Transient response analysis and modeling of near wall flow conditions in a micro channel: evidence of slip flow

Abstract

An experimental tool for determination of the near wall transport parameters in a micro channel, supported by flow simulation, is presented. The method is based on the transient flow response due to convective diffusion, in absence of specific adsorption. An approximately step-function type temporal solute concentration variation serves as the input signal. The associated response signal of a surface plasmon resonance sensor, acting as an integral part of a micro channel, has been taken as the output signal. It provides the flow-dependent change of the NaOH solute concentration in the channel within the optical detection and near wall distance interval 0 < d < 0.5 μm. The temporal signal evolution and response time, until an initially plain aqueous solution is replaced by the solute, varies inversely with solute concentration and flow rate. In the asymptotic limits, the near wall forced convective and diffusive channel transit times, along with the associated velocities, can be extracted and separated. A low convective near wall flow speed would account for 100% adsorption efficiency. The validity of the scaling relation for Fickian diffusive transport has been confirmed by experiments. Convective near wall flow reveals a distorted parabolic flow profile. This indicates relaxation of the no-slip condition, and presence of slip flow. Neither boundary layer formation, nor near wall micro turbulences have been observed. Eventually, a compact mathematical transient flow model, outlined in the Laplace domain for the electrical equivalent analogue circuit and applicable to the convective diffusion equation, has been developed for the flow transients.