General model for mass transport to planar and nanowire biosensor surfaces

Mass transport to the sensor surface is a critical step in biosensing, often being the factor determining the limit of detection. Modeling transport of the analyte to a surface under convection and diffusion is a challenging task often requiring complex simulation. Herein, we provide a general model for mass transport to planar and nanowire biosensors under flow that is applicable over a wide range of variables. The model is then used to examine the importance of radial diffusion compared with planar diffusion under flow. Only under diffusive transport nanowires are found to have greatly reduced settling times compared with planar sensors due to radial diffusion. However, the presence of flow restricts the growth of the depletion region, resulting in comparable settling times between nanowires and planar sensors of the same size. Under flow conditions in typical experiments, radial diffusion associated with nanowire sensors is inessential for fast mass transport. Instead, the sensor length in the flow direction is the critical parameter as it limits the concentration drop that can occur as the analyte flows past the sensor. Decreasing the sensor length along the flow direction is found to greatly reduce settling times for both cases of planar and radial diffusion, even approaching the reaction limited case. Similarly, decreasing the channel height decreases the settling time due to restriction of the depletion region, but not as significantly as decreasing the sensor length.