Real-time monitoring of complex moduli from micro-rheology

We describe an approach to on-line analysis of micro-rheology data using a multi-scale time-correlation method. The method is particularly suited to processing high-volume data streams and compressing the relevant information in real time. Using this, we can obtain complex moduli of visco-elastic media without our method suffering from the high-frequency artefacts that are associated with the truncation errors in the most widely used versions of micro-rheology. Moreover, the present approach obviates the need to choose the time interval for data acquisition beforehand. We test our approach first on an artificial data set and then on experimental data obtained both for an optically trapped colloidal probe in water and for a similar probe in polyethylene glycol solutions at various concentrations. In all cases, we obtain good agreement with the bulk rheology data in the region of overlap. We compare our method with the conventional Kramers-Kronig (KK) transform approach and find that the two methods agree over most of the frequency regime. For the same data set, the present approach is superior to the KK one at high frequencies and can be made to perform at least comparably at low frequencies.