Abstract

We revisit Jeffery’s classical 1922 solution for the creeping (Stokes) flow around a rigid triaxial ellipsoid and reconstruct the complete exterior Stokes boundary-value problem in modern tensorial notation. Starting from the harmonic-potential formulation in confocal ellipsoidal coordinates, we derive compact tensor representations for the velocity and pressure fields and reformulate Jeffery’s original component equations in coordinate-free form. The algebraic no-slip system is reconstructed explicitly, including Giesekus’ correction to Jeffery’s original coefficients. The resulting formulation is verified symbolically by computer algebra and shown to satisfy the force- and torque-free conditions. In addition, the classical Jeffery equation for spheroids is recovered as a special case, while the fully triaxial problem leads naturally to coupled evolution equations for the principal directions of the ellipsoid. The present work provides a modern tensorial reinterpretation of Jeffery’s original harmonic-potential solution and clarifies several structural aspects of the underlying Stokes boundary-value problem.

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