Flocculation modelling: A review

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.