Original scientific paper

Coagulation as a Second Order Process - a Basis for Computer Simulation

Mirko Mirnik ; Laboratory of Physical Chemistry Faculty of Science, University of Zagreb, 41001 Zagreb, P. O. Box 163, Yugoslavia

Abstract

Coagulation is interpreted as a second-order process caused by efficient collisions either between free primary particles (FPPs),
FPPs and aggregates (AGGs) or between AGGs themselves. The following relations and definitions are derived theoretically: size distribution of AGGs: Pi (I) = (T-l)P0 + I^Pa = TP„< Pr (I) =
= (T -f 1) Po — I + 1 for 1 I P0; total number of PPs present in AGGs defined by the distribution parameter T: SP (T) = 2V (T) PQ
Po
2 21 = 4V (T) Po (2Po — 1); relative volume in which AGGs defined
i = i
by a given T are present: V (T) = (T + 1) V (T = l)/2; number of AGGs of size Pi (I) and Pr(I): Ai (I) = Nv (1)1 Pi and Ar (I) =
= Np(I)/Pr; number of PPs in AGGs of size Pi (I) and Pr (I):
Np (I) = V (T) P021; coagulation time of FPPs: Tf = Tfab/Tf2 =
= Sp (Po)/[Sp — Sp (Po)] where SP = SP (P0,max); coagulation time of AGGs: Tc = Tcah/TC2 = 1 /(Aa— 1); number of AGGs of average size Pa; Aa (T) = Sp (T)/Pa = V (T) To/T where T0 = Sp/P0, 1 £ T ^ T0 and 0 < Tc ^ oc. it is demonstrated that Aa is the reciprocal ratio of reactant concentration, Pa is the relative reaction product concentration for the coagulation of AGGs. The reaction product concentration for the coagulation of FPPs is SP (PQ)/V (T = 1) and [Sp (Po,max) — Sp (P0)]/V (T = 1) is the reactant concentration. The relative coagulation times of FPPs and of AGGs reap, are defined as the ratio [reaction product]/[reactant] of second order reactions.
The formation of AGGs defined by P0 = 6 from FPPs and the growth of AGGs defined by T = 1 into those defined by T = 2 in steps of AT = 1/PG is also demonstrated numerically as an example. Simple programs can be set up to demonstrate graphically the shift of the histograms ”Ai, Ar vs, Pi, Pr” and ”NP vs.
Pi, Pr” with increasing Tc and to calculate the values Aa for any value of Po the computer can process. One of the aims of the experiments should be to evaluate the values of SP (exp). Then, as rule, a Po value can be established for which SP (Pc) < SP (exp) <
Sp (Po + 1) is valid and a correction factor F for which F = Sp (exp)/
/Sp (Po) is valid. Then is F the number of AGGs of maximal size.
When only T-th AGG size is present in the coagulating sol, then the smallest AGG size is Pi (I = 1) = T and the width of the histogram is defined by P0’ = TP0 instead of Po.
Notation: PD = parameter defining the width of the AGG size (= number of PPs) histogram; P0,max = the same when all FPPs

Keywords

Hrčak ID:

137393

URI

https://hrcak.srce.hr/137393

Publication date:

10.8.1990.

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