Stokes Number

Compute the ratio of particle response time to flow time scale.

visual calculatorTurbulence & Wall Modeling

Read the flow shape before trusting the number.

This page turns a CFD setup into regime, scale, and dominant-effect cues. Adjust the calculator below and compare the moving graphic with the computed result.

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StokesparticlemultiphaseLagrangian

formula

KaTeX rendered

\begin{aligned}\text{St = tau\_p / tau\_f = (rho\_p d\_p\^{}2 / 18 mu) (U / L)}\end{aligned}

ASCII source

St = tau_p / tau_f = (rho_p d_p^2 / 18 mu) (U / L)

ρ_p — particle density (kg/m³)d_p — particle diameter (m)μ — fluid dynamic viscosity (Pa·s)L — flow length scale (m)U — flow velocity (m/s)

St = τ_p / τ_f

0.7631

regime

Max clustering — inertial focus

Particles cluster at St ≈ 1

τ_p (particle time)

0.0076 s

τ_f (flow time)

0.0100 s

Re_p = 33.0 > 1 — Stokes drag assumption invalid. Use Schiller-Naumann or Haider-Levenspiel correction.

Stokes law valid for Re_p ≪ 1. τ_p = ρ_p d_p² / (18μ).

Stokes particle multiphase Lagrangian