Boundary Effects in Microchannel Flows

Navier-Stokes (NS) theory becomes invalid as the near-wall rotation dominates. Recent experimental data suggest that NS fails to predict fundamental flow metrics, e.g. volume flow rate, in fluidics system at the micrometer range. Researchers have been resorting to first-principles based simulations; however such methods tend to be computationally expensive. This study introduces an additional term to the classical NS equations through the couple stress theory (CST) which is related to the volumetric collisions between the fluid elements. CST involves a new length scale parameter which leads to a new energy dissipation mechanism. This new mechanism is used to explain why NS is invalid for microfluidics system while demonstrating a theoretically rigorous correlation between CST and NS theory. These equations combined with appropriate boundary conditions are solved numerically to study the fully developed behavior of the flow in a rectangular channel. The detailed comparisons between the numerical results and experimental measurements present a clear picture for the complicated flow physics when the boundary effects dominate.