# Aggregation rate determination

Overall aggregation rate is the cumulative increase over time of the aggregate concentration of bigger size. It is the rate of the transfer of aggregates from the bin (size interval) of smaller diameter to the bin of  larger diameter.

 1. Measure particle distribution two subsequent times (t and t-1).   2. Compute the aggregation rate  $$\lambda _{add}(t)=\frac{1}{\Delta t\Delta d}\sum_{i}(\sum_{n}^{bin=i}c_{t}-\sum_{n}^{bin=i}c_{t-1})$$where c is particle concentration (m-3), n is the number of bins (i.e. size intervals), Δd is the bin size and Δt is the time step. 3. Compute e.g. 1st order aggregation rate constant λagg.

## Used for

 This procedure is valid if particles are neither added nor removed from the system and particle size is not influenced by other processes. Particle size distribution can be determined by NTA, DLS and ELS. Exploring the time evolution of the aggregation rate requires multiple measurements across time points. This can be performed by NTA with sample loading from an autosampler. A 96 deep well plate allows experimental design of large time series or multiple repeat measurements of a single sample.

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## Contact

Kamil Nešetřil

Technical University of Liberec (TUL)

Email: kamil.nesetril@tul.cz