The Digester

Correction tensor generalises Cunningham drag law for arbitrary particle shapes across Knudsen numbers

Mar 10th 2026

A new, parameter free form of the Cunningham correction factor is proposed and extended into an element wise correction tensor that predicts gas drag on slow-moving, non-spherical particles across the full Knudsen number range; the heuristic matches sphere experiments, DSMC and kinetic solutions for spheroids and a thin disc with generally small errors but still needs further testing and extension to rotational coupling.

  • Author proposes a parameter free correction factor C_new = exp(-(B-A)Kn) + B Kn that satisfies both small and large Knudsen number limits for spheres and serves as a predictive heuristic
  • The scalar correction is expanded element wise into a correction tensor to approximate the 3x3 translational resistance tensor for non-spherical particles across Knudsen numbers
  • Evaluating the tensor requires three limit tensors: the continuum resistance from Stokes no-slip, the first-order slip term from a reciprocal theorem integral, and the free molecular limit from a surface integral or DSMC
  • Validation against sphere experiments, kinetic theory and DSMC/BGK solutions for spheroids and an infinitely thin disc shows generally excellent agreement with errors typically within a few percent and largest discrepancies near Kn ~ 1
  • The method has practical advantages over the adjusted sphere method because it has no fitted parameters and enforces the correct small-Kn slope of the resistance tensor
  • Limitations include its heuristic nature, reliance on the Maxwell slip model and the assumption that principal axes do not change with Kn, and it may need modification when B-A < 0 or when rotational coupling matters

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