Physical Chemistry of Foods

by small-molecule surfactants. If then aggregation will only occur when

protein covered patches come very close to each other, the aggregation rate

would bey^2 times the value of fully protein covered particles.

Some other important complications are discussed in Sections

13.2.2–4.

13.2.2 Orthokinetic Aggregation

The termorthokineticsignifies that particles encounter each other due to

velocity gradients in the liquid. See Section 5.1.1 for types of flow and

velocity gradient.

‘‘Fast’’ Aggregation. Smoluchowski has worked out a theory for

the case of simple shear flow, further assuming that particles will stick and

remain aggregated when colliding with each other. The situation is

illustrated in Figure 13.6 for spheres of equal size, neglecting

hydrodynamic interaction forces for the moment. A particle (e.g., A) will

meet a reference particle (B) if its center is in a half cylinder of radiusac

(which equals the collision radius 2a), as depicted. The linear rate of

approach of particle A will be proportional to d (0<d<a). Four

subsequent positions of particle A are shown. Near position 3, A and B

collide and stick. The doublet formed now rotates in the shear field; in fact,

Smoluchowski assumed the particles to fuse into one sphere. From simple

geometric considerations it then follows that the decrease in particle number

FIGURE13.6 Orthokinetic aggregation of particles of equal diameter in simple
shear flow, as envisaged by Smoluchowski. At left, the flow velocity profile is shown.
Particle A moves from left to right (positions 1 to 5), particle B is in a stationary
position, but it does rotate. At right a cross section is given that illustrates the
geometry of the half-cylinder containing the centers of the particles to the left of B
that will ‘‘collide’’ with B.