Choose a method, select a target variable, and enter the known values. Unit conversion is applied before calculation.
The Navier slip boundary condition relates the wall slip velocity to the wall-normal velocity gradient:
us = b · (du/dn)
Here, b is the slip length (meters), us is the tangential slip velocity, and du/dn is the near-wall gradient (1/s) for simple shear.
A common alternative uses an interfacial friction coefficient κ: b = μ / κ, where μ is the dynamic viscosity.
- Select the method that matches your available data.
- Choose the target variable you want to solve for.
- Enter the known values and select their units.
- Press Calculate to view results above the form.
- Use CSV or PDF buttons to save your result summary.
| Scenario | Method | Inputs | Output slip length |
|---|---|---|---|
| Microchannel shear test | Navier condition | us=0.45 mm/s, du/dn=150 1/s | b=3.00 µm |
| Hydrophobic surface fit | Navier condition | us=12 µm/s, du/dn=400 1/s | b=30.0 nm |
| Molecular friction model | Friction relation | μ=1.0 mPa·s, κ=3.0×106 Pa·s/m | b=0.333 nm |
Navier Slip Length: Technical Notes
1) What slip length represents
In classical no-slip flow, the fluid velocity at a solid wall is zero. Many coated, smooth, or structured surfaces show partial slip, where the near-wall velocity remains finite. The Navier slip length b is an extrapolation distance: extend the near-wall profile linearly until it reaches zero; that distance is b.
2) Boundary condition used in this calculator
The calculator uses us = b(du/dn), where us is tangential slip velocity and du/dn is the wall-normal gradient. For simple shear, du/dn is often treated as a wall shear rate in 1/s.
3) Friction-based interpretation
A complementary form is b = μ/κ. Here μ is dynamic viscosity (Pa·s) and κ is an interfacial friction coefficient (Pa·s/m, also written N·s/m³). For water near room temperature, μ is about 1.0 mPa·s, so large κ usually implies nanometer-scale slip.
4) Typical magnitudes you may encounter
Reported slip lengths depend on chemistry, roughness, and wetting state. Smooth hydrophilic solids often show b ≈ 0–10 nm. Hydrophobic coatings commonly fall around 10–100 nm. Gas-trapping textures can reach 0.1–10 µm when the gas fraction is stable.
5) How b is estimated from measurements
In microflows, us can be obtained from near-wall velocimetry or from fitting flow-rate and pressure-drop data. The gradient du/dn can be extracted from resolved profiles, or inferred from wall stress models. Repeating tests across conditions helps identify shear-dependent slip. Typical reporting includes uncertainty bounds and the fitted wall position.
6) Impact on channel flow and drag
Slip can increase flow rate in small channels. For laminar flow between plates of gap H, a common enhancement estimate is 1 + 4b/H when both walls slip similarly. If b approaches H, pressure requirements can drop significantly.
7) Data checks and unit handling
Because b is often nanometers to micrometers, unit mistakes are common. This tool converts all inputs to SI before computing, then reports b in meters, micrometers, and nanometers. Avoid using a zero shear rate or zero slip length when solving ratios.
8) Practical guidance for design studies
For engineering work, compare b to a characteristic dimension (channel height, pore size, or boundary-layer thickness). If b/H < 0.01, effects are usually minor; if b/H ≥ 0.1, slip can change performance and calibration. Record temperature and surface preparation with every result.
FAQs
1) Is slip length a real physical length inside the wall?
No. It is an extrapolation distance from the near-wall velocity profile. It summarizes interfacial physics into a single parameter, useful for continuum models and comparison across surfaces.
2) Can slip length be negative?
It can appear negative if the fitted wall position is offset, the velocity gradient is misestimated, or roughness alters the effective hydrodynamic boundary. Re-check wall location and calibration before interpreting.
3) What is a “good” slip length value?
It depends on geometry. Compare b to channel height or boundary-layer thickness. Values below about 10 nm often behave close to no-slip, while micrometer-scale slip can strongly alter microflows.
4) Why does temperature matter?
Temperature changes viscosity μ and can change surface chemistry or dissolved gas. Since b = μ/κ, a lower μ can reduce b for the same κ. Record temperature with every dataset.
5) Should I use Navier or friction method?
Use the Navier method when you have slip velocity and a near-wall gradient or shear rate. Use the friction method when you know viscosity and an interfacial friction coefficient from fits or simulations.
6) Does slip depend on shear rate?
Often it can. Some polymers, complex fluids, and textured surfaces show shear-dependent slip. Run multiple conditions and report b as a function of shear rate or wall stress, not a single point.
7) How do I report uncertainty?
Propagate uncertainties from velocity and gradient measurements, or from μ and κ. Small errors in du/dn can dominate b. Report confidence intervals and note your fitting and wall-position uncertainty.