Some analytical and numerical solutions for colloidal aggregation with fragmentation

Reversible Agglomeration: A Kinetic Model for the Peptization of Titania Nanocolloids

“…Only the slow decrease was fitted using Eq. [13]. The approach to steady state is described by a single decaying exponential, as shown by the inset in Fig.…”

“…Moreover, Eq. [13] should only be applied sufficiently close to steady state. For the data set shown in Fig.…”

“…The deagglomeration rate, K d , is obtained directly from the time constant of the exponential fit in Eq. [13]. The agglomeration rate constant, K a , is then calculated from Eq.…”

“…We reiterate that Eq. [13] is valid only sufficiently close to the steady-state value and that it is based on the assumption that the rate constants for fragmentation and agglomeration do not depend on size. The latter assumption is highly simplified and its applicability must be assessed by comparing the model predictions with experimental data.…”

“…The problem of simultaneous fragmentation/reagglomeration, or reversible agglomeration, has received considerable attention due to its relevance to a broad range of problems in colloidal science, polymerization reactions, and multiphase dispersions (7)(8)(9)(10)(11). Much of the theoretical work in the area of reversible agglomeration has focused on the solution of the population balance and on scaling relationships for the time evolution of the mean size for various size dependencies of the fragmentation and agglomeration rate constants (12)(13)(14). From an experimental point of view, the available data are usually limited to size measurements, while size distributions are rarely known, especially for colloids in the nanometer range.…”