Stokes Number formula |
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\( Stk \;=\; \dfrac{ \tau_p }{ \tau_p }\) (Stokes Number) \( \tau_p \;=\; Stk \cdot \tau_p \) \( \tau_f \;=\; \dfrac{ \tau_p }{ Stk }\) |
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| Symbol | English | Metric |
| \( Stk \) = Stokes Number | \( dimensionless \) | \( dimensionless \) |
| \( \tau_p \) = particle relaxation time (how quickly the particle adjusts to changes in flow) | \(sec\) | \(s\) |
| \( \tau_f \) = characteristic time scale of the fluid (the time it takes for the fluid to change direction or speed) | \(sec\) | \(s\) |
Stokes number, abbreviated as Stk or St, a dimensionless number, characterizes the behavior of particles suspended in a fluid flow. It represents the ratio of the particle's momentum response time to the characteristic time scale of the fluid flow. In other words, It tells you how much inertia a particle has compared to the drag force of the fluid. This helps predict whether a particle will keep moving straight (due to inertia) or follow the flow of the fluid (due to drag).
Stokes Number Interpretation
- Low Stokes Number () - Particles with a low Stokes number have a short relaxation time, meaning they quickly adjust to the fluid's motion. These particles closely follow the fluid streamlines.
- Intermediate Stokes Number () - In this regime, the particle's behavior is influenced by both its inertia and the fluid forces, leading to interesting phenomena like preferential concentration in turbulent flows.
- High Stokes Number () - Particles with a high Stokes number have a long relaxation time due to their inertia. They tend to continue along their initial trajectory and are less likely to follow the fluid as it changes direction around an obstacle. These particles are more likely to impact or separate from the flow.
