Study on Improving the Turbidity Measurement of the Absolute Coagulation Rate Constant

Abstract

The existing theories dealing with the evaluation of the absolute coagulation rate constant by turbidity measurement were experimentally tested for different particle-sized (radius = a) suspensions at incident wavelengths (lambda) ranging from near-infrared to ultraviolet light. When the size parameter alpha = 2pi a/lambda > 3, the rate constant data from previous theories for fixed-sized particles show significant inconsistencies at different light wavelengths. We attribute this problem to the imperfection of these theories in describing the light scattering from doublets through their evaluation of the extinction cross section. The evaluations of the rate constants by all previous theories become untenable as the size parameter increases and therefore hampers the applicable range of the turbidity measurement. By using the T-matrix method, we present a robust solution for evaluating the extinction cross section of doublets formed in the aggregation. Our experiments show that this new approach is effective in extending the applicability range of the turbidity methodology and increasing measurement accuracy.

A study on independently using static and dynamic light scattering methods to determine the coagulation rate

“…14 Since the formula for evaluating coagulation rates in SLS measurement have quite similar formation as that used in turbidity measurement, we believed that the blind points would also exist in SLS method. These blind points will be the angles (blind angles), instead of the wavelength for the turbidity measurement, that make I 2 (q)/2I 1 (q) − 1 equal to zero so that dI(q, t)/dt will also be zero correspondingly.…”

“…At this stage, only collisions of single particles which form doublets need to be considered. Therefore, the change of particle number concentrations can be approximately expressed as 14,29 …”

“…To acquire reliable coagulation rates, turbidity measurements should be performed at a wavelength some distance from the blind point. 14,28 Considering the formula for evaluating coagulation rates by SLS and turbidity measurement are quite similar. 28 The only difference between them is that the variable in SLS formula is the scattering angle with the operating wavelength fixed while the variable in the turbidity formula is the wavelength with the angle fixed.…”

“…[14][15][16][17][18] Specifically, turbidity measurement, static light scattering (SLS) and dynamic light scattering (DLS) are the most widely adopted methods. The major difficulty in determining coagulation rate by light scattering is how to theoretically calculate the so-called optical factor I 2 (q)/2I 1 (q), where I 1 (q) and I 2 (q) (q is the scattering vector, see below for the definition) are the scattered intensity of a singlet and a doublet, respectively.…”

“…21 In turbidity measurement, we have effectively used T-matrix method in evaluating the extinction cross section of doublets to determine the coagulation rates of large sized particle dispersions. 14,15 It is supposed that if the T-matrix method is employed to achieve I 2 (q)/2I 1 (q), either SLS or DLS method should be able to be used alone in determining the coagulation rates, instead of combining both of them.…”