Dynamic electrical response of colloidal micro-spheres in compliant micro-channels from optical tweezers velocimetry

We report the dynamic response of colloidal silica in aqueous electrolytes to oscillatory electric fields at frequencies up to approximately 50 kHz. Particles were optically trapped at various positions across the gap of straight and crossed parallel-plate micro-channels. Using back-focal-plane interferometry, we measured the apparent electrophoretic mobility in NaCl and CaCl(2) electrolytes over a wide range of salt concentrations. The mobility has a strikingly complex dependence on channel position and forcing frequency that cannot be understood on the basis of standard electrokinetic theory for rigid micro-channels. We ascribe the anomalous dynamics to coupling of electro-osmotic flow and elastic modes of the micro-channel and auxiliary hardware. By integrating into the classical theory a complex-valued channel-compliance parameter--that modulates the phase and amplitude of the dynamic electro-osmotic flow--theoretical interpretation of the frequency-dependent mobility furnishes robust measurements of the intrinsic particle electrophoretic mobility and the upper and lower channel-wall zeta-potentials. Together, the single-particle experiments and accompanying theoretical interpretation highlight--for the first time--how spatially and temporally resolved particle dynamics are exquisitely sensitive to channel compliance. Accordingly, specially designed compliant micro-fluidic channels and flexible tube connections might be tailored for dynamic electrical micro-fluidic diagnostic applications.