Uniform spheres packed in regular array form a non-cylindrical cyclic capillary, characterized by a maximum and minimum capillary rise with intermediate positions of possible equilibrium. In practice spheres may be packed to a variety of porosities P thus requiring a mixture of regular and irregular pilings arranged in a very distorted pattern. However the meniscus is also distorted to conform in a general way with the distortions of the lattice. Accordingly positions of maximum and minimum rise may be expected. The meniscus for maximum rise tends to pass through the plane of centers of neighboring spheres. Slight deviations from this condition due to the rise at sphere contacts are shown to be of minor importance. Any piling may be treated statistically as a hexagonal array with a spacing 2r+d where d is computed to give the observed porosity. In such a system three types of cell occur with a definite frequency, and these cell types are assumed present in the meniscus with the same frequency distribution. Hence it is possible to evaluate pr/a = ρghr/σ where p = perimeter, r = grain radius, a = area of pore opening, g = acceleration of gravity, σ = surface tension, ρ = density and h = capillary rise. The final formula so derived reduces to pra=ρghrσ=2[0.9590/(1−P)2/3]−1.This agreed with experiments made with several sizes of grains, porosities, and liquids. The minimum rises were also determined but a satisfactory interpretation in terms of a model has not been effected.
The pore space in an assemblage of uniform spheres was initially filled with liquid. After very slow drainage the amount of liquid retained by the spheres was experimentally measured. The liquid is retained in the form of rings at the contacts of adjacent spheres. The radii of curvature of the ring surfaces are computed in terms of surface tension, grain radius and pressure drop across the liquid-vapor interface, permitting calculation of the volume retained per sphere contact. The number of contacts per unit volume of spheres is obtained from porosity measurements using the theory developed earlier. Computed and observed data on total volume of retained liquid are in agreement.TF THE pore spaces in an assemblage of spheres be completely filled by •* a liquid which is then allowed to drain, a portion of the liquid is retained. The retention occurs during the passage of the liquid-gas interface through the grain assemblage. It is current opinion, as expressed in the semi-technical literature, that such liquid remains in the form of a fairly uniform layer which envelops the separate grains. In order to account for the observed retention, the thickness of the layer would have to be several thousand molecular diameters. Molecular forces, however, decrease extremely rapidly with distance, and unless chemical reactions, such as those involving gel formation, take place, layers exceeding three molecular diameters are improbable. Much of the work on retention has been done with comparatively fine sands and the actual mechanism of the phenomenon has escaped notice. Under the microscope, however, one may readily observe that a small ring of liquid is retained at the point of contact of two spheres. This type of retention is easily demonstrated by dipping two small balls or shot in a liquid and observing the retained liquid when the spheres, in contact, are withdrawn. It also follows from thermodynamical considerations that the major retention occurs in this manner. Equilibrium requires a minimum of free energy, and when the spheres are sufficiently small that gravitational effects are negligible, a given amount of retained fluid must be so distributed that the surface energy is a minimum. This occurs when the liquid is collected about the points of contact of the spheres.The ring volume can be calculated approximately. Consider a capillary ring of liquid as shown in Fig. 1 with the two principal radii of curvature y and R taken as positive numbers. Complete wetting or zero contact angle with the spheres is assumed. Let Ap be the difference in pressure just outside and inside the liquid surface, and let a be the surface tension. Then 524
Measurement of photo-electric ionization in gases.-The current from a filament, normally limited by space change, is increased by the presence of positive ions. As shown by Kingdon this effect may be greatly magnified if a small cathode is practically enclosed by the anode so that the ions are imprisoned. This method was used for the detection of photo-electric ionization. Besides possessing extreme sensitivity it is unaffected by photo-electric emission from the electrodes.Photo-electric effect in caesium vapor.-The change in thermionic current with the unresolved radiation from a mercury arc was measured as functions of the applied voltage, filament temperature, and vapor pressure. Then the photo-electric effect as a function of wave-length was studied using a monochromatic illuminator to disperse light from the arc or a Mazda lamp. The ionization per unit flux was found to increase with increasing wave-length to a sharp maximum at the limit Is = 3184A of the principal series, as is required by the Bohr theory. For longer wave-lengths the ionization decreased to about 10 percent at 3400A. Photo-excitation. The simple theory does not admit of ionization by wave-lengths greater than 3184A but the data are in qualitative agreement with the hypothesis that such radiation produces excited atoms which upon collision with other atoms acquire sufficient additional energy to become ionized. Hence, unlike an x-ray limit, the photo-ionization effect for a valence electron is not sharply discontinuous at the true threshold for direct ionization.Photo-ionization photometer and intensitometer.
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