Numerical Simulation of Fluid Flow in Microchannels With Superhydrophobic Walls
Bibliographic record
Abstract
The three-dimensional flow of a Newtonian fluid in a microchannel with superhydrophobic walls is computed using a finite element analysis. Calculations of the fully-developed laminar flow of water under a pressure gradient of 1 psi/cm in an 80 μm high channel with superhydrophobic upper and lower surfaces containing a 2 μm pitch array of 0.2 μm square posts shows a 40 percent flow enhancement relative to the smooth, non-patterned surface case, and an apparent slip length of 5.4 μm. A sharp gradient is observed in the axial velocity field within 0.5 μm of the post surface and normal to the post center. The calculated axial velocity field away from the superhydrophobic surface agrees well with the analytical solution for two-dimensional channel flow with Navier’s slip condition applying at the channel wall. Mesh refinement studies indicate the important role that adequate resolution of the sharp gradient in the velocity field adjacent to the post surface plays in obtaining accurate flow enhancement predictions. Decreasing the relative contact area of the fluid with the solid portion of the channel surface, either by increasing the post-to-post spacing or decreasing the post size, results in a monotonic increase in the flow enhancement. Wetting of the fluid into the post structure is shown to dramatically decrease the calculated flow enhancement. Calculations of the flow enhancement for fixed surface properties and varying channel heights result in apparent slip lengths that agree to within 1 percent, suggesting that the macroscopic flow behavior is adequately characterized in terms of an apparent slip model, with the magnitude of the slip length a function of the post size, post spacing and wetting behavior that characterize the local flow field.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".