The modelling of the flocculation process is reviewed. Recent developments
in this area are discussed with reference to the classical analytical expre
ssion of Smoluchowski defining collision frequency and originally published
in 1917. The constraints imposed by six principal assumptions made by Smol
uchowski are considered individually, with the key models that have been de
veloped to address specific limitations discussed in detail. These assumpti
ons comprise: (1) all particle collisions lead to attachment, (2) fluid mot
ion is limited to laminar shear, (3) particles are monodispersed (i.e. all
of them are the same size), (4) no breakage of flocs occurs, (5) all partic
les are spherical in shape and remain so after collision and (6) collisions
take place only between two particles. The discussion incorporates an exam
ination of particle dynamics (i.e. rectilinearity vs curvilinearity), parti
cle surface chemistry (van der Waals attraction and electrostatic repulsion
), mixing parameters (mixing intensity and the Camp number) and the key fle
e growth parameter of fractal dimension D. In doing so limitations of moder
nised theories are identified. It is concluded that constraints imposed on
the interpretation of models based on microscopic aspects of the system, pe
rtaining mainly to those phenomena presiding at the particle:solution inter
face, severely restrict their application in real systems. The more recent
microscopic approach based on characterisation of the system through determ
ination of the fractal dimension as a function of time offers the opportuni
ty of a simpler yet more representative modelling, but none-the-less, curre
ntly relies on empirical measurement using fairly sophisticated experimenta
l techniques. (C) 1999 Elsevier Science Ltd. All rights reserved.