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Studies of Clay Particles with the Electron Microscope: III. Hydrodynamic Considerations in Relation to Shape of Particles
Author(s) -
Kelley O. J.,
Shaw B. T.
Publication year - 1943
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj1943.036159950007000c0010x
Subject(s) - relation (database) , state (computer science) , electron microscope , citation , library science , computer science , physics , optics , algorithm , data mining
N all the physical and chemical properties of clays are affected by the amount of specific surface present. The specific surface can be determined if the size and shape of the particles are known. In the past there has been no means of measuring the dimensions of clay particles directly, nor has there been any adequate means to view them directly and study their shape. With the advent of the electron microscope it is now possible to measure two of the three dimensions and to study the shapes of the various types of clay particles (i, 2). By making use of hydrodynamic theory and by using the electron microscope in the determination of two of the dimensions, it should be possible to calculate the third and thus determine the specific surface. This information should aid considerably in the study of the various clay minerals. Marshall (7) developed an equation for the settling velocity of ellipsoids of rotation. He considered Ra and Rb as the equivalent spherical radii of particles falling in the direction of the a and b axes and calculated these in terms of b, using Miiller's (10) formulae. In Marshall's usage, a is considered the semi-axis of rotation and b is the mean semi-axis perpendicular to a. Marshall considered the kinetic energy of a particle due to its Brownian movement of rotation and came to the conclusion that particles with diameters less than 2 n would not be oriented in the force fields commonly used in mechanical analysis. He expressed the mean value of the equivalent radius of ellipsoids of revolution in random orientation as Rm = 1/3 (Ra + 2Rb). He expressed this as F X b, where F is a factor depending on shape only. At equilibrium under gravity, 4/3 TT ab (d2 — di)g = 67rr7bvF, so that his equation for the settling velocity of a plate-shaped particle is 2ab (d2 di) g V 9F^ Where a = semi-thickness of plate b = semi-diameter of plate d% = density of particle di = density of liquid = viscosity of liquid 77 Marshall used Miiller's formulae to calculate the value of F. Miiller obtained his formulae from an evaluation of Lamb's (5) expression. According to Lamb, the resistance experienced by a slowly moving ellipsoid in steady translocation in a viscous liquid is given by the expression resistance = 6 w rj R v where R = the radius of a sphere that would produce the same disturbance as the ellipsoid. Lamb shows that for motion parallel to a