Accuracy of external force measurements based on particle tracking velocimetry

In microfluidic systems external forces are frequently applied to fluids or colloidal suspensions in order to accomplish or enhance mass transport tasks. The complexities of microscale geometries and material properties, however, can cause discrepancies between theoretical predictions and the actual values of the applied force. Therefore a calibration experiment is necessary to validate the actual magnitude of the applied force. One method of such in vivo calibration is through observations of tracer particle motions using particle tracking velocimetry (PTV). In microfluidic applications, the tracer particles of choice are typically submicron in diameter and therefore undergo significant Brownian motion. Further complicating the matter is the presence of the solid channel boundaries whose presence can lead to hindered Brownian motion and position-dependent hydrodynamic drag. In this paper we present a Langevin simulation study of the effects of normal and hindered Brownian motions, and the time between image acquisitions on the accuracy of external force measurements based on PTV. It is found that the relative strength between the random forces that cause Brownian motion and the applied external force plays a critical role in measurement accuracy. We also found that hindered Brownian motion and the associated sampling trajectory biases contribute additional force measurement inaccuracies when PTV is conducted in the vicinity of a solid boundary.