Capillary Retention of Liquids in Assemblages of Homogeneous Spheres

Abstract

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by dipping two small balls or shot in a liquid and observing the retained liquid when the spheres, in contact, are withdrawn.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

Experimental verification of power-law non-Newtonian axisymmetric porous gravity currents

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The Preparation of Mesoscopic Rings in Colloidal Crystal Templates

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