Principle of a Counter-streaming Centrifuge for the Separation of Particles of Different Sizes

Abstract

WHEN a liquid containing suspended particles of uniform density streams through a conical tube, the velocity of the particles is greatest at the apex of the cone and decreases in the direction of the base. If the tube is placed in a centrifuge with the apex pointed away from the centre of rotation, in the direction of which the liquid is made to flow, the particles acquire, in addition to the velocity due to the liquid stream, a velocity in the opposite direction owing to the centrifugal effect. If Z is the distance between the apex and the centre of rotation, R the radius of the cone at the distance L from the apex, V the volume of liquid passing across any section of the tube in unit time, and x the distance from the centre of rotation, then the streaming velocity ƒ over any cross-section of the tube is The velocity of the particles in the direction away from the centre of rotation, however, increases linearly with the distance from the latter. In a certain cross-section (e) the two velocities are equal for a given particle size. Particles of this size situated centripetally from e are transported in the centrifugal direction and vice versa. Thus, when dynamic equilibrium has been attained, they have been accumulated in a very short section of the tube. Other particles are similarly accumulated in sections characteristic of their sizes ; the smaller their radii (r), the nearer the centre of rotation are their planes of equilibrium. The distribution of these planes along the radius of rotation is derived from Stokes' law and the above expression for the streaming velocity : where n is number of revolutions per min., η is viscosity of liquid, S is density of particles, S' is density of suspension medium. For x = Z/3, r has a minimum value :