[Notes on Curtis and "Collision Efficiency"]

Date:
1970
Reference:
PP/CRI/H/4/21
Catalogue details

Licence: In copyright

Credit: [Notes on Curtis and "Collision Efficiency"]. Source: Wellcome Collection.

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    Off printed from the Transactions of The Faraday Society, No. 570, Vol. 66, Part 6, June, 1970 Collision Efficiency of Equal Spherical Particles in a Shear Flow The Influence of London-Van der Waals Forces By. A. S. G. Curtis * and L. M. Hocking * Received 15 th August, 1969 A theoretical and experimental approach to the investigation of the influence of London-Van der Waals forces on orthokinetic flocculation is described. The theoretical treatment evaluates the effect of these forces on the interaction of two spherical particles in a laminar shear flow, to give a value of the collision efficiency (stability ratio). The experimental measurements on the flocculation of monodisperse polystyrene beads in a laminar shear flow reported provide a test of the theory. By making use of the theoretical approach described in this paper the London-Hamaker constant for polystyrene in aqueous suspension can be calculated from measurements of orthokinetic flocculation : the values obtained are in good agreement with those derived by other methods. The method additionally provides a means of measuring the characteristic wavelength of these forces. For particles of diameter greater than 1 /im, orthokinetic flocculation tends to be of greater importance than perikinetic flocculation in conditions of shear flow. 1 However, no measurements have been made of the rate of orthokinetic flocculation under conditions where London-Van der Waals force may act, nor has a general theory of the influence of this force on such flocculation been developed. This situation may be contrasted with the several theoretical and experimental studies of the influence of this force on perikinetic flocculation, e.g., Ottewill. 2, 3 In this paper we present a theoretical and experimental approach to the problem of ortho kinetic flocculation. The experimental and theoretical treatments are based on the evaluation of the collision efficiency E ; the experimental tests make use of the treat ment of flocculation in a shear flow developed by Swift and Friedlander 4 from Von Smoluchowski's studies of orthokinetic flocculation. theoretical A theoretical description of the process of coagulation requires the determination of the collision efficiency (stability ratio) for two particles, in this instance, in a shear flow. If the particles always moved with the undisturbed shear velocity, any one particle would collide with another of given size if it were within a cylinder, of radius equal to the sum of the radii of the particles, with its axis parallel to the flow direction. The cross-section area within which the particle lies if collision occurs when allowance is made for the effect of hydrodynamic and London forces, as a fraction of the geo metrical cross-section, is the collision efficiency for particles of the two sizes. A comparatively simple special case is for two equal spherical particles and it is the value of the collision efficiency for such particles which is determined in this paper. The particles are small in that the Reynolds number for their motion in the fluid is less than unity, but they are large enough for Brownian motions to be neglected. A mono-dispersed suspension of such particles, when sheared at a known rate, will yield a calculable proportion of doublets and large aggregates, provided the collision 1381