide equilibrium results have been used to improve the free energy of formation curve for the formation of CaO-SiO 2 melts, and to construct a similar curve for CaO-Al 2 O 3 melts. The temperature coefficient of the sulphide capacity for CaO-SiO 2 melts has been combined with other data and used to extend the heat of formation curve for CaO-SiO 2 melts. The sulphur capacities, and presumably the lime activities, of the ternary melts CaO-SiO 2 -Al 2 O 3 , have been shown to be a maximum at compositions for which the molar proportions of SiO 2 and Al 2 O 3 are equal; this behaviour would be expected because the energy of interaction of SiO 2 and Al 2 O 3 is much greater than that of either CaO and SiO 2 or CaO and Al 2 O 3 . It follows the pattern established for FeO activity coefficients in CaO-SiO 2 and CaO-P 2 O 5 melts, these rising to a maximum at CaO : SiO 2 and CaO; P 2 O 5 molar ratios of 2:1 and 3:1 respectively.

Some instabilities of a completely ionized plasma

Abstract: Two cases of equilibrium for a highly conducting plasma are investigated for their stability In the first case, a plasma is supported against gravity by the pressure of a horizontal magnetic field This equilibrium is found unstable, in close correspondence to the classical case of a heavy fluid supported by a light one The second case refers to the so-called pinch effect Here a plasma is kept within a cylinder by the pressure of a toroidal magnetic field which in turn is caused by an electric current within the plasma This equilibrium is found unstable against lateral distortions

On cnoidal waves and bores

Abstract: For a train of gravity waves of finite amplitude in a frame of reference in which they are stationary, it is suggested that, in addition to the volume flow per unit span Q and the total head R , one may usefully study a third constant S , the rate of flow of horizontal momentum(corrected for pressure force, and divided by the density). The values of Q , R and S probably determine the wave-train uniquely; this is proved explicitly for long waves in a new presenta­tion of the ‘cnoidal wave’ theory (§3). The combinations of Q , R and S which are possible in the general case are illustrated by a diagram (figure 2) in which the co-ordinates are r = R / R c and s = S / S c ; here suffix c refers to ‘critical’ flow at the volume rate Q . There are two barriers on this diagram beyond which no stationary waves, or other steady flows, are possible; at the left-hand barrier (corresponding to uniform subcritical flows) the amplitude tends to zero; at the right-hand barrier (corresponding to uniform supercritical flows) the wave-length tends to infinity (case of the solitary wave). The diagram needs to be completed by a third barrier corresponding to ‘waves of greatest height’. This starts at the point marked Z and moves to infinity within the unshaded region without ever intersecting the left-hand barrier. The diagram may be used to determine what losses of momentum and energy a given stream can undergo, without departing from the condition of steady flow. Thus, one can determine the maximum wave resistance on a cylindrical obstacle athwart a given subcritical stream, or on a two-dimensional ‘step’ in the bed, in the absence of energy dissipation. Again, one can study the transition to a wave-train behind a bore. Such a wave-train (present in all but very strong bores) is shown to be capable of absorbing almost the whole energy which according to classical theory is liberated at the bore, although some minute residual dissipation of energy still appears to be necessary.

The Complementary Structure of Deoxyribonucleic Acid

Abstract: This paper describes a possible structure for the paracrystalline form of the sodium salt of deoxyribonucleic acid. The structure consists of two DNA chains wound helically round a common axis, and held together by hydrogen bonds between specific pairs of bases. The assumptions made in deriving the structure are described, and co-ordinates are given for the principal atoms. The structure of the crystalline form is discussed briefly.

The flow of heat through the floor of the Atlantic Ocean

Abstract: The measurement of the temperature gradient and thermal conductivity in the sediments beneath the floor of the North Atlantic Ocean is described. Measurements were made at five stations. The mean heat flow and conductivity were found to be 0$\cdot $98 $\times $ 10$^{-6}$ cal/cm$^{2}$s and 25 $\times $ 10$^{-4}$ cal/cm degrees Cs. The heat flows at the individual stations range from 0$\cdot $58 to 1$\cdot $42 $\times $ 10$^{-6}$ cal/cm$^{2}$s. The high heat flow is an unexpected result, and it is difficult to find a source for so much heat.

The structure of haemoglobin - IV. Sign determination by the isomorphous replacement method

Abstract: Native horse haemoglobin contains free sulphydryl groups and forms crystalline compounds with para -mercuribenzoate groups and with silver ions. Crystals in which two of the four available SH groups are so combined are exactly isomorphous with normal monoclinic methaemoglobin, but exhibit significant changes in the intensities of many reflexions. The changes in F ( h 0 l ) were used to determine the x and z parameters of the pair of heavy atoms attached to each haemoglobin molecule; this was done both for the normal wet lattice and for one of the acid-expanded lattices. The positions of the heavy atoms proved to be slightly different in each case, giving rise to three sets of diffraction fringes, each set making measurable contributions in different areas of the reciprocal net. In each case the isomorphous substitution allowed the signs of just over two-thirds of the reflexions to be found with certainty. Between them the three sets of diffraction fringes determined the signs over the entire area of the h 0 l plane so far investigated. These signs were then superimposed on the waves of the transform described in previous papers of this series. All the sign relations established by the transform method were confirmed and the remaining uncertainties cleared up. Comparison of the transform with the three sets of isomorphous replacement results allowed the consistency of the signs to be rigorously checked; not a single inconsistent sign was found. In the normal wet lattice the mercury and the silver compounds between them allowed the signs of 87 out of 94 reflexions to be found with certainty. This suggests that the isomorphous replacement method may offer a way of finding the phases in protein crystals even when practical difficulties preclude the use of the transform method.

The laminar flame speed of propane/air mixtures with heat extraction from the flame

Abstract: This paper describes the measurement of flame speed by means of the flat flame formed downstream of a cooled porous plate through which flows a mixture of propane and air. A flat flame has been stabilized over a wide range of mixture ratios and with flame speeds ranging between 4 and 38 cm/s; the adiabatic flame speeds are obtained by extrapolation. Good agreement is obtained with the results of other investigators as to the effect of temperature on flame speed. Cellular flames are observed in rich, weak and stoichiometric mixtures; cell size varies both with mixture ratio and heat-extraction rate.

X-Ray Scattering from Coals

Abstract: This paper describes the results of X-ray scattering experiments on a series of vitrain-coals of varying rank. The scattering at high angles is interpreted in terms of condensed aromatic layers; the diameters of the layers are determined and are found to increase with increasing rank; the percentage carbon in the form of layers is also estimated. Fourier transforms calculated for the scattering at lower angles show that the layers occur partly singly, and partly in groups of two, three or more stacked parallel to each other. The degree of local parallel stacking increases with increasing rank. There is a preferred orientation of the layers parallel to the bedding plane, which becomes more marked the higher the rank of the coal. The diffraction peak at $\sim $ 20 angstrom, found for coals with 85 to 94% C, is considered to be a consequence of 'liquid-type' packing of the most frequently occurring groups containing two to three layers. The diameters of the layers determined from the transforms ($\sim $ 8 angstrom) are in good agreement with the results of intensity calculations, and the values obtained from the scattering at high angles. The scattering at very small angles is measured with a two-crystal spectrometer for spacings up to $\sim $ 5000 angstrom. The scattering is related to porosity; the scattering curves do not support the existence of a close-packed arrangement of 'micelles' of fairly constant diameter less than $\sim $ 5000 angstrom, but suggest that there are anisotropic cracks and pores of a wide range of sizes, some of which must exceed $\sim $ 5000 angstrom. The total scattering indicates the existence of disk cracks preferentially orientated parallel to the bedding plane. In terms of a proposed structural model, coalification is a process of condensation, ordering of the layers, and flattening of the structure. A 'liquid-type' structure is formed, which is most perfect at $\sim $ 89% C and accounts for the minimum of porosity. Anthracitization is probably accompanied by a clustering of the layers, which results in a rapid increase of layer diameter, in irregular packing, and in an increase of porosity. The properties of the proposed structure model of coal are discussed and compared with the known physical and chemical properties of coal, e.g. density, optical data, porosity and mechanical properties, and some of the problems still outstanding are indicated.

The hollow-cathode effect and the theory of glow discharges

Abstract: The nature of the processes in the cathode dark space and the negative glow of a glow discharge is not well understood. Moreover, the existing theory leading to relations between the cathode fall in potential, the current density, the width of the dark space and the electric field distribution in it is based on dubious assumptions and does not indicate the important physical processes in operation. Thus further experimental evidence would be valuable in developing the theory. By exploring the electric field between two plane-parallel cathodes with an electron beam, and observing simultaneously the other discharge parameters, new information was obtained. A double (hollow) cathode was used because in a conventional glow discharge the dark space, cathode fall and current density are interdependent; here the cathode separation controls the width of the dark space. When the separation is sufficiently reduced the two negative glows coalesce and the light emitted as well as the cathode current density rise greatly. This is the hollow-cathode effect. Results show that the field in the two dark spaces of a hollow cathode falls linearly with the distance from the cathode, and thus the net space-charge density is constant, as it is known to be in the conventional discharge. From the same observations the dark-space length is found. The conclusions drawn from these results lead to an elementary theory which covers both the hollow and the conventional glow discharge in various gases as indeed it should, since with increasing cathode separation the first goes over into the second type. The main feature is the contribution of the ultra-violet quanta from the glow to the photo-electric emission from the cathodes which is regarded as the essential factor in secondary electron emission. Another result comes from a reconsideration of the motion of positive ions in the dark space based on atomic beam studies and the modem theory of elastic collisions between ions and atoms. The discrepancy between earlier experiments showing that ions of energy of the order of the cathode fall in potential arrive at the cathode and classical calculations leading to low ion energies is resolved by allowing for small-angle scattering and charge transfer.

The Electronic Structure of the Borides MB$_{6}$

Abstract: The electronic structure of the metallic borides MB$_{6}$ is investigated theoretically by the tight-binding approximation. The stability of the crystal lattice is interpreted and it is predicted that if M is a bivalent metal the crystal should be an insulator or photoconductor, but that if M has a valency greater than 2 the crystal should exhibit metallic conductivity. These predictions are consistent with the scanty experimental evidence.

The Turbulent Transport of Suspended Sediment in Open Channels

Abstract: Fine sediment is carried in suspension by turbulent flow under steady conditions, provided that similar material is present on the bed. An equation is deduced for the variation with depth of the sediment concentration for two-dimensional flow. It is found necessary to take account of the volume occupied by the sediment, this being particularly important near the bed. The result agrees with recent observations by Vanoni (1946). A velocity distribution obtained by Karman, using a linear variation of shear with depth, is generalized by omitting the infinite velocity gradient condition at the bed and is found to be in good agree­ment with Vanoni’s measurements. A slight difference is found between the mean sediment velocity in the direction of flow and that of the water.

The Effect of Drop Size on Flame Propagation in Liquid Aerosols

Abstract: A method has been developed whereby suspensions of controlled uniform drop size can be prepared from pure liquids. Using tetralin as the fuel, it has thus been possible, within limits, to study the effect of the drop size on the combustion properties of a liquid-in-air suspension. Through a study of limits of inflammability, nitrogen dilution limits and burning velocities, it has been shown that the mechanism of flame propagation is completely transformed within the drop-size range 7 to 55 μ . Below 10 μ the suspension behaves like a vapour, but above 40 μ the drops burn individually, in their own air envelope, and one burning drop ignites adjacent ones, thus spreading combustion. At intermediate sizes, behaviour is transitional. A practical consequence of this transformation is that the lower concentration limit of inflammability is reduced and the rate of burning increased for the larger drops.

High-angle Kikuchi patterns

Abstract: A cylindrical specimen chamber and camera have been used to study the high-angle Kikuchi patterns obtained by reflexion of electrons, of energy 6 to 50 keV, from the cleavage surfaces of crystals with the sodium chloride structure. Angles of scattering ranging from 0 to 164° were covered. The relative intensity of the pattern at different scattering angles was measured using a photographic technique. The intensity distribution was found to become less steep as the energy of the incident electrons decreased. In photographs taken with a large value of the glancing angle of incidence, defect bands were found, starting near the shadow edge of the pattern; these changed to excess bands at higher angles of scattering. The most striking feature of the results is the remarkable intensity and clarity at the highest scattering angles of the pattern produced by crystals such as lead sulphide and potassium iodide, the constituents of which have a relatively high elastic scattering cross-section. In marked contrast, a relatively low intensity and low clarity was found at these angles for lithium fluoride under the same experimental conditions. An investigation of the width of Kikuchi bands, visible over the whole available angular range, showed that the electrons forming these bands had the same energy as that of the incident electrons within the experimental error of 10%. A possible mechanism is discussed by means of which electrons can be diffused through large angles with high efficiency, relative to small angles, and with relatively little loss of energy.

Molecular-weight changes in the degradation of long-chain polymers

Abstract: The changes in molecular weight of a long-chain polymer (initially of arbitrary molecular-weight distribution) are studied when the main chain is subjected to random fracture, such as occurs when certain polymers are exposed to high-energy radiation. For several distributions studied, all trace of the initial distribution curve is lost after an average of some 3 to 8 main-chain fractures per molecule. For lower degrees of degradation the shape of the curve of weight average against degradation can provide information as to the initial weight average, z average, z + 1 average molecular weights. The initial number-average can be obtained by a method of extrapolation.

The slip modes of titanium and the effect of purity on their occurrence during tensile deformation of single crystals

Abstract: Single-crystal test specimens of van Arkel titanium were obtained by a modification of the strain anneal technique.The modes of slip have been identified as (1010) [1120],(1011) [1120], and (0001) [1120]. It has been shown that not only does the interstitial impurity affect the magnitude of the critical resolved shear stress but also the relative values for the three slip systems. (1010) is the principal slip system and is favoured by increasing purity. A possible mechanism for the role of oxygen and nitrogen in this effect is put forward wherein it is shown that the interstitial sites occupied are such that interstitial elements render slip more difficult on two of the three slip planes in titanium.

The Thermal Decomposition of Ammonium Perchlorate. I. Introduction, Experimental, Analysis of Gaseous Products, and Thermal Decomposition Experiments

Abstract: The thermal decomposition of ammonium perchlorate in vacuo and under small initial pressures of nitrogen, to suppress sublimation, has been investigated in the temperature ranges 220 to 280°C and 380 to 450°C. The experimental techniques for following the decomposition and subsequent analysis of the products are described and gas analysis results given. In the low -temperature range only 30% decomposition occurred though the ‘residue’ was still ammonium perchlorate. In vacuo sublimation occurred all the time and also after decomposition had ceased which indicated that the reaction was not in the vapour phase. Some of the properties of the sublimed material and the ‘residue’ were investigated; in particular, it was found that the residue which was porous in texture (the decomposition had occurred throughout the crystal) could be ‘rejuvenated’ by exposure to a solvent vapour. The crystal transformation at 240°C from orthorhombic to cubic, the addition of impurities which might be intermediate decomposition products, and the addition of some metallic oxide catalysts, were also investigated.

The Statistical Mechanics of Assemblies of Axially Symmetric Molecules. I. General Theory

Abstract: A general method for investigating the thermodynamic effects of the dependence of the intermolecular potential on orientation is described. The intermolecular potential for axially symmetric molecules is expanded in such a way that the central-force part can be separated uniquely and the remaining directional parts classified in terms of various angular symmetries. Several simple types of directional intermolecular force are treated in this way as examples. The free energy of an assembly of such systems is then calculated by treating the directional parts of the field as a perturbation on the central-force part. This leads to a simple expression for the extra free energy due to directional forces in terms of the molecular distribution functions of an assembly of molecules interacting according to a central-force law. A corresponding treatment of multicomponent systems is also given.

On the Propagation of Elastic Waves in Aeolotropic Media. I. General Principles

Abstract: Using the principle of least action the equations of motion and momentum conditions for elastic disturbances in any continuous medium are derived. Consideration of energy flux defines the form of the wave surface as the first negative pedal of the surface of phase velocities for elastic plane waves in the medium . A general method for obtaining the forms of these surfaces and an associated inverse surface is given and general conclusions about the propagation of disturbances are drawn.