Laminar Entrance Length in Microtubes

The goal of this study was to determine the entrance length — the distance from a microtube entrance to the point where flow is fully developed — for laminar liquid flow in smooth, straight, circular-microtubes and trapezoidal microchannels. Knowledge of the entrance length and pressure losses in this region for microtubes are of interest in microfluidic devices, in porous media, and in other networks of small ducts or pores. Although laminar entrance length has been studied extensively in macroscale tubes, only recently has attention been paid problem of entrance length in microtubes. Some differences do exist in macro versus micro flow, sometimes attributed to the relatively small volume to surface area ratio at the microscale. The entrance length determined in this study is intended to provide a means to analyze and design microtubes or networks of microtubes. The inlet velocity was varied to provide a Reynolds number of 10 to 2000 and the length was varied based on Reynolds number to ensure the length captured the entire entrance region. Simulations of water at standard conditions were performed using FLUENT and a custom written computer code, which automated the process of creating the flow geometries, extracting results, and determining the entrance length for each run. A grid resolution study was performed to ensure grid size was not a factor. Pressure and velocity distributions as a function of position were extracted to determine flow characteristics. Fluid velocity magnitudes from the tube centerline to 95% of the distance to the tube wall were used to determine when fully developed flow was reached by finding the point at which all velocity magnitudes did not change by more than 1% for additional distance along the tube. Results were compared to results from the literature for entrance length in macro-scale tubes and found to be qualitatively the same. The entrance length (in units of the number of diameters) for circular tubes is often expressed as C times the Reynolds number. For Reynolds numbers greater than 100, this study found C to be 0.0505, which is in general agreement with macroscale experiments and simulations, where C is reported to be between 0.05 and 0.2. For trapezoidal microchannels we found a relationship for entrance length over hydraulic diameter that is proportional (slope of 0.674) to Reynolds number for Reynolds number over 100. As Reynolds numbers get small the value of entrance length over hydraulic diameter goes to 0.674.