Particle Motions in Sheared Suspensions Iii.: Further Observations on Collisions of Spheres

Abstract

Two-body interactions between glass spheres of diameters n, and a2 caused by velocity gradients vary with al/ap. When I < al/a2 < 2 , well-dehned collisions similar to those previo~~sly reported for spheres of equal size can be observed. Fair agreement is found between the experimentally observed and calc~llated collision frequencies over a range of particle concentrations and velocity gradients. \i'hen al/a? > 2 the particles are separated a t all times and the phenomena of interaction are Inore complex. Single air bubbles rotate a t the same angular velocity as rigid spheres. When two air bubbles of equal size are bro~lght into collision a d o~~b l e t is formed; instead of the mirror-image separation observed with neutral rigid spheres, the do~tblet continues to rotate for as many as 60 rotations before coalescence occurs. Less f r e q~~e n t l y a do~tblet with distinct particle separation is observed. Periods of rotation of both types of doublet and certain details of the rotational orbit of a d o~~b l e t of touching air bubbles have been measured and compared with values predicted from Jeffery's theoretical equations for rigid ellipsoids. Apart from their intrinsic interest, the phenomena described are of importance in theories of viscosity and coag~~lation of suspensions and colloidal dispersions. INTRODUCTIONIn an earlier paper (5), the two-body collisions of rigid neutral spheres of equal size suspended in a liquid subjected to a velocity gradient were described in some detail. I t was shown experimentally that in a simple field of fluid shear described by [I] u = Gy, v , w = O where u, v, and w are the respective velocities along the X-, Y-, and Z-axes and G is the rate of shear, two spheres can approach one another along an undisturbed rectilinear path parallel to the X-axis until they come into apparent collision at the rate 121 f = 4a3nG/3[31 = 8 c G / r . Here, f denotes the number of collisions per particle per unit time, a the particle diameter, n the number of particles per unit volume of suspension, and c the volume of particles in the suspension.The doublet formed by two colliding spheres rotates about the Z-axis a t a constant angular velocity [41 a = G/2 until it reaches the mirror image through the Y-Z plane of the initial position of contact; the two particles then separate.LManzrscript received J a n z~a r y 17, 1955.

The rheology of suspensions of solid particles

“…with B = 2.5 and 7.35 B 1 14.1 derived from consideration of particle-particle interactions (Guth & Gold 1938;Vand 1948;Manley & Mason 1955). Lower values of B 1 have been found when Brownian motion (Saito 1950;Batchelor 1977) and inertia (de Bruijn 1942) are important.…”

On the viscosity of composite suspensions of aluminum and ammonium perchlorate particles dispersed in hydroxyl terminated polybutadiene—New empirical model

“…Presently, there are a lot of empirical and semiempirical models, taking into consideration the above mentioned effects. Some of the important models are outlined here, however, further models can be found in literature [17][18][19][20][21][22].…”

Relative viscosity and concentration

“…Vor bimodal distributions the effect is greater. No doublets are formed then, the smaller spheres moving as planetes around the larger ones (31). Sherman (32) proposed, for emulsions, to combine sphere size and concentration into one parameter, for relative viscosity, the mean sphere distance d, but the scattering of the results was rather high.…”